gismo Namespace Reference

The G+Smo namespace, containing all definitions for the library. More...

Namespaces
namespace	bspline
	This namespace contains implementation of B-spline related algorithms.
namespace	expr
	This namespace contains expressions used for FE computations.
namespace	internal
	This namespace contains functionalities that are internal to the library.
namespace	math
	This namespace contains common mathematical functions.
namespace	memory
	This namespace contains functions related to memory management.
namespace	trilinos
	This namespace contains wrappers for the Trilinos library.
namespace	util
	the gsFuncData is a cache of pre-computed function sets values.

Classes
struct	ale_method
	Specifies method used for mesh deformation in fluid-structure interaction. More...
class	Base64
	Encode for base64 export. More...
struct	boundary
	Struct that defines the boundary sides and corners and types of a geometric object. More...
struct	boundary_condition
	Class that defines a boundary condition for a side of a patch for some unknown variable of a PDE. More...
struct	boundaryInterface
	Struct which represents an interface between two patches. More...
struct	boxComponent
	Struct which represents a certain component (interior, face, egde, corner). More...
struct	boxCorner
	Struct which represents a certain corner of a hyper-cube. More...
class	boxSide
	Struct which represents a certain side of a box. More...
struct	condition_type
	Specifies the type of boundary condition. More...
struct	corner_value
	Class prescribing a value related to a corner of a patch. More...
struct	coupled_boundary
	Class prescribing a value related to a corner of a patch. More...
struct	decodeMat_id
	Decodes the material model and implementation. More...
struct	encodeMat_id
	Encodes the material model and implementation. More...
struct	gsAABB
	Struct of for an Axis-aligned bounding box. More...
class	gsAbsError
	Generates a field with value the absolute difference (error) between and isogeometric function and a function defined on the physical domain. More...
class	gsAdaptiveMeshing
	Provides adaptive meshing routines. More...
class	gsAdditiveOp
	Generic preconditioner which applies an arbitrary linear operator to the residual. More...
class	gsAffineFunction
	Representation of an affine function. More...
class	gsALMBase
	Performs the arc length method to solve a nonlinear system of equations. More...
class	gsALMConsistentCrisfield
	Performs the Consistent Crisfield arc length method to solve a nonlinear equation system. More...
class	gsALMCrisfield
	Performs the Crisfield arc length method to solve a nonlinear equation system. More...
class	gsALMLoadControl
	Performs the load-controlled arc length method to solve a nonlinear equation system. More...
class	gsAlmostC1
	Constructs the D-Patch, from which the transformation matrix can be called. More...
class	gsALMRiks
	Performs the Riks arc length method to solve a nonlinear equation system. More...
class	gsApproxC1Spline
	Class describing the approximate \(C^1\) spline. More...
class	gsAsConstMatrix
	Creates a mapped object or data pointer to a const matrix without copying data. More...
class	gsAsConstVector
	Creates a mapped object or data pointer to a const vector without copying data. More...
class	gsAsMatrix
	Creates a mapped object or data pointer to a matrix without copying data. More...
class	gsAssembler
	The assembler class provides generic routines for volume and boundary integrals that are used for for matrix and right-hand side generation. More...
struct	gsAssemblerOptions
class	gsAsVector
	Creates a mapped object or data pointer to a vector without copying data. More...
class	gsBarrierCore
	gsBarrierCore More...
class	gsBarrierPatch
	Computes a patch parametrization given a set of boundary geometries. Parametrization is not guaranteed to be non-singular. Works for planar surfaces and volumes. More...
class	gsBaseAssembler
	Extends the gsAssembler class by adding functionality necessary for a general nonlinear solver. Potentially, can be merged back into gsAssembler. More...
class	gsBasis
	A basis represents a family of scalar basis functions defined over a common parameter domain. More...
class	gsBasisFun
	Represents an individual function in a function set, or a certain component of a vector-valued function. More...
class	gsBasisRefs
	Simple class to hold a list of gsBasis which discretize a PDE system on a given patch. More...
class	gsBiCgStab
	Biconjugate gradient stabilized solver. More...
class	gsBiharmonicAssembler
	Implementation of a homogeneous Biharmonic Assembler. More...
class	gsBiharmonicPde
	A Biharmonic PDE. More...
class	gsBlockOp
	Simple class create a block operator structure. More...
class	gsBlockPrecondStokes
	Block diagonal preconditioner for the Stokes problem. More...
class	gsBlockPrecondStokesTriang
	Block triangular preconditioner for the Stokes problem. More...
class	gsBoundaryConditions
	Class containing a set of boundary conditions. More...
class	gsBoundedPriorityQueue
	An implementation of the bounded priority queue abstraction. More...
class	gsBoxTopology
	Defines a topological arrangement of a collection of "boxes" (e.g., parameter domains that map to physical-domain patches). More...
class	gsBSpline
	A B-spline function of one argument, with arbitrary target dimension. More...
class	gsBSplineBasis
	A univariate B-spline basis. More...
class	gsBSplineSolver
struct	gsBSplineTraits
	Traits for BSplineBasis in more dimensions. More...
class	gsBucklingSolver
	Performs linear buckling analysis given a matrix or functions of a matrix. More...
class	gsBulk
	Abstract base class representing a 4D bulk. More...
class	gsCauchyStressFunction
	Compute Cauchy stresses for a previously computed/defined displacement field. Can be pushed into gsPiecewiseFunction to construct gsField for visualization in Paraview. More...
class	gsCDRAssembler
	Implementation of an (multiple righ-hand side) Poisson solver. More...
class	gsCmdLine
	Class for command-line argument parsing. More...
class	gsCompositePrecOp
	This class represents the composition of preconditioners of type gsPreconditionerOp. More...
class	gsConjugateGradient
	The conjugate gradient method. More...
class	gsConstantBasis
	Class defining a dummy basis of constant functions. This is used for compatibility reasons. More...
class	gsConstantFunction
	Class defining a globally constant function. More...
class	gsContinuationBase
	Base class for simple continuation schemes. More...
class	gsControlDisplacement
	Simple class for displacement control given a static solver. More...
class	gsConvDiffRePde
	A convection-diffusion-reaction PDE, including source term on the right-hand side. More...
class	gsCoonsPatch
	Computes a Coons' patch parametrization given a set of boundary geometries. Parametrization is not guaranteed to be non-singular. Works for surface, volumes, or any dimension. More...
class	gsCPPInterface
	Provides a mapping between the corresponding sides of two patches sharing an interface, by means of a closest point projection. More...
class	gsCrossApPatch
	Computes a parametrization based on low rank cross approximation, given a set of boundary geometries. More...
class	gsCurvatureSmoothing
	Class for computing a closed B-spline curve with a smaller number of curvature extrema compared to a given closed B-spline curve. More...
class	gsCurve
	Abstract base class representing a curve. More...
class	gsCurveFitting
	Class for performing a least squares fit to get a open/closed B-Spline curve for some given data. More...
class	gsCurveLoop
	A closed loop given by a collection of curves. More...
class	gsDetFunction
	Compute jacobian determinant of the geometry mapping. Can be pushed into gsPiecewiseFunction to construct gsField for visualization in Paraview. More...
class	gsDiffScaledOuterNormalField
	Function returning the (unit) outer normal vector scaled by the difference of a target value and values of a given scalar field. More...
class	gsDofMapper
	Maintains a mapping from patch-local dofs to global dof indices and allows the elimination of individual dofs. More...
class	gsDomain
	Class representing a domain. i.e. a collection of elements (triangles, rectangles, cubes, simplices. More...
class	gsDomainIterator
	Class which enables iteration over all elements of a parameter domain. More...
class	gsDPatch
	Constructs the D-Patch, from which the transformation matrix can be called. More...
class	gsDPatchBase
	Constructs the D-Patch, from which the transformation matrix can be called. More...
class	gsDynamicBase
	Performs the arc length method to solve a nonlinear system of equations. More...
class	gsDynamicBathe
	Performs the arc length method to solve a nonlinear system of equations. More...
class	gsDynamicExplicitEuler
	Performs the arc length method to solve a nonlinear system of equations. More...
class	gsDynamicImplicitEuler
	Performs the arc length method to solve a nonlinear system of equations. More...
struct	gsDynamicLibrary
	Class defining a dynamic library. More...
class	gsDynamicNewmark
	Performs the arc length method to solve a nonlinear system of equations. More...
class	gsDynamicRK4
	Performs the arc length method to solve a nonlinear system of equations. More...
class	gsDynamicWilson
	Performs the arc length method to solve a nonlinear system of equations. More...
class	gsDynamicXBraid
	Performs the arc length method to solve a nonlinear system of equations. More...
struct	gsEigenAdaptor
	Adaptor for Eigen types. More...
class	gsEigenProblemBase
	Base class for buckling and modal analyses. More...
class	gsElasticityAssembler
	Assembles the stiffness matrix and the right-hand side vector for linear and nonlinear elasticity for 2D plain stress and 3D continua. The matrix and vector have a block structure associated with components of the displacement vector, each block corresponding to one component. Supports mixed displacement-pressure formulation. More...
class	gsElementErrorPlotter
	This class provides a function that returns a constant error on each element. More...
class	gsElTimeIntegrator
	Time integation for equations of dynamic elasticity with implicit schemes. More...
class	gsEulerBernoulliBeamPde
	The differential equation describing the linear Euler-Bernoulli beam. More...
class	gsExprAssembler
class	gsExprEvaluator
	Generic evaluator of isogeometric expressions. More...
class	gsExprHelper
struct	gsFeSpaceData
	Struct containing information for matrix assembly. More...
class	gsFiberMatrix
	A specialized sparse matrix class which stores each row as a separate sparse vector. More...
class	gsField
	A scalar of vector field defined on a m_parametric geometry. More...
struct	gsFieldCreator
	Class that creates standard fields on a given parametric (multipatch) geometry. More...
class	gsFileData
	This class represents an XML data tree which can be read from or written to a (file) stream. More...
class	gsFileManager
	File-system related functionality. More...
class	gsFitting
	Class for performing a fit of a parametrized point cloud with a gsGeometry. More...
class	gsFlowAssemblerBase
	A base class for all assemblers in gsIncompressibleFlow. More...
class	gsFlowBndEvaluator
	A base class for boundary evaluators. More...
class	gsFlowBndEvaluator_flowRate
	Flow rate evaluator. More...
class	gsFlowLinSystSolver
	Interface for classes solving linear systems inside the incompressible flow solvers (classes derived from gsFlowSolverBase). More...
class	gsFlowLinSystSolver_direct
	Direct solver for linear systems inside the incompressible flow solvers (classes derived from gsFlowSolverBase). More...
class	gsFlowLinSystSolver_iter
	G+Smo/Eigen iterative solver for linear systems inside the incompressible flow solvers (classes derived from gsFlowSolverBase). More...
class	gsFlowLinSystSolver_iterSP
	G+Smo/Eigen iterative solver for saddle-point linear systems inside the incompressible flow solvers (classes derived from gsFlowSolverBase) with block preconditioners. More...
class	gsFlowSolverBase
	A base class for all flow solvers in gsIncompressibleFlow. More...
class	gsFlowSolverParams
	A class that holds all parameters needed by the incompressible flow solver. More...
class	gsFlowTerm
	A class computing individual terms of the weak formulation appearing in incompressible flow problems. More...
class	gsFlowTerm_Diffusion
	A class for integrals of the form: viscosity * test function gradient * shape function gradient. More...
class	gsFlowTerm_GradGrad
	A class for integrals of the form: test function gradient * shape function gradient. More...
class	gsFlowTerm_rhs
	A class for integrals of the form: test function value * rhs function value. More...
class	gsFlowTerm_TimeDiscr
	A class for integrals of the form: (1 / time step) * test function value * shape function value. More...
class	gsFlowTerm_ValVal
	A class for integrals of the form: test function value * shape function value. More...
class	gsFlowTermNonlin
	A class computing nonlinear terms of the weak formulation appearing in incompressible flow problems. More...
class	gsFlowVisitor
	Base class for incompressible flow visitors. More...
class	gsFsiLoad
	Loading function to transfer fluid action to the solid. Used in Fluid-Structure Interaction simulation. Different parametrizations can be used for the geometry+ALE and velocity+pressure. More...
class	gsFuncCoordinate
	Represents a certain component of a vector-valued function. More...
class	gsFunction
	A function \(f:\mathbb{R}^n\rightarrow\mathbb{R}^m\) from a n-dimensional domain to an m-dimensional image. More...
class	gsFunctionAdaptor
	Adaptor to see a given gsFunction as (the objective of) an unconstrained optimization problem. More...
class	gsFunctionExpr
	Class defining a multivariate (real or vector) function given by a string mathematical expression. More...
class	gsFunctionSet
	Interface for the set of functions defined on a domain (the total number of functions in the set equals to \(S\) ) More...
class	gsGaussRule
	Class that represents the (tensor) Gauss-Legendre quadrature rule. More...
class	gsGaussSeidelOp
	Gauss-Seidel preconditioner. More...
class	gsGenericAssembler
	Assembles mass and stiffness matrices and right-hand sides on a given domain. More...
class	gsGenericStopwatch
	A Stopwatch object can be used to measure execution time of code, algorithms, etc. More...
class	gsGenericTensorBasis
	Class for a quasi-tensor B-spline basis. More...
class	gsGeometry
	Abstract base class representing a geometry map. More...
class	gsGeometrySlice
	gsGeometrySlice is a class representing an iso parametric slice of a geometry object. It stores a pointer to the geometry object, which is only valid as long as this object is alive. Methods for printing to paraview are available in gsWriteToParaview.h More...
class	gsGeometryTransform
	Representation of a transformed geometry. More...
class	gsGMRes
	The generalized minimal residual (GMRES) method. More...
class	gsGradientDescent
	This class describes the gradient descent method. More...
class	gsGradientField
	Generates a field with value being the gradient of an isogeometric function. More...
class	gsGradientMethod
	The gradient method. More...
class	gsGridHierarchy
	Grid Hierarchy. More...
class	gsGridIterator< T, CWISE, d, false >
	Iterator over a Cartesian product of points, which is given by coordinate-wise point sets. More...
class	gsGridIterator< T, mode, d, false >
	Iterator over a Cartesian product of uniformly distributed numeric points inside a (hyper-)cube. More...
class	gsGridIterator< Z, mode, d, true >
	Iterator over the Cartesian product of integer points in a tensor-product grid. More...
class	gsHalfEdgeMesh
	gsHalfEdgeMesh is a gsMesh implementation that handles Halfedges More...
class	gsHBox
	This class provides a Hierarchical Box (gsHBox) More...
class	gsHBoxCheck
	Base class for performing checks on gsHBox objects. More...
class	gsHBoxContainer
	The Hierarchical Box Container provides a container for gsHBox objects. More...
struct	gsHBoxUtils
	The gsHBoxUtils provide basic utilities to modify HBoxes. More...
class	gsHBSpline
	A hierarchical B-Spline function, in d dimensions. More...
class	gsHBSplineBasis
	A hierarchical B-spline basis of parametric dimension d. More...
class	gsHDomain
	Class with a hierarchical domain structure represented by a box k-d-tree. More...
class	gsHDomainBoundaryIterator
	Re-implements gsDomainIterator for iteration over all boundary elements of a hierarchical parameter domain. More...
class	gsHDomainIterator
	Re-implements gsDomainIterator for iteration over all boundary elements of a hierarchical parameter domain. More...
class	gsHDomainLeafIter
	Iterates over the leaves of an gsHDomain (tree). More...
class	gsHDomainSliceIter
	Iterates over the leaves of an gsHDomain (tree) that intersect with a slice position. More...
class	gsHeatEquation
	Constructs the assembler for the discretized isogeometric heat equation. More...
class	gsHFitting
	This class applies hierarchical fitting of parametrized point clouds. More...
class	gsHTensorBasis
	Class representing a (scalar) hierarchical tensor basis of functions \( \mathbb R^d \to \mathbb R \). More...
class	gsIdentityOp
	Identity operator. More...
class	gsIetiMapper
	Ieti Mapper. More...
class	gsIetiSystem
	This class represents a IETI system. More...
class	gsIncompleteLUOp
	Incomplete LU with thresholding preconditioner. More...
class	gsINSAssembler
	A base class for incompressible Navier-Stokes assemblers. More...
class	gsINSAssemblerSteady
	The steady incompressible Navier–Stokes assembler. More...
class	gsINSAssemblerUnsteady
	The unsteady incompressible Navier–Stokes assembler. More...
class	gsINSBlockPrecondAL
	Augmented Lagrangian preconditioner. More...
class	gsINSBlockPrecondBase
	Base class for block preconditioners for linear systems arising from linearized Navier-Stokes of form. More...
class	gsINSBlockPrecondLSC
	Least-squares commutator preconditioner. More...
class	gsINSBlockPrecondMSIMPLER
	MSIMPLER preconditioner. More...
class	gsINSBlockPrecondPCD
	Pressure convection-diffusion preconditioner. More...
class	gsINSBlockPrecondPCDmod
	Modified pressure convection-diffusion preconditioner. More...
class	gsINSBlockPrecondSIMPLE
	SIMPLE preconditioner. More...
class	gsINSBlockPrecondSIMPLER
	SIMPLER preconditioner. More...
class	gsINSPrecondBlock
	A base class for individual blocks of block preconditioners. More...
class	gsINSPrecondBlockF
	Class for block F of block preconditioner of the form. More...
class	gsINSPrecondBlockFdiag
	Base class for block F of block preconditioner of the form. More...
class	gsINSPrecondBlockFmod
	Base class for block F of (modified) block preconditioner of the form. More...
class	gsINSPrecondBlockFwhole
	Class for block F of block preconditioner of the form. More...
class	gsINSPrecondBlockMod
	Base class for block F of (modified) block preconditioner of the form. More...
class	gsINSSolver
	A base class for incompressible Navier-Stokes solvers. More...
class	gsINSSolverSteady
	The steady incompressible Navier-Stokes solver. More...
class	gsINSSolverUnsteady
	The unsteady incompressible Navier-Stokes solver. More...
class	gsINSTerm_PvalUdiv
	A class for integrals of the form: pressure shape function value * velocity test function divergence. More...
class	gsINSTerm_UdivPval
	A class for integrals of the form: velocity shape function divergence * pressure test function value. More...
class	gsINSTerm_UsolGradVal
	A class for integrals of the form: velocity solution * shape function gradient * test function value. More...
class	gsIpOpt
	Class defining an optimization problem. More...
class	gsIterative
	A general iterative solver for nonlinear problems. An equation to solve is specified by an assembler class which provides the following interfaces: More...
class	gsIterativeSolver
	Abstract class for iterative solvers. More...
class	gsIterativeSolverOp
	This wrapper class allows gsIterativeSolver to be used as gsLinearOperator. More...
class	gsJacDetField
	Generates a field with value the Jacobian determinant of a geometry. More...
class	gsJacobiOp
	Jacobi preconditioner. More...
class	gsJITCompiler
	Class defining a just-in-time compiler. More...
struct	gsJITCompilerConfig
	Struct definig a compiler configuration. More...
struct	gsJITLang
	Supported languages. More...
struct	gsKdNode
	Struct representing a kd-tree node. More...
class	gsKDTree
	An interface representing a kd-tree in some number of dimensions. More...
class	gsKnotVector
	Class for representing a knot vector. More...
class	gsKroneckerOp
	Class for representing a Kronecker product of operators of type gsLinearOperator. More...
struct	gsL2Projection
	Class that performs an L2 projection. More...
class	gsLagrangeBasis
	A univariate Lagrange basis. More...
class	gsLagrangePoly
	The geometry class of a Lagrange Polyomial curve. More...
class	gsLanczosMatrix
	Class for representing a Lanczos matrix and calculating its eigenvalues. More...
class	gsLaplacePde
	The Laplace equation. More...
class	gsLargerErrCompare
	Checks if the error of a gsHBox is larger than a threshold. More...
class	gsLegendreBasis
	A univariate Legendre basis. More...
class	gsLevenbergMarquardt
	This class describes the gradient descent method. More...
class	gsLinearLambdaOp
	Wrapper that allows to use lambdas as a gsLinearOperator. More...
class	gsLinearOperator
	Simple abstract class for discrete operators. More...
class	gsLineSegment
	Represents a line segment in d dimensions. More...
class	gsLobattoRule
	Class that represents the (tensor) Gauss-Lobatto quadrature rule. More...
class	gsMapData
	the gsMapData is a cache of pre-computed function (map) values. More...
class	gsMappedSingleBasis
	Class gsMappedSingleBasis represents an indivisual .....of a. More...
class	gsMappedSingleSpline
	Class gsMappedSingleSpline represents an individual .....of a. More...
class	gsMassAssembler
	Assembles the mass matrix and right-hand side vector for linear and nonlinear elasticity for 2D plain stress and 3D continua. The matrix has a block structure associated with components of the displacement vector, each block corresponding to one component. Supports mixed displacement-pressure formulation. More...
class	gsMaterialMatrixBase
	This class defines the base class for material matrices. More...
class	gsMaterialMatrixBaseDim
	This class defines the base class for material matrices. More...
class	gsMaterialMatrixComposite
	This class defines a linear material laminate. More...
class	gsMaterialMatrixContainer
	This class serves as the evaluator of material matrices, based on gsMaterialMatrixBase. More...
class	gsMaterialMatrixEvalSingle
	This class serves as the evaluator of material matrices, based on gsMaterialMatrixBase. More...
class	gsMaterialMatrixIntegrateSingle
	This class serves as the integrator of material matrices, based on gsMaterialMatrixBase. More...
class	gsMaterialMatrixLinear
	This class defines a linear material. More...
class	gsMaterialMatrixNonlinear
	This class defines hyperelastic material matrices. More...
class	gsMaterialMatrixTFT
	This class defines a linear material. More...
class	gsMatrix
	A matrix with arbitrary coefficient type and fixed or dynamic size. More...
class	gsMatrixBlockView
	Represents a block-view of the given matrix. More...
class	gsMatrixOp
	Simple adapter class to use a matrix (or matrix-like object) as a linear operator. Needed for the iterative method classes. More...
class	gsMaxLvlCompare
	Checks if the level of a gsHBox is smaller than a maximum level. More...
class	gsMesh
	Class Representing a triangle mesh with 3D vertices. More...
class	gsMinimalResidual
	The minimal residual (MinRes) method. More...
class	gsMinLvlCompare
	Checks if the level of a gsHBox is bigger than a minimum level. More...
class	gsMinResQLP
	The minimal residual (MinRes-QLP) method. More...
class	gsModalSolver
	Performs linear modal analysis given a matrix or functions of a matrix. More...
class	gsMonomialBasis
	An univariate monomial polynomial basis. If the degree is p the basis is given by: [ 1, x, x^2, ..., x^p ] The basis functions are numbered, starting from zero, as stated above. More...
class	gsMPBESBasis
	Purely abstract class gsMappedBasis, which gives means of combining basis functions to new, global ones. More...
class	gsMPBESBSplineBasis
	A univariate Lagrange basis. More...
class	gsMPBESHSplineBasis
	A univariate Lagrange basis. More...
class	gsMPBESMapB2D
	A univariate Lagrange basis. More...
class	gsMPBESMapHB2D
	A univariate Lagrange basis. More...
class	gsMPBESMapTensor
	A univariate Lagrange basis. More...
class	gsMultiBasis
	Holds a set of patch-wise bases and their topology information. More...
class	gsMultiGridOp
	Multigrid preconditioner. More...
class	gsMultiPatch
	Container class for a set of geometry patches and their topology, that is, the interface connections and outer boundary faces. More...
class	gsMuscleAssembler
	Assembler for incompressible nonlinear elasticity problem with a muscle material model. The material model is based on the paper by M.H.Gfrerer and B.Simeon "Fiber-based modeling and simulation of skeletal muscles". More...
class	gsMvLegendreBasis
	A multivariate Legendre basis. More...
class	gsNavStokesPde
	An incompressible Navier-Stokes PDE. More...
class	gsNewtonCotesRule
	Class that represents the (tensor) Newton-Cotes quadrature rule. More...
class	gsNewtonIterator
	Performs Newton iterations to solve a nonlinear system of PDEs. More...
class	gsNormalField
	Generates the normal field of a geometry. More...
class	gsNsAssembler
	TODO: write. More...
class	gsNsTimeIntegrator
	Time integation for incompressible Navier-Stokes equations. More...
class	gsNurbs
	A NURBS function of one argument, with arbitrary target dimension. More...
class	gsNurbsBasis
	A univariate NURBS basis. More...
struct	gsNurbsCreator
	Class gsNurbsCreator provides some simple examples of Nurbs Geometries. More...
class	gsOptim
	Base class for the Optim wrapper. More...
class	gsOptimBFGS
	Binding to Optim's BFGS solver. More...
class	gsOptimCG
	Binding to Optim's CG solver. More...
class	gsOptimDE
	Binding to Optim's DE solver. More...
class	gsOptimDEPRMM
	Binding to Optim's DEPRMM solver. More...
class	gsOptimGD
	Binding to Optim's GD solver. More...
class	gsOptimizer
	Class defining an optimizer. More...
class	gsOptimLBFGS
	Binding to Optim's LBFGS solver. More...
class	gsOptimNM
	Binding to Optim's NM solver. More...
class	gsOptimPSO
	Binding to Optim's PSO solver. More...
class	gsOptimPSODV
	Binding to Optim's PSODV solver. More...
class	gsOptimSUMT
	Binding to Optim's SUMT solver. More...
struct	gsOptimWrapper
	Wraps the objective of an optimization problem to a function accepted by Optim. More...
struct	gsOptimWrapperConstraint
	Wraps the constraint of an optimization problem to a function accepted by Optim. More...
class	gsOptionList
	Class which holds a list of parameters/options, and provides easy access to them. More...
class	gsOptProblem
	Class defining an optimization problem. More...
class	gsOptProblemStatic
	A class representing a static optimization problem. More...
class	gsOverIntegrateRule
	Class that defines a mixed quadrature rule with different rules for the interior and the boundaries. More...
class	gsOverlapCompare
	Checks if the coarsening neighborhood of a box is empty and if it overlaps with a refinement mask. More...
struct	gsPanelCreator
	Class gsPanelCreator provides some simple examples of Nurbs Geometries. More...
class	gsParametrization
	Class that maintains parametrization This class Parametrization stores the mesh information and the two-dimensional parameter points. The parameter points are stored in a vector, where the i-th vector element is the parameter point for the vertex with index i. This means that the first n elements in the vector are the inner parameter points, the rest of them are the boundary parameter points. More...
class	gsParamField
	Generates a field that attaches the parameter values on each physical point. More...
class	gsParaviewCollection
	This class is used to create a Paraview .pvd (collection) file. More...
class	gsParaviewDataSet
	This class represents a group of vtk (Paraview) files that refer to one multiPatch, for one timestep. More...
class	gsPatchGenerator
	Abstract class that accepts a set of input boundaries and computes a new geometry. More...
class	gsPatchIdField
	Generates a field that indicates the boundary sides on the geometry. More...
class	gsPatchPreconditionersCreator
	Provides robust preconditioners for single patch geometries. More...
class	gsPatchRule
	Class that represents the (tensor) patch quadrature rule. More...
class	gsPatchwiseFunction
	A function depending on an index i, typically referring to a patch/sub-domain. More...
class	gsPde
	Abstract class representing a PDE (partial differential equation). More...
class	gsPeriodicOverlap
class	gsPeriodicStitch
class	gsPiecewiseFunction
	A function depending on an index i, typically referring to a patch/sub-domain. On each patch a different gsFunction object is used. More...
class	gsPlanarDomain
	Class representing a Planar domain with an outer boundary and a number of holes. More...
class	gsPoint
	A Point in T^d, with an index number. More...
class	gsPointLoads
	Class containing a set of points on a multi-patch isogeometric domain, together with boundary conditions. More...
class	gsPoissonAssembler
	Implementation of an (multiple right-hand side) Poisson assembler. More...
class	gsPoissonPde
	A Poisson PDE. More...
class	gsPreconditionerFromOp
	Simple class allowing to construct a preconditioner from a linear operator. More...
class	gsPreconditionerOp
	Simple abstract class for perconditioners. More...
class	gsPrimalSystem
	This class represents the primal system for a IETI-DP algorithm. More...
class	gsProductOp
	Class for representing the product of objects of type gsLinearOperator as gsLinearOperator. More...
class	gsProgressBar
	Simple progress bar class. More...
struct	gsQuadrature
	Helper class for obtaining a quadrature rule. More...
class	gsQuadRule
	Class representing a reference quadrature rule. More...
struct	gsQuasiInterpolate
	Quasi-interpolation operators. More...
class	gsRationalBasis
	Class that creates a rational counterpart for a given basis. More...
class	gsRationalTHBSpline
	A rational truncated hierarchical B-Spline function of parametric dimension d, with arbitrary target dimension. More...
class	gsRationalTHBSplineBasis
	A rational Truncated Hierarchical B-Spline basis. More...
class	gsReadFile
	Reads an object from a data file, if such the requested object exists in the file. More...
class	gsRemapInterface
	Provides a mapping between the corresponding sides of two patches sharing an interface. More...
class	gsRichardsonOp
	Richardson preconditioner. More...
class	gsScaledDirichletPrec
	This class represents the scaled Dirichlet preconditioner for a IETI problem. More...
class	gsScaledOp
	Allows an operator to be multiplied with a scalar. More...
class	gsScaledOuterNormalField
	Function returning the (unit) outer normal vector scaled by values of a given scalar field. More...
class	gsSerialComm
	A serial communication class. More...
class	gsSerialGroup
	A sequential communicator group class. More...
class	gsSerialRequest
	A sequential communicator request class. More...
class	gsSerialStatus
	A sequential communicator status class. More...
class	gsShellStressFunction
	Compute Cauchy stresses for a previously computed/defined displacement field. Can be pushed into gsPiecewiseFunction to construct gsField for visualization in Paraview. More...
class	gsSmallerErrCompare
	Checks if the error of a gsHBox is smaller than a threshold. More...
class	gsSmoothInterfaces
	Constructs the D-Patch, from which the transformation matrix can be called. More...
class	gsSolid
	Class for representing a solid made up of vertices, edges, faces, and volumes. More...
class	gsSolverOp
	Simple adapter class to use an Eigen solver (having a compute() and a solve() method) as a linear operator. More...
class	gsSolverUtils
	Utility class for PDE's solver related utils. More...
class	gsSortedVector
	This class is derived from std::vector, and adds sort tracking. More...
class	gsSparseEntries
	Class that provides a container for triplets (i,j,value) to be filled in a sparse matrix. More...
class	gsSparseMatrix
	Sparse matrix class, based on gsEigen::SparseMatrix. More...
class	gsSparseMatrixIter
	Iterator over the non-zero entries of a sparse matrix. More...
class	gsSparseSolver
	Abstract class for solvers. The solver interface is base on 3 methods: -compute set the system matrix (possibly compute the factorization or preconditioners) -solve solves for a given right hand side -succeed returns true if solving succeded according to solver dependent criteria (usually tolerance based) So in order to solve \( A x = b \) with a solver s two functions must be called: s.compute(A) and s.solve(b). The calls can be chained as in s.compute(A).solve(b). More...
class	gsSparseSystem
	A sparse linear system indexed by sets of degrees of freedom. More...
class	gsSparseVector
	Sparse vector class, based on gsEigen::SparseVector. More...
class	gsSpectraGenSymShiftSolver
class	gsSpectraGenSymSolver
class	gsSpectraSolver
	Eigenvalue solver for general real matrices. More...
class	gsSpectraSymShiftSolver
	Shifted Eigenvalue solver for real symmetric matrices. More...
class	gsSpectraSymSolver
	Eigenvalue solver for real symmetric matrices. More...
class	gsSpringPatch
	Computes a parametrization based on the spring patch technique, given a set of boundary geometries. More...
class	gsSquaredDistance
	Squared distance function from a fixed point to a gsGeometry. More...
class	gsStaticBase
	Base class for static solvers. More...
class	gsStaticComposite
	Static solver using a newton method. More...
class	gsStaticDR
	Static solver using the Dynamic Relaxation method. More...
class	gsStaticNewton
	Static solver using a newton method. More...
class	gsStaticOpt
	Static solver using the Dynamic Relaxation method. More...
class	gsStdVectorRef
	Simple wrapper class for a vector of objects. More...
class	gsStokesPde
	A stationary Stokes PDE. More...
struct	gsStructuralAnalysisOps
	Operators for the gsStructuralAnalysis module. More...
class	gsSumOp
	Class for representing the sum of objects of type gsLinearOperator as gsLinearOperator. More...
class	gsSurface
	Abstract base class representing a surface. More...
class	gsSurfMesh
	A halfedge data structure for polygonal meshes. More...
class	gsTemplate
	Class gsTemplate object. More...
class	gsTensorBasis
	Abstract base class for tensor product bases. More...
class	gsTensorBSpline
	A tensor product of d B-spline functions, with arbitrary target dimension. More...
class	gsTensorBSplineBasis
	A tensor product B-spline basis. More...
class	gsTensorBSplineBasis< 1, T >
	A univariate B-spline basis. More...
class	gsTensorDomainBoundaryIterator
	Re-implements gsDomainIterator for iteration over all elements of the boundary of a tensor product parameter domain. See gsDomainIterator for more detailed documentation and an example of the typical use!!! More...
class	gsTensorDomainIterator
	Re-implements gsDomainIterator for iteration over all elements of a tensor product parameter domain. See gsDomainIterator for more detailed documentation and an example of the typical use!!! More...
class	gsTensorNurbs
	A tensor product Non-Uniform Rational B-spline function (NURBS) of parametric dimension d, with arbitrary target dimension. More...
class	gsTensorNurbsBasis
	A tensor product Non-Uniform Rational B-spline (NURBS) basis. More...
class	gsTHBSpline
	A truncated hierarchical B-Spline function, in d dimensions. More...
class	gsTHBSplineBasis
	Truncated hierarchical B-spline basis. More...
class	gsThermoAssembler
	Assembles stiffness and mass matrices and right-hand side vector for linear and nonlinear elasticity for 2D plain stress and 3D continua. Matrices and vector have a block structure associated with components of the displacement vector, each block corresponding to one component. More...
class	gsThinShellAssembler
	Assembles the system matrix and vectors for 2D and 3D shell problems, including geometric nonlinearities and loading nonlinearities. The material nonlinearities are handled by the gsMaterialMatrixIntegrate class. More...
class	gsThinShellAssemblerBase
	Base class for the gsThinShellAssembler. More...
class	gsThinShellAssemblerDWRBase
	Base class for the gsThinShellAssembler. More...
class	gsTriMeshToSolid
	Class gsTriMeshToSolid object. More...
class	gsTrimSurface
	Class for a trim surface. More...
class	gsVector
	A vector with arbitrary coefficient type and fixed or dynamic size. More...
class	gsVector3d
	A fixed-size, statically allocated 3D vector. More...
class	gsVertex
	gsVertex class that represents a 3D vertex for a gsMesh. More...
class	gsVisitorBiharmonic
	Visitor for the biharmonic equation. More...
class	gsVisitorCDR
	Visitor for the convection-diffusion-reaction equation. More...
class	gsVisitorDg
	Visitor for adding the interface conditions for the interior penalty methods of the Poisson problem. More...
class	gsVisitorGradGrad
	The visitor computes element grad-grad integrals. More...
class	gsVisitorMass
	The visitor computes element mass integrals. More...
class	gsVisitorMoments
	Visitor for the moment vector of a function. More...
class	gsVisitorNeumann
	Implementation of a Neumann BC for elliptic assemblers. More...
class	gsVisitorNeumannBiharmonic
	Visitor for Neumann boundary condition for the biharmonic equation. More...
class	gsVisitorNitsche
	Visitor for adding the terms associated to weak (Nitsche-type) imposition of the Dirichlet boundary conditions. More...
class	gsVisitorNitscheBiharmonic
	Visitor for the weak imposition of the first-type dirichlet boundary condition. More...
class	gsVisitorPoisson
	Visitor for the Poisson equation. More...
class	gsVolume
	Provides declaration of Volume abstract interface. More...
class	gsVSegment
	Class for representing a vertical line segment in 2D. Helper for the class gsAAPolyline. More...
class	gsXBraid
	Class defining the XBraid wrapper. More...
class	gsXBraid< gsMatrix< T > >
	Specializations for gsXBraid<gsMatrix<T>> More...
class	gsXBraid< gsVector< T > >
	Specializations for gsXBraid<gsVector<T>> More...
class	gsXBraidAccessStatus
	Class defining the XBraid access status wrapper. More...
class	gsXBraidBufferStatus
	Class defining the XBraid buffer status wrapper. More...
class	gsXBraidCoarsenRefStatus
	Class defining the XBraid coarsen and refinement status wrapper. More...
struct	gsXBraidMultigrid
	The p-multigrid class implements a generic p-multigrid solver that can be customized by passing assembler and coarse solver as template arguments. More...
struct	gsXBraidMultigridBase
	The p-multigrid base class provides the basic methods (smoothing, prolongation, restriction) for implementing p-multigrid methods. More...
class	gsXBraidObjectiveStatus
	Class defining the XBraid step objective wrapper. More...
class	gsXBraidStepStatus
	Class defining the XBraid step status wrapper. More...
class	gsXBraidSyncStatus
	Class defining the XBraid sync status wrapper. More...
struct	iteration_type
	@briefly Specifies iteration type for an iterative solver More...
struct	linear_solver
	Specifies linear solver to use if it is hidden within some other class (like Newton's method or time integrators) More...
struct	material_law
	Specifies the material law to use. More...
struct	MPITraits
	A traits class describing the mapping of types onto MPI_Datatypes. More...
struct	MPITraits< gsMatrix< T, _Rows, _Cols, _Options > >
	Specialization for fixed-size gsMatrix class. More...
struct	MPITraits< gsVector< T, _Rows, _Options > >
	Specialization for fixed-size gsVector class. More...
struct	ns_assembly
	Specifies the iteration type used to solve nonlinear systems. More...
struct	patchComponent
	Struct which represents a certain component (interior, face, egde, corner) of a particular patch. More...
struct	patchCorner
	Struct which represents a certain corner of a patch. More...
struct	patchSide
	Struct which represents a certain side of a patch. More...
struct	point_load
	Struct defining a point together with a scalar or vector load. More...
class	preAAParam
struct	shell_coupling
	Defines the coupling type over interfaces. More...
struct	solver_verbosity
	Specifies the verbosity of the iterative solver. More...
class	SpectraOps
class	SpectraOps< MatrixType, Spectra::GEigsMode::RegularInverse >
class	SpectraShiftOps
class	SpectraShiftOps< MatrixType, Spectra::GEigsMode::Buckling >
struct	stabilizerCDR
	Stabililzer for the CDR discretization. More...
struct	stress_components
	method was interrupted because the current solution is invalid More...
struct	stress_type
	Specifies the type of stresses to compute. More...
class	submoduleClass
	I am an example how to use the class in submodules. More...
class	submoduleClass2
	I am an example how to use the class in submodules. More...
struct	time_integration
	Specifies the time integration scheme, see Wriggers, Nonlinear FEM, p. 205. More...

Typedefs
typedef Point	Color
	Color type.
typedef gsGenericStopwatch< CPUClock >	gsCPUStopwatch
	A stop-watch measuring CPU time.
typedef gsEigen::PermutationMatrix< Dynamic, Dynamic, index_t >	gsPermutationMatrix
	reorderMapperTarget permutes the target indices of mapper according to permutation. If permutation does not contain all indices then the order of the remaining indices is preserved and the specified indices are appended to the end.
typedef gsGenericStopwatch< WallClock >	gsStopwatch
	A stop-watch measuring real (wall) time.
typedef Point	Normal
	Normal type.
typedef Point	Texture_coordinate
	Texture coordinate type.

Enumerations
enum	gsGridIteratorMode {   CUBE ,   BDR ,   VERTEX ,   CWISE }
	Specifies aliases describing the modes for gismo::gsGridIterator. More...
enum class	gsHNeighborhood
	The gsHNeighborhood is a struct that classifies the type of admissible refinement.
enum	gsNeedEnum {   NEED_VALUE ,   NEED_DERIV ,   NEED_GRAD ,   NEED_JACOBIAN ,   NEED_MEASURE ,   NEED_GRAD_TRANSFORM ,   NEED_DIV ,   NEED_CURL ,   NEED_DERIV2 ,   NEED_2ND_DER ,   NEED_HESSIAN ,   NEED_LAPLACIAN ,   NEED_ACTIVE ,   NEED_NORMAL ,   NEED_OUTER_NORMAL ,   NEED_2ND_FFORM ,   SAME_ELEMENT }
enum struct	gsStatus {   Success ,   NotConverged ,   AssemblyError ,   SolverError ,   NotStarted ,   OtherError }
enum class	Implementation : short_t
	This class describes the way material models are implemented. More...
enum class	Material : short_t
	This class describes a material model.
enum class	MaterialOutput : short_t
	This class describes the output type. More...
enum class	MatIntegration : short_t
	This class describes if an object is integrated through-thickness or not. More...
enum	solver_status { }
	Specifies the status of the iterative solver. More...
enum class	ThinShellAssemblerStatus {   Success ,   AssemblyError ,   DimensionError }

Functions
template<class T >
void	addBCs (gsBoundaryConditions< T > &bcInfo, std::vector< std::pair< int, boxSide > > &bndIn, std::vector< std::pair< int, boxSide > > &bndWall, gsFunctionExpr< T > Uin, gsFunctionExpr< T > Uwall)
	Define boundary conditions for the corresponding boundary parts.
template<class T >
void	addConstraints (gsMatrix< T > const &C1, gsMatrix< T > const &d1, gsMatrix< T > const &C2, gsMatrix< T > const &d2, gsMatrix< T > &C, gsMatrix< T > &d)
	addConstraints
template<typename obj >
std::vector< obj * >	asVectorPtr (const std::vector< obj > &matv)
	Constructs a vector of pointers from a vector of objects.
template<unsigned n, unsigned r>
unsigned	binomial ()
	Returns binomial(n,r) as a compile time constant.
template<typename Z >
Z	binomial (const Z n, const Z r)
	Computes the binomial expansion coefficient binomial(n,r)
void	binomial_into (unsigned n, gsVector< unsigned > &v)
	Returns a vector containing all the binomials (n,r) with n fixed.
template<class T >
gsTensorBSpline< 3, T >	BSplineBlock (int deg, const T llx, const T lly, const T llz, const T a, const T b, const T c, int numSep=0)
	Returns a B-spline parametrization of a 3D block of a given degree in all directions.
template<class T >
gsMultiPatch< T >	BSplineCavity2D (int deg, const T a, const T b, const int np=1, int numSep=0)
	Returns a B-spline multipatch domain for 2D problems of flow in a cavity.
template<class T >
gsMultiPatch< T >	BSplineCavity3D (int deg, const T a, const T b, const T c, int numSep=0)
	Returns a B-spline multipatch domain for 3D problems of flow in a cavity.
template<class T >
gsTensorBSpline< 2, T >	BSplineRectangle (int deg, const T llx, const T lly, const T a, const T b, int numSep=0)
	Returns a B-spline parametrization of a rectangle of a given degree in both directions.
template<class T >
gsMultiPatch< T >	BSplineStep2D (int deg, const T a, const T b, const T a_in, T h=0, bool periodic=false)
	Returns a B-spline multipatch domain for 2D problems of flow over a backward facing step.
template<class T >
gsMultiPatch< T >	BSplineStep3D (int deg, const T a, const T b, const T c, const T a_in, T h=0, bool periodic=false)
	Returns a B-spline multipatch domain for 3D problems of flow over a backward facing step.
template<typename T >
gsMatrix< T >	CalcIntervals (const gsMonomialPoly< T > &poly, T eps, gsMatrix< T > rootIntervals)
template<typename Base , typename Derived >
std::vector< Base * >	castVectorPtr (std::vector< Derived * > pVec)
	Casts a vector of pointers.
template<typename T >
T	CauchyBound (gsMonomialPoly< T > &poly)
	returns the Cauchy Bound of a Polynomial, which is 1+max(abs(a_i/a_n))
template<class T >
index_t	checkDisplacement (gsMultiPatch< T > const &domain, gsMultiPatch< T > const &displacement)
	Checks whether the deformed configuration is bijective, i.e. det(Jac(geo+disp)) > 0; returns -1 if yes or the number of the first invalid patch; samples the Jacobian elementwise at the quadrature points and the corners.
template<class T >
index_t	checkGeometry (gsMultiPatch< T > const &domain)
	Checks whether configuration is bijective, i.e. det(Jac(geo)) > 0; returns -1 if yes or the number of the first invalid patch; samples the Jacobian elementwise at the quadrature points and the corners.
template<typename Derived , typename Base >
bool	checkVectorPtrCast (std::vector< Base * > pVec)
	Returns true if all instances of Base cast to Derived.
template<typename ContIn , typename ContOut >
void	cloneAll (const ContIn &in, ContOut &out)
	Clones all pointers in the container in and stores them as raw pointers in container out.
template<typename It , typename ItOut >
void	cloneAll (It start, It end, ItOut out)
	Clones all pointers in the range [start end) and stores new raw pointers in iterator out.
template<class T >
gsMatrix< T >	combine (gsMatrix< T > const &A, gsMatrix< T > const &B, T x, index_t iA=0, index_t iB=0, bool cols=false)
	compute a convex combination of two points given as ROWS of matrices numbered <iA> and <iB>; set <cols> to <true> to give points as COLUMNS
template<class T >
T	combine (T a, T b, T x)
	compute a convex combintation (1-x)a+xb
template<class T >
gsWeightMapper< T > *	combineMappers (const std::vector< gsWeightMapper< T > * > &mappers, std::vector< index_t > &shifts, bool needShifting=true)
	combineMappers Given a set of mappers it creates a new mapper that combines all. It can be used to construct a global mapper for the cartesian product of spaces or to map both unknown and test space.
template<class T >
T	conditionedAngle (gsVector3d< T > vec1, gsVector3d< T > vec2)
	Angle between two vector: 0 <= angle <= pi.
template<class T >
T	conditionedAngle (gsVector3d< T > vec1, gsVector3d< T > vec2, gsVector3d< T > normal)
template<short_t d, class T >
void	constructCoefsForSlice (index_t dir_fixed, const index_t index, const gsMatrix< T > &fullCoefs, const gsVector< index_t, d > &sizes, gsMatrix< T > &result)
template<class T >
gsMatrix< T >	convert2Zero (gsMatrix< T > const &mat)
	convert a with abs(a) < eps=2.220446049250313e-16 into 0
template<typename T = real_t>
void	convertFreeVectorToMultiPatch (const gsVector< T > &gsFreeVec, const gsDofMapper &mapper, gsMultiPatch< T > &mp)
	Convert free control points from a vector into a multi-patch.
template<typename T = real_t>
gsVector< T >	convertMultiPatchToFreeVector (const gsMultiPatch< T > &mp, const gsDofMapper &mapper)
	Computes a patch parametrization given a set of boundary geometries. Parametrization is not guaranteed to be non-singular. Works for planar surfaces and volumes.
template<class T , class U >
void	copy_n (T begin, const size_t n, U *result)
	Small wrapper for std::copy mimicking memcpy (or std::copy_n) for a raw pointer destination, copies n positions starting from begin into result. The latter is expected to have been allocated in advance.
template<class T >
gsMatrix< T >	createVectorOfUniqueIndices (const gsMatrix< T > &mat)
	Creates a one-column matrix (vector) of unique values from the input matrix (useful for creating a unique list of active basis functions in several quadrature points).
template<class T >
gsVector< T >	criticalPointOfQuadratic (gsMatrix< T > &A, gsMatrix< T > &C, gsVector< T > &d)
template<class T >
gsMatrix< T >	criticalPointOfQuadratic (gsMatrix< T > const &A, gsMatrix< T > const &b, gsMatrix< T > const &C, gsMatrix< T > const &d)
template<class T >
gsMatrix< T >	criticalPointOfQuadratic (gsMatrix< T > const &A, gsMatrix< T > const &C, gsMatrix< T > const &d)
template<class T >
gsMatrix< T >	crossNorm2Mat (gsMatrix< T > const &mat1, gsMatrix< T > const &mat2)
template<typename Z , int d>
void	cubeIsometry (const gsVector< bool, d > &flip, const gsVector< index_t, d > &perm, gsVector< Z > &result)
	Computes the isometry of the unit d-cube implied by a permutation perm of the cube directions plus a relocation flip of the cube vertices.
template<int d>
void	cubeIsometryMatrix (const gsVector< bool, d > &flip, const gsVector< index_t, d > &perm, gsMatrix< int, d, d > &result)
	Computes the rotation matrix implied by a permutation perm of the cube directions plus a relocation flip.
template<class T >
T	curveDistance (gsGeometry< T > const &curveA, gsGeometry< T > const &curveB, index_t numSamples=1000)
	returns a distance in L2 sense between two curves parametrized from 0 to 1
template<class T >
T	curveLength (const gsGeometry< T > &geo)
	compute curve length
template<class T >
void	defineBCs_cavity (gsBoundaryConditions< T > &bcInfo, std::vector< std::pair< int, boxSide > > &bndWall, int dim, const int np=1, std::string lidVel="1")
	Define boundary conditions for the lid-driven cavity problem.
template<class T >
void	defineBCs_cavity2D (gsBoundaryConditions< T > &bcInfo, const int np, std::vector< std::pair< int, boxSide > > &bndWall, std::string lidVel="1")
	Define boundary conditions for the 2D lid-driven cavity problem.
template<class T >
void	defineBCs_cavity3D (gsBoundaryConditions< T > &bcInfo, std::vector< std::pair< int, boxSide > > &bndWall, std::string lidVel="1")
	Define boundary conditions for the 3D lid-driven cavity problem.
template<class T >
void	defineBCs_profile2D (gsBoundaryConditions< T > &bcInfo, std::vector< std::pair< int, boxSide > > &bndIn, std::vector< std::pair< int, boxSide > > &bndOut, std::vector< std::pair< int, boxSide > > &bndWall, T inVelX, T inVelY)
	Define boundary conditions for the 2D blade profile problem.
template<class T >
void	defineBCs_step (gsBoundaryConditions< T > &bcInfo, std::vector< std::pair< int, boxSide > > &bndIn, std::vector< std::pair< int, boxSide > > &bndOut, std::vector< std::pair< int, boxSide > > &bndWall, int dim, bool periodic=false, std::string inVel="default")
	Define boundary conditions for the backward-facing step problem.
template<class T >
void	defineBCs_step2D (gsBoundaryConditions< T > &bcInfo, std::vector< std::pair< int, boxSide > > &bndIn, std::vector< std::pair< int, boxSide > > &bndOut, std::vector< std::pair< int, boxSide > > &bndWall, bool periodic=false, std::string inVel="default")
	Define boundary conditions for the 2D backward-facing step problem.
template<class T >
void	defineBCs_step3D (gsBoundaryConditions< T > &bcInfo, std::vector< std::pair< int, boxSide > > &bndIn, std::vector< std::pair< int, boxSide > > &bndOut, std::vector< std::pair< int, boxSide > > &bndWall, bool periodic=false, std::string inVel="default")
	Define boundary conditions for the 3D backward-facing step problem.
template<class T , int MatOrder>
void	diagInvMatrix_into (const gsSparseMatrix< T, MatOrder > &mat, gsSparseMatrix< T, MatOrder > &diagInv, int repeat, bool lumping=false)
	Fill a diagonal approximation of an inverse matrix.
template<class Vec >
index_t	dimCubeElement (const Vec &cur)
	Returns the dimension of an element (face) of the d-cube [0,1]^d. The element is expected to contain 0,1 (corresponding to cube extrema) and the special value 2 at the position of "free" coordinates.
GISMO_DEPRECATED index_t	direction (index_t s)
	Returns the parametric direction that corresponds to side s.
template<class T >
T	displacementJacRatio (gsMultiPatch< T > const &domain, gsMultiPatch< T > const &displacement)
	Returns min(Jacobian determinant) divided by max(Jacobian determinant) for geo+disp samples the Jacobian elementwise at the quadrature points and the corners.
template<class T >
T	distance (gsMatrix< T > const &A, gsMatrix< T > const &B, index_t i=0, index_t j=0, bool cols=false)
	compute a distance between the point number in the set and the point number <j> in the set ; by default, points are given as ROWS of matrices; set <cols> to <true> to give points as COLUMNS
template<class T >
gsVector< unsigned >	distributePoints (const gsGeometry< T > &geo, unsigned numPoints)
	distributes sampling points according to the length of the patch in each parametric direction
unsigned	factorial (unsigned n)
	Returns the factorial of n i.e. n! Remember that factorial grow too fast and only n! with n<=13 can be stored in a 32bit that is an unsigned.
template<typename T >
unsigned	findHyperPlaneIntersections (const gsBSpline< T > &curve, const gsVector< T > &normal, T reference, T tolerance, std::vector< Root< T > > &roots)
	find intersections of a BSpline curve with an hyperplane
template<typename T >
gsMatrix< T >	FindRootIntervals (gsMonomialPoly< T > &poly, T eps)
template<class Vec >
void	firstCombination (const unsigned n, const unsigned r, Vec &res)
	Computes the first r-combination of {0,..,n-1}.
template<class Vec >
void	firstComposition (typename Vec::Scalar sum, index_t dim, Vec &res)
	Construct first composition of sum into dim integers.
template<class Vec >
void	firstCubeElement (Vec &cur, const index_t k=0)
	Updates cur to contain the lexicographically first element (face) of the cube [0,1]^d of dimension k. For k==d the face (2..2) is returned, corresponding to the cube itself.
template<class Vec , class Mat >
void	firstMultiComposition (const Vec &a, index_t k, Mat &res)
	Constructs first multi-composition of a = (a_1,..,a_d) into k integers.
template<class Vec >
void	firstPermutation (Vec &current)
	changes current to the first permutation of 0 ... size(current)-1 note that you must resize the vector to specify the number of elements
template<class T >
gsGeometry< T >::uPtr	fittingDirichlet (gsMatrix< T > const &params, gsMatrix< T > const &points, gsBasis< T > const &basis)
	fits a given parametrized point cloud with a curve using a given basis; the resulting curve interpolates the first and the last points
template<class T >
gsMatrix< T >	flipLR (const gsMatrix< T > &mat)
	Flip columes from left to right and vice versa.
template<typename T , int d>
void	flipTensorVector (const int dir, const gsVector< index_t, d > &sz, gsMatrix< T > &coefs)
	Flips tensor directions in place.
template<typename Cont >
void	freeAll (Cont &cont)
	Frees all pointers in the container Cont.
template<typename It >
void	freeAll (It begin, It end)
	Frees all pointers in the range [begin end)
template<int d>
int	fromTensorIndex (const gsVector< unsigned, d > &idx, const gsVector< unsigned, d > &sz)
	Helper function to compute a lexicographically numbered index from tensor indices.
template<class T >
gsGeometry< T >::uPtr	genCircle (gsBasis< T > &basis, T radius=1., T x0=0., T y0=0., T angle0=0., T arcAngle=2 *EIGEN_PI)
template<class T >
gsGeometry< T >::uPtr	genCircle (index_t deg, index_t num, T radius=1., T x0=0., T y0=0., T angle0=0., T arcAngle=2 *EIGEN_PI)
template<class T >
gsGeometry< T >::uPtr	genCylinder (gsGeometry< T > const &base, index_t deg, index_t num, T height)
	generates a 3D tensor product B-spline cylindrical patch
template<class T >
gsGeometry< T >::uPtr	genLine (index_t deg, index_t num, gsMatrix< T > const &A, gsMatrix< T > const &B, index_t iA=0, index_t iB=0)
template<class T >
void	genMuscleMP (gsGeometry< T > const &muscleSurface, gsMultiPatch< T > &result)
	This is more of a script than a function. I use it to generate a multi-parametrization for the biceps model given its surface.
template<class T >
gsGeometry< T >::uPtr	genPatchInterpolation (gsGeometry< T > const &A, gsGeometry< T > const &B, index_t deg, index_t num, bool xiDir=false)
template<class T >
gsGeometry< T >::uPtr	genPatchScaling (gsGeometry< T > const &boundary, index_t deg, index_t num, T scaling, gsVector< T > const &center)
	generates a tensor product B-spline bdry south | front patch by scaling a given geometry object \ / | | | towards a given center point; (x,y) north | back oppositely lying bdry is generated by scaling the original boundary with <scaling> coeff
template<class T >
gsGeometry< T >::uPtr	genQuad (index_t xiDeg, index_t xiNum, index_t etaDeg, index_t etaNum, gsMatrix< T > const &A, gsMatrix< T > const &B, gsMatrix< T > const &C, gsMatrix< T > const &D, index_t iA=0, index_t iB=0, index_t iC=0, index_t iD=0)
	generates a quad patch given by its four C—D corners with the following orientation; | | the points are given as ROWS of matrices A—B
template<class T >
void	genSamplingPoints (const gsVector< T > &lower, const gsVector< T > &upper, const gsQuadRule< T > &quRule, gsMatrix< T > &points)
	Generates a matrix of sampling points for a given parametric element; includes quadrature points for the element as well as the corner points.
template<class T >
gsGeometry< T >::uPtr	genScrew (gsGeometry< T > const &base, index_t deg, index_t num, T height, T pitch, T x0=0., T y0=0.)
	generates a 3D tensor product B-spline screw-like patch
template<class T >
gsGeometry< T >::uPtr	genSphere (gsKnotVector< T > &xiKnots, gsKnotVector< T > &etaKnots, T xi0=0., T xi1=2 *EIGEN_PI, T eta0=-EIGEN_PI/2, T eta1=EIGEN_PI/2)
	generates a tensor product B-spline spherical patch with radius 1 and center at 0 given knot vectors for two parametric dimensions
template<class T >
gsGeometry< T >::uPtr	genSphere (index_t xiDeg, index_t xiNum, index_t etaDeg, index_t etaNum, T xi0=0., T xi1=2 *EIGEN_PI, T eta0=-EIGEN_PI/2, T eta1=EIGEN_PI/2)
	generates a tensor product B-spline spherical patch with radius 1 and center at 0 given the degrees and number of control points in two parametric dimensions
template<class T >
gsGeometry< T >::uPtr	genSpring (gsGeometry< T > const &crossSection, T springRadius=6.0, T springPitch=2.60258, index_t numQuarterSegments=12, bool nurbs=false)
	generates a 3D NURBS spring using provided geometry as a cross-section
template<class T >
T	geometryJacRatio (gsMultiPatch< T > const &domain)
	Returns min(Jacobian determinant) divided by max(Jacobian determinant); samples the Jacobian elementwise at the quadrature points and the corners.
template<typename T >
gsMatrix< T >	getFace (const boxSide side, const gsMatrix< T > &box)
	get the matrix containing the lower and upper corner of the specified side of the given box
template<short_t d, class T >
gsMaterialMatrixBase< T >::uPtr	getMaterialMatrix (const gsMultiPatch< T > &mp, const gsFunctionSet< T > &thickness, const std::vector< gsFunctionSet< T > * > &parameters, const gsFunctionSet< T > &rho, const gsOptionList &options)
	Gets a material matrix based on options.
template<short_t d, class T >
gsMaterialMatrixBase< T >::uPtr	getMaterialMatrix (const gsMultiPatch< T > &mp, const gsFunctionSet< T > &thickness, const std::vector< gsFunctionSet< T > * > &parameters, const gsOptionList &options)
	Gets a material matrix based on options.
template<class T , int MatOrder>
gsVector< index_t >	getNnzVectorPerOuter (const gsSparseMatrix< T, MatOrder > &mat)
	Get a vector of nonzero entries per outer index (row or column depending on the matrix storage order).
template<typename S >
S	give (S &x)
template<typename matrix_t1 , typename matrix_t2 >
bool	gsAllCloseAbsolute (const matrix_t1 &a, const matrix_t2 &b, const typename matrix_t1::Scalar &tol)
	tests if the difference between two matrices is bounded by tol in \( L^\infty \) norm
template<typename matrix_t1 , typename matrix_t2 >
bool	gsAllCloseRelAndAbsWithRef (const matrix_t1 &a, const matrix_t2 &b, const typename matrix_t1::Scalar &tol, const typename matrix_t1::Scalar &ref)
	Tests whether the difference between two matrices is bounded by tol in \( L^\infty \) norm.
template<typename matrix_t1 , typename matrix_t2 >
bool	gsAllCloseRelativeToMax (const matrix_t1 &a, const matrix_t2 &b, const typename matrix_t1::Scalar &tol)
	tests if the difference between two matrices is bounded by tol in \( L^\infty \) norm
template<class T , class KnotVectorType , class Mat >
void	gsBoehm (KnotVectorType &knots, Mat &coefs, T val, int r=1, bool update_knots=true)
	Performs insertion of multiple knot on "knots" and coefficients "coefs".
template<class KnotVectorType , class Mat , class ValIt >
void	gsBoehmRefine (KnotVectorType &knots, Mat &coefs, int p, ValIt valBegin, ValIt valEnd, bool update_knots=true)
template<class T , class iter , class Mat >
void	gsBoehmSingle (iter knot, Mat &coefs, int p, T val)
template<class T , class KnotVectorType , class Mat >
void	gsBoehmSingle (KnotVectorType &knots, Mat &coefs, T val, bool update_knots=true)
	Performs knot insertion once on "knots" and coefficients "coefs".
template<typename T >
bool	gsClose (const T &a, const T &b, const T &tol)
	tests if the difference between two numbers is below tolerance
template<class T , class KnotVectorType >
void	gsDeboor (const gsMatrix< T > &u, const KnotVectorType &knots, int deg, const gsMatrix< T > &coefs, gsMatrix< T > &result)
template<class T , class KnotVectorType >
void	gsDeboorDeriv (const gsMatrix< T > &u, const KnotVectorType &knots, int deg, const gsMatrix< T > &coefs, gsMatrix< T > &result)
template<class T >
gsBSpline< T >	gsInterpolate (gsKnotVector< T > &kv, const gsMatrix< T > &preImage, const gsMatrix< T > &image, const gsMatrix< T > &preNormal, const gsMatrix< T > &normal, const gsMatrix< T > &preImageApp, const gsMatrix< T > &imageApp, T const &w_reg, T const &w_app, gsMatrix< T > &outPointResiduals, gsMatrix< T > &outNormalResiduals)
template<class T >
gsTensorBSpline< 2, T >::Ptr	gsInterpolateSurface (const gsMatrix< T > &exactPoints, const gsMatrix< T > &exactValues, const gsMatrix< T > &appxPointsEdges, const gsMatrix< T > &appxValuesEdges, const gsMatrix< T > &appxPointsInt, const gsMatrix< T > &appxValuesInt, const gsMatrix< T > &appxNormalPoints, const gsMatrix< T > &appxNormals, T wEdge, T wInt, T wNormal, T wReg, const gsKnotVector< T > &kv1, const gsKnotVector< T > &kv2, bool force_normal)
template<typename T >
bool	gsIsfinite (T a)
template<typename T >
bool	gsIsnumber (T a)
template<class T >
void	gsMarkElementsForRef (const std::vector< T > &elError, int refCriterion, T refParameter, std::vector< bool > &elMarked)
	Marks elements/cells for refinement.
	gsMpi (const int &argc, char **argv)
	calls MPI_Init with argc and argv as parameters
gsMpi &	gsMpiSingleton (const int &argc, char **argv)
	Singleton function returning the gsMpi helper object.
template<class T , class CwiseContainer >
gsMatrix< T >	gsPointGrid (CwiseContainer const &cwise)
	Construct a grid of points by coordinate vectors in the container cwise.
template<class T , class CwiseContainer >
void	gsPointGrid (CwiseContainer const &cwise, gsMatrix< T > &res)
template<class T >
gsMatrix< T >	gsPointGrid (gsMatrix< T > const &ab, int numPoints)
template<class T >
gsMatrix< T >	gsPointGrid (gsVector< T > const &a, gsVector< T > const &b, gsVector< unsigned > const &np)
	Construct a Cartesian grid of uniform points in a hypercube, using np[i] points in direction i.
template<class T >
void	gsRefineMarkedElements (gsMultiBasis< T > &basis, const std::vector< bool > &elMarked, index_t refExtension=0)
	Refine a gsMultiBasis, based on a vector of element-markings.
template<typename T , typename KnotVectorType , typename Mat >
void	gsTensorBoehm (KnotVectorType &knots, Mat &coefs, T val, int direction, gsVector< unsigned > str, int r=1, bool update_knots=true)
template<typename KnotVectorType , typename Mat , typename ValIt >
void	gsTensorBoehmRefine (KnotVectorType &knots, Mat &coefs, int direction, gsVector< unsigned > str, ValIt valBegin, ValIt valEnd, bool update_knots=true)
template<short_t d, typename KnotVectorType , typename Mat , typename ValIt >
void	gsTensorBoehmRefineLocal (KnotVectorType &knots, const unsigned index, Mat &coefs, gsVector< index_t, d > &nmb_of_coefs, const gsVector< index_t, d > &act_size_of_coefs, const gsVector< index_t, d > &size_of_coefs, const unsigned direction, ValIt valBegin, ValIt valEnd, const bool update_knots)
	Local refinement algorithm.
template<short_t d, typename T , typename KnotVectorType , typename Mat >
void	gsTensorInsertKnotDegreeTimes (const KnotVectorType &knots, Mat &coefs, const gsVector< index_t, d > &size_of_coefs, T val, const unsigned direction, gsVector< index_t, d > &start, gsVector< index_t, d > &end)
	Inserts knot val such that multiplicity of a val in knot vector is equal degree.
template<class T >
void	gsTraceCurvePart (std::pair< gsFunction< T > *, gsFunction< T > * > &map, gsMatrix< T > const &x, gsBSpline< T > *bs, T t0, T t1, gsMatrix< T > &result, const int n_points=50, const T tolerance=0.0001)
template<class T >
void	gsTraceLine (std::pair< gsFunction< T > *, gsFunction< T > * > &map, gsMatrix< T > const &x, gsMatrix< T > const &p, gsMatrix< T > &result)
template<class T >
void	gsUnrefineMarkedElements (gsMultiBasis< T > &basis, const std::vector< bool > &elMarked, index_t refExtension=0)
	Unrefine a gsMultiBasis, based on a vector of element-markings.
template<typename Object >
void	gsWrite (const Object &obj, const std::string &fname)
	Write an arbitrary Gismo object to an XML file with the given filename.
template<class T >
void	gsWriteCsv (std::string const &filename, const gsMatrix< T > &matrix, const std::vector< std::string > &headers=std::vector< std::string >())
	Export a gsMatrix to a .csv (comma separated values) file.
template<typename T >
void	gsWriteGoTools (const gsGeometry< T > &geom, const std::string &fileName)
template<typename T >
void	gsWriteGoTools (const gsGeometry< T > &geom, std::ofstream &out)
template<typename T >
void	gsWriteGoTools (const gsMultiPatch< T > &multiPatch, const std::string &fileName)
template<short_t d, typename T >
void	gsWriteGoToolsBodySpline (const gsTensorBSpline< d, T > &bspl, std::ofstream &out)
	Writes body part of GoTools (.g2) format to a file.
template<short_t d, typename T >
void	gsWriteGoToolsSpline (const gsTensorBSpline< d, T > &bspl, std::ofstream &out)
void	gsWriteOutput (std::ofstream &file, const std::string output, bool fileOutput, bool dispInTerminal)
	Writes an output into the given file and optionally also into terminal.
void	gsWriteOutputLine (std::ofstream &file, const std::string line, bool fileOutput, bool dispInTerminal)
	Writes an output line into the given file and optionally also into terminal.
template<class T >
void	gsWriteParaview (const gsField< T > &field, std::string const &fn, unsigned npts=NS, bool mesh=false, const std::string pDelim="")
	Write a file containing a solution field (as color on its geometry) to paraview file.
template<class T >
void	gsWriteParaview (const gsGeometry< T > &Geo, std::string const &fn, unsigned npts=NS, bool mesh=false, bool ctrlNet=false)
	Export a gsGeometry (without scalar information) to paraview file.
template<class T >
void	gsWriteParaview (const gsGeometrySlice< T > &Geo, std::string const &fn, unsigned npts=NS)
	Export a Geometry slice to paraview file.
template<class T >
void	gsWriteParaview (const gsHBox< 2, T > &box, std::string const &fn)
	Export gsHBox to paraview files.
template<class T >
void	gsWriteParaview (const gsHBoxContainer< 2, T > &box, std::string const &fn)
	Export gsHBox to paraview files.
template<class T >
void	gsWriteParaview (const gsMatrix< T > &box, const gsVector< T > &values, std::string const &fn)
	Export an element box to paraview files.
template<class T >
void	gsWriteParaview (const gsMatrix< T > &box, std::string const &fn, T value=0.0)
	Export an element box to paraview files.
template<class T >
void	gsWriteParaview (const gsMultiBasis< T > &mb, const gsMultiPatch< T > &domain, std::string const &fn, unsigned npts)
	Export a computational mesh to paraview file.
template<class T >
void	gsWriteParaview (const gsMultiPatch< T > &Geo, std::string const &fn, unsigned npts=NS, bool mesh=false, bool ctrlNet=false, const std::string pDelim="_")
	Export a multipatch Geometry (without scalar information) to paraview file.
template<class T >
void	gsWriteParaview (const gsTrimSurface< T > &ts, std::string const &fn, unsigned npts=NS, bool trimCurves=false)
	Visualizing a gsTrimSurface.
template<typename T >
void	gsWriteParaview (const gsVolumeBlock< T > &volBlock, std::string const &fn, unsigned npts=NS)
	Export a volumeBlock.
template<typename T >
void	gsWriteParaview (const std::vector< gsMesh< T > > &meshes, std::string const &fn)
	Export a vector of meshes, each mesh in its own file.
template<class T >
void	gsWriteParaview (gsBasis< T > const &basis, std::string const &fn, unsigned npts=NS, bool mesh=false)
	Export Basis functions to paraview files.
template<class T >
void	gsWriteParaview (gsBasis< T > const &basis, std::vector< index_t > const &indices, std::string const &fn, unsigned npts=NS, bool mesh=false)
	Export Basis functions to paraview files.
template<class T >
void	gsWriteParaview (gsCurveLoop< T > const &cloop, std::string const &fn, unsigned npts)
	Visualizing a gsCurveLoop.
template<class T >
void	gsWriteParaview (gsFunction< T > const &func, gsMatrix< T > const &supp, std::string const &fn, unsigned npts=NS, bool graph=true)
	Export a function plot to paraview file.
template<class T >
void	gsWriteParaview (gsFunctionSet< T > const &func, std::string const &fn, unsigned npts=NS)
	Export a functionSet plot to paraview file.
template<class T >
void	gsWriteParaview (gsFunctionSet< T > const &geo, gsFunctionSet< T > const &func, std::string const &fn, unsigned npts=NS, const std::string pDelim="")
	Write a file containing a solution func (as color on its geometry geo), defined using functionsets, to paraview file.
template<class T >
void	gsWriteParaview (gsFunctionSet< T > const &geom, gsMappedBasis< 2, T > const &mbasis, std::string const &fn, unsigned npts=NS, const bool fullsupport=false, const std::vector< index_t > indices=std::vector< index_t >())
	Writes a gsMappedBasis over a gsMappedSpline geometry.
template<class T >
void	gsWriteParaview (gsMappedSpline< 2, T > const &mspline, std::string const &fn, unsigned npts=NS)
	Writes a gsMappedSpline geometry.
template<class T >
void	gsWriteParaview (gsMesh< T > const &sl, std::string const &fn, bool pvd)
	Visualizing a mesh.
template<class T >
void	gsWriteParaview (gsMesh< T > const &sl, std::string const &fn, const gsMatrix< T > &params)
	Export a mesh to paraview file.
template<class T >
void	gsWriteParaview (gsMultiPatch< T > const &mp, gsMultiBasis< T > const &mb, std::string const &fn, unsigned npts=NS)
	Plot the basis functions of a multi-basis.
template<class T >
void	gsWriteParaview (gsMultiPatch< T > const &patches, typename gsBoundaryConditions< T >::bcContainer const &bcs, std::string const &fn, unsigned npts=NS, bool ctrlNet=false)
	Visualizing boundary conditions.
template<class T >
void	gsWriteParaview (gsPlanarDomain< T > const &pdomain, std::string const &fn, unsigned npts=NS)
	Visualizing a gsPlanarDomain.
template<class T >
void	gsWriteParaview (gsSolid< T > const &sl, std::string const &fn, unsigned numPoints_for_eachCurve=50, int vol_Num=0, T edgeThick=0.01, gsVector3d< T > const &translate=gsVector3d< T >(0, 0, 0), int color_convex=0, int color_nonconvex=20, int color_eloop=10, std::vector< unsigned > const &eloop=std::vector< unsigned >())
	Export tensor-structured point set with field data to Paraview file.
template<class T >
void	gsWriteParaview (std::vector< gsGeometry< T > * > const &Geo, std::string const &fn, unsigned npts=NS, bool mesh=false, bool ctrlNet=false, const std::string pDelim="_")
	Export a multipatch Geometry (without scalar information) to paraview file.
template<class T >
void	gsWriteParaview_basisFnct (int i, gsBasis< T > const &basis, std::string const &fn, unsigned npts=NS)
	Export i-th Basis function to paraview file.
template<class T >
void	gsWriteParaviewBdr (gsMultiPatch< T > const &patches, std::string const &fn, unsigned npts, bool ctrlNet)
	Writes the boundaries of a multipatch to paraview.
template<class T >
void	gsWriteParaviewBezier (const gsMultiPatch< T > &mPatch, std::string const &filename, bool ctrlNet=false)
	Export a multipatch Geometry (without scalar information) to paraview file using Bezier elements.
template<class T >
void	gsWriteParaviewIfc (gsMultiPatch< T > const &patches, std::string const &fn, unsigned npts, bool ctrlNet)
	Writes the interfaces of a multipatch to paraview.
template<class T >
void	gsWriteParaviewMultiPhysics (std::map< std::string, const gsField< T > * > fields, std::string const &fn, unsigned npts=NS, bool mesh=false, bool ctrlNet=false)
	Write a file containing several fields defined on the same geometry to ONE paraview file.
template<class T >
void	gsWriteParaviewMultiPhysicsSinglePatch (std::map< std::string, const gsField< T > * > fields, const unsigned patchNum, std::string const &fn, unsigned npts)
	Extract and evaluate geometry and the fields for a single patch.
template<class T >
void	gsWriteParaviewMultiPhysicsTimeStep (std::map< std::string, const gsField< T > * > fields, std::string const &fn, gsParaviewCollection &collection, int time, unsigned npts=NS)
	Write a file containing several fields defined on the same geometry to ONE paraview file and adds it as a timestep to a Paraview collection.
template<class T >
void	gsWriteParaviewMultiTPgrid (gsMatrix< T > const &points, std::map< std::string, gsMatrix< T > > &data, const gsVector< index_t > &np, std::string const &fn)
	Utility function to actually write prepaired matrices with data into Paraview file.
template<class T >
void	gsWriteParaviewPoints (gsMatrix< T > const &points, std::string const &fn)
	Export Point set to Paraview file.
template<class T >
void	gsWriteParaviewPoints (gsMatrix< T > const &X, gsMatrix< T > const &Y, gsMatrix< T > const &Z, gsMatrix< T > const &V, std::string const &fn)
	Export 3D Point set to Paraview file.
template<class T >
void	gsWriteParaviewPoints (gsMatrix< T > const &X, gsMatrix< T > const &Y, gsMatrix< T > const &Z, std::string const &fn)
	Export 3D Point set to Paraview file.
template<class T >
void	gsWriteParaviewPoints (gsMatrix< T > const &X, gsMatrix< T > const &Y, std::string const &fn)
	Export 2D Point set to Paraview file.
template<class T >
void	gsWriteParaviewSolid (gsSolid< T > const &sl, std::string const &fn, unsigned numSamples=NS)
	Export a gsSolid to Paraview file.
template<typename T >
void	gsWriteParaviewTrimmedCurve (const gsTrimSurface< T > &surf, const unsigned idLoop, const unsigned idCurve, const std::string fn, unsigned npts=NS)
	Export a boundary/hole curve in trimmed surface.
template<typename T >
gsVector< T >	HornerEval (gsMatrix< T > &mat, T num)
template<typename T >
T	HornerEvalPoly (const gsVector< T > &vec, T num)
	evaluates a gsVector (which represents the coefficients of a polynomial) at value num
template<typename Derived >
bool	isfinite (const gsEigen::MatrixBase< Derived > &x)
	Check if all the entires if the matrix x are not INF (infinite)
template<typename Derived >
bool()	isnumber (const gsEigen::MatrixBase< Derived > &x)
	Check if all the entires if the matrix x are not NAN (not a number)
void	makeCollection (std::string const &fn, std::string const &ext, int n=0)
template<typename T >
bool	makeHierarchicalMesh (const gsBasis< T > &basis, std::vector< gsMesh< T > > &meshes, int n=0)
template<class T , class iterator >
gsMatrix< T >	makeMatrix (iterator it, index_t n, index_t m)
	Utility to make a matrix out of an iterator to values.
template<class T >
void	makeMesh (const gsBasis< T > &basis, gsMesh< T > &mesh, int n=0)
	Returns the computational mesh of basis.
template<class Vec >
bool	nextCombination (Vec &v, const unsigned n)
	Computes the next r-combination of {0,..,n-1}, where r = v.size(). The input v is expected to be a valid combination.
template<class Vec >
bool	nextComposition (Vec &v)
	Returns (inplace) the next composition in lexicographic order.
template<class Vec >
bool	nextCubeBoundary (Vec &cur, const Vec &start, const Vec &end)
	Iterates in lex-order through the boundary points of the cube [start,end]. Updates cur with the current point and returns true if another point is available. Cube may be degenerate.
template<class Vec >
bool	nextCubeBoundaryOffset (Vec &cur, const Vec &start, const Vec &end, Vec &loffset, Vec &uoffset)
	Iterates in lex-order through the boundary points of the cube [start,end], with offset loffset from \ start and roffset .from the end. Updates cur with the current point and returns true if another point is available. Cube may be degenerate.
template<class Vec >
bool	nextCubeBoundaryOffset (Vec &cur, const Vec &start, const Vec &end, Vec &offset)
	Iterates in lex-order through the boundary points of the cube [start,end], with an \ offset to the interior. Updates cur with the current point and returns true if another point is available. Cube may be degenerate.
template<class Vec >
bool	nextCubeElement (Vec &cur, const index_t k)
	Iterates in lexicographic order through the elements (faces) of dimension k of the cube [0,1]^d. Updates cur with the current element (face) and returns true if another element (face) of dimension k is available. Coordinates with value 2 indicate free/not-fixed dimensions.
template<class Vec >
bool	nextCubePoint (Vec &cur, const Vec &end)
	Iterate in lexigographic order through the points of the integer lattice contained in the cube [0,end]. Updates cur with the current point and returns true if another point is available. Cube may be degenerate.
template<class Vec >
bool	nextCubePoint (Vec &cur, const Vec &start, const Vec &end)
	Iterates in lexigographic order through the points of the integer lattice contained in the cube [start,end]. Updates cur with the current point and returns true if another point is available. Cube may be degenerate.
template<class Vec >
bool	nextCubeVertex (Vec &cur)
	Iterate in lexigographic order through the vertices of the unit cube. Updates cur with the lexicographically next vertex and returns true if another point is available. This is equivalent to iterating over all possible binary sequences of length cur.size(). The input cur is expected to contain only zeros and ones (or true/false).
template<class Vec >
bool	nextCubeVertex (Vec &cur, const Vec &end)
	Iterate in lexicographic order through the vertices of the cube [0,end]. Updates cur with the current vertex and returns true if another vertex is available. Cube may be degenerate.
template<class Vec >
bool	nextCubeVertex (Vec &cur, const Vec &start, const Vec &end)
	Iterate in lexicographic order through the vertices of the cube [start,end]. Updates cur with the current vertex and returns true if another vertex is available. Cube may be degenerate.
template<class Vec >
bool	nextLexicographic (Vec &cur, const Vec &size)
	Iterates through a tensor lattice with the given size. Updates cur and returns true if another entry was available End values (size) are not included in the enumerated points, as with iterators.
template<class Vec >
bool	nextLexicographic (Vec &cur, const Vec &start, const Vec &end)
	Iterate through a tensor lattice with the given start and end points. end coordinates are not included in the enumerated points, as with iterators. Updates cur and returns true if another entry was available.
template<class Mat >
bool	nextMultiComposition (Mat &m)
	Returns (inplace) the next multi-composition in lexicographic order.
template<class Vec >
bool	nextPermutation (Vec &current)
	Changes current to the next lexicographically ordered permutation.
template<class T >
T	normL2 (gsMultiPatch< T > const &domain, gsMultiPatch< T > const &solution)
	@ Compute norm of the isogeometric solution
unsigned	numCompositions (int sum, short_t dim)
	Number of compositions of sum into dim integers.
index_t	numCubeElements (const index_t k, const index_t d)
	Returns the number of elements (faces) of dimension k of a d-cube.
template<class Vec >
unsigned	numMultiCompositions (const Vec &a, index_t k)
	Number of multi-composition of a = (a_1,..,a_d) into k integers.
template<class T >
bool	operator!= (gsVertex< T > const &lhs, gsVertex< T > const &rhs)
bool	operator< (const gsOptionList::OptionListEntry &a, const gsOptionList::OptionListEntry &b)
	Objects of class gsOptionList::OptionListEntry can be ordered by label.
std::ostream &	operator<< (std::ostream &os, const boundaryInterface &i)
	Print (as string) an interface.
std::ostream &	operator<< (std::ostream &os, const boxSide &o)
	Print (as string) a box side.
template<class T >
std::ostream &	operator<< (std::ostream &os, const gsBoundaryConditions< T > &bvp)
	Print (as string)
template<class T >
std::ostream &	operator<< (std::ostream &os, const gsCurveLoop< T > &b)
	Print (as string) operator to be used by all derived classes.
std::ostream &	operator<< (std::ostream &os, const gsDofMapper &b)
	Print (as string) a dofmapper structure.
template<class T >
std::ostream &	operator<< (std::ostream &os, const gsDomain< T > &b)
	Print (as string) operator to be used by all derived classes.
template<class T >
std::ostream &	operator<< (std::ostream &os, const gsField< T > &b)
	Print (as string) operator to be used by all derived classes.
template<class T >
std::ostream &	operator<< (std::ostream &os, const gsFunction< T > &b)
	Print (as string) operator to be used by all derived classes.
template<class T >
std::ostream &	operator<< (std::ostream &os, const gsFunctionSet< T > &b)
	Print (as string) operator to be used by all derived classes.
template<class T >
std::ostream &	operator<< (std::ostream &os, const gsGeometry< T > &b)
	Print (as string) operator to be used by all derived classes.
std::ostream &	operator<< (std::ostream &os, const gsJITCompiler &c)
	Print (as string) operator to be used by all derived classes.
std::ostream &	operator<< (std::ostream &os, const gsJITCompilerConfig &c)
	Print (as string) operator to be used by all derived classes.
template<class T >
std::ostream &	operator<< (std::ostream &os, const gsMultiBasis< T > &b)
	Print (as string) a multibasis structure.
template<class T >
std::ostream &	operator<< (std::ostream &os, const gsMultiPatch< T > &b)
	Print (as string) a multipatch structure.
std::ostream &	operator<< (std::ostream &os, const gsOptionList &b)
	Objects of class gsOptionList can be printed using the standard io-streams.
std::ostream &	operator<< (std::ostream &os, const gsOptionList::OptionListEntry &b)
	Objects of class gsOptionList::OptionListEntry can be printed using the standard io-streams.
template<class T >
std::ostream &	operator<< (std::ostream &os, const gsPde< T > &pde)
	Print (as string) operator to be used by all derived classes.
template<class T >
std::ostream &	operator<< (std::ostream &os, const gsPointLoads< T > &pls)
	Print (as string)
std::ostream &	operator<< (std::ostream &os, const gsSerialGroup &obj)
	Prints the group object as a string.
std::ostream &	operator<< (std::ostream &os, const gsSerialRequest &obj)
	Prints the request object as a string.
std::ostream &	operator<< (std::ostream &os, const gsSerialStatus &obj)
	Prints the status object as a string.
template<class T >
std::ostream &	operator<< (std::ostream &os, const gsSolidHalfEdge< T > &me)
	Print (as string) operator to be used by all mesh elements.
template<class T >
std::ostream &	operator<< (std::ostream &os, const gsSparseSolver< T > &b)
	Print (as string) operator for sparse solvers.
template<class T >
std::ostream &	operator<< (std::ostream &os, const gsTemplate< T > &b)
	Print (as string) a template.
template<class T >
std::ostream &	operator<< (std::ostream &os, const gsVSegment< T > a)
	Print (as string) operator.
std::ostream &	operator<< (std::ostream &os, patchSide const &i)
	Print (as string) a patch side.
template<class T >
bool	operator== (gsVertex< T > const &lhs, gsVertex< T > const &rhs)
template<class T >
bool	operator> (gsVertex< T > const &lhs, gsVertex< T > const &rhs)
template<class T >
gsMatrix< T >	optQuadratic (gsMatrix< T > const &A, gsMatrix< T > const &b, gsMatrix< T > const &C, gsMatrix< T > const &d)
	Find X which solves: min (AX-b)^T (AX-b), s.t. CX=d.
template<class T >
gsMatrix< T >	optQuadratic (gsMatrix< T > const &A1, gsMatrix< T > const &b1, T const &w1, gsMatrix< T > const &A2, gsMatrix< T > const &b2, T const &w2, gsMatrix< T > const &C, gsMatrix< T > const &d)
	Find X which solves: min w_1 (A_1 X-b_1)^T (A_1 X-b_1) + w_2 (A_2 X-b_2)^T (A_2 X-b_2), s.t. CX=d.
template<class T >
gsMatrix< T >	optQuadratic (gsMatrix< T > const &A1, gsMatrix< T > const &b1, T const &w1, gsMatrix< T > const &A2, gsMatrix< T > const &b2, T const &w2, gsMatrix< T > const &C, gsMatrix< T > const &d, T const &w3, gsMatrix< T > const &Q)
GISMO_DEPRECATED bool	parameter (int s)
	Returns the parameter value (false=0=start, true=1=end) that corresponds to side s.
template<class T >
T	patchLength (const gsGeometry< T > &geo, short_t dir=0)
	compute length of a patch in a given parametric direction as a mean of all boundary edges corresponding to this direction
template<typename T , int d>
void	permuteTensorVector (const gsVector< index_t, d > &perm, gsVector< index_t, d > &sz, gsMatrix< T > &coefs)
template<class T >
void	plotDeformation (const gsMultiPatch< T > &initDomain, const gsMultiPatch< T > &displacement, std::string const &fileName, gsParaviewCollection &collection, index_t step)
	plot a deformed isogeometric mesh and add it to a Paraview collection
template<class T >
void	plotDeformation (const gsMultiPatch< T > &initDomain, const std::vector< gsMultiPatch< T > > &displacements, std::string fileName, index_t numSamplingPoints=10000)
template<class T >
void	plotGeometry (const gsMultiPatch< T > &domain, std::string const &fileName, gsParaviewCollection &collection, index_t step)
	plot an isogeometric mesh and add to collection
template<class T >
void	plotGeometry (gsMultiPatch< T > const &domain, std::string fileName, index_t numSamples)
	Plots the mesh and the jacobian (if <numSamples> > 0) to Paraview.
template<typename T >
gsMonomialPoly< T >	PolyDerivWithSameDegree (const gsMonomialPoly< T > &poly)
template<typename T >
gsMonomialPoly< T >	PolyDivision (const gsMonomialPoly< T > &dividendPoly, const gsMonomialPoly< T > &divisorPoly, int num)
template<class T >
void	refineBasis_cavity (gsMultiBasis< T > &basis, int numRefine, int numRefineLocal, int dim, int numSep=0)
	Refine basis for the 2D lid-driven cavity problem.
template<class T >
void	refineBasis_profile2D (gsMultiBasis< T > &basis, int numRefine, int numRefineBlade, int numRefineLead)
	Refine basis for the 2D profile problem.
template<class T >
void	refineBasis_step (gsMultiBasis< T > &basis, int numRefine, int numRefineWalls, int numRefineCorner, int numRefineU, real_t addRefPart, int dim, real_t a, real_t b, real_t c=0.0)
	Refine basis for the backward-facing step problem.
template<int d, class T >
void	refineFirstKnotSpan (gsMultiBasis< T > &basis, int numRefine, int patch, int dir)
	Refine basis near wall (the first knot span).
template<int d, class T >
void	refineLastKnotSpan (gsMultiBasis< T > &basis, int numRefine, int patch, int dir)
	Refine basis near wall (the last knot span).
template<int d, class T >
void	refineLocal_step (gsMultiBasis< T > &basis, int numRefineWalls, int numRefineCorner)
	Refine basis for the backward-facing step problem near walls.
template<class T >
void	removeCol (gsMatrix< T > &mat, int const &removeEnds, int const &nPoints)
	remove columes 0, nPoints, 2*nPoints,.. of a given matrix
template<typename T >
void	RootIsolation (T leftBound, T rightBound, T eps, gsMatrix< T > &sturmSeq, gsMatrix< T > &rootIntervals)
	Algorithm for the isolation of the roots.
template<class T >
void	sampleGridGeometry (const gsMultiPatch< T > &mp, const index_t &numPatch, const index_t &numSamples, gsMatrix< T > &params, gsMatrix< T > &points)
	sampleGridGeometry: samples a grid point cloud from a given geometry
template<class T >
void	sampleScatteredGeometry (const gsMultiPatch< T > &mp, const index_t &numPatch, const index_t &numSamples, index_t &numBdr, gsMatrix< T > &params, gsMatrix< T > &points)
	sampleScatteredGeometry: samples a scattered point cloud from a given geometry
template<class T >
void	scaleFrom01 (T tMin, gsGeometry< T > &geo, T tMax, bool verbose)
	Scale the geometry geo from [0, 1]^D to [tMin, tMax]^D.
template<class T >
void	scaleFrom01 (T tMin, gsMatrix< T > &mT, T tMax, bool verbose)
	Scale the matrix mT entries from [0, 1] to [tMin, tMax].
template<class T >
T	scaleFrom01 (T tMin, T t, T tMax)
	Scale the inteval [0,1] to [tMin, tMax].
template<class T >
void	scaleGeo (const std::string &fin, const std::string &fout, T tMin, T tMax, bool verbose)
	Scale the geometry contained in file fin from [0, 1]^D to [tMin, tMax]^D and save it to fout.
template<class T >
void	scalePoints (const gsMatrix< T > &xyz, gsMatrix< T > &points)
	Function to scale the input points xyz in [0,1]^D and saves it to points.
template<class T >
void	scalePts (const std::string &fin, const std::string &fout, index_t uvIdIn, index_t uvIdOut, index_t xyzIdIn, index_t xyzIdOut, T tMin, T tMax, bool verbose)
	Scale the points contained in file fin from [0, 1]^D to [tMin, tMax]^D and save it to fout.
template<class T >
void	scaleTo01 (gsMatrix< T > &xyz, bool verbose)
	Scale the matrix xyz entries to [0, 1]^D.
template<class T >
void	scaleTo01 (real_t tMin, gsMatrix< T > &mT, real_t tMax)
	Scale the matrix mT entries to [0, 1].
template<class T >
T	scaleTo01 (T tMin, T t, T tMax)
	Scale the interval [tMin, tMax] to [0, 1].
template<typename T >
gsVector< T >	ShiftRight (const gsVector< T > &vec, int num)
int	sideOrientation (short_t s)
template<class T >
gsGeometry< T >::uPtr	simplifyCurve (gsGeometry< T > const &curve, index_t additionalPoints=0, index_t degree=0, index_t numSamples=1000)
	generates a simplified curve by fitting with the coarsest basis of the same degree; then reparametrizes it using the basis of the original curve; <additionalPoints> increases the number of degrees of freedom; <numSamples> is a number of sampling points for reparametrization
template<class T >
void	sortPointCloud (gsMatrix< T > &parameters, gsMatrix< T > &points, std::vector< index_t > &corners)
	sortPointCloud: sorts the point cloud into interior and boundary points. parameters and points ordered by : interior (parameters/points) and boundary (parameters/points) ordered anticlockwise south-east-north-west edges, plus the 4 corner domains stored in a vector [c1, c2, c3, c4].
template<typename T >
gsMatrix< T >	SortRoots (gsMatrix< T > &unsort)
template<class Vec >
Vec	stridesOf (const Vec &sz)
	Computes the of a vector.
void	stringReplace (std::string &str, const std::string &oldStr, const std::string &newStr)
	An univariate polynomial in monomial basis.
template<typename T >
gsMatrix< T >	SturmSequence (gsMonomialPoly< T > &poly)
	returns the sturm sequence in a gsMatrix
template<typename T , int d>
void	swapTensorDirection (int k1, int k2, gsVector< index_t, d > &sz, gsMatrix< T > &coefs)
template<short_t d, typename T >
void	tensorCombineTransferMatrices (gsSparseMatrix< T, RowMajor > B[d], gsSparseMatrix< T, RowMajor > &transfer)
	Combine component-wise transfer matrices into a transfer matrix for the tensor product basis.
template<typename VectIn , typename VectOut >
void	tensorStrides (const VectIn &sz, VectOut &strides)
	Helper to compute the strides of a d-tensor.
template<class T >
void	threeOnDiag (const gsSparseMatrix< T > &block, gsSparseMatrix< T > &result)
template<class MatrixType >
std::string	toDataArray (const MatrixType &matrix, std::map< std::string, std::string > attributes={{"",""}}, unsigned precision=5, const bool &export_base64=false)
	Formats the coordinates of points as a <DataArray> xml tag for ParaView export.
std::string	toDataArray (index_t num, std::map< std::string, std::string > attributes)
	Converts an integer to a 'DataArray' xml tag, which is returned as a string.
template<class E >
std::vector< std::string >	toVTK (const expr::_expr< E > &expr, gsExprEvaluator<> *evaltr, unsigned nPts=1000, unsigned precision=5, std::string label="SolutionField", const bool &export_base64=false)
	Evaluates one expression over all patches and returns all <DataArray> xml tags as a vector of strings, as no points are exported, no need to enforce 1:3D fields.
template<class T >
std::vector< std::string >	toVTK (const gsFunctionSet< T > &funSet, unsigned nPts=1000, unsigned precision=5, std::string label="", const bool &export_base64=false)
	Evaluates gsFunctionSet over all pieces( patches ) and returns all <DataArray> xml tags as a vector of strings.
template<typename T >
gsMatrix< T >	uniformPointGrid (const gsVector< T > &lower, const gsVector< T > &upper, int numPoints=1000)
template<class T >
gsVector< T >	vectorIntersect (gsVector< T > const &tangent1, gsVector< T > const &tangent2, gsMatrix< T > const &Vert1, gsMatrix< T > const &Vert2)
	intersection of two vectors
void	verboseLog (const std::string &message, const index_t &verbose)
	helper function to set optimizer options
gsMatrix< real_t >	vtkIDTransform (index_t nU, index_t nV)
	ID transformation between G+Smo and vtk control point IDs.
template<class T >
void	writeSingleBasisMesh (const gsBasis< T > &basis, std::string const &fn)
	Export a parametric mesh.
template<class T >
void	writeSingleBox (const gsMatrix< T > &box, std::string const &fn, T value)
	Export an element box.
template<class T >
void	writeSingleCompMesh (const gsBasis< T > &basis, const gsGeometry< T > &Geo, std::string const &fn, unsigned resolution=8)
	Export a computational mesh.
template<class T >
void	writeSingleControlNet (const gsGeometry< T > &Geo, std::string const &fn)
	Export a control net.
template<class T >
void	writeSingleCurve (gsFunction< T > const &func, gsMatrix< T > const &supp, std::string const &fn, unsigned npts)
	Export a curve geometry represented by func.
template<class T >
void	writeSingleGeometry (gsFunction< T > const &func, gsMatrix< T > const &supp, std::string const &fn, unsigned npts)
	Export a geometry represented by func.
template<class T >
void	writeSingleHBox (const gsHBox< 2, T > &box, std::string const &fn)
	Export a gsHBox.
template<class T >
void	writeSinglePatchField (const gsField< T > &field, int patchNr, std::string const &fn, unsigned npts)
	Write a file containing a solution field over a single geometry.
	~gsMpi ()
	calls MPI_Finalize

Detailed Description

The G+Smo namespace, containing all definitions for the library.

The generic geometry class represents a function defined as coefficients times basis function defined in a basis.

Note

This Source Code Form is subject to the terms of the Mozilla Public License, v. 2.0. If a copy of the MPL was not distributed with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

This is a generic implementation with minimal functionality. For common geometry types (B-splines, tensor-product B-splines, hierarchical splines) specific classes are implemented, which provide additional functionalities.

Typedef Documentation

gsPermutationMatrix

typedef gsEigen::PermutationMatrix<Dynamic,Dynamic,index_t> gsPermutationMatrix

reorderMapperTarget permutes the target indices of mapper according to permutation. If permutation does not contain all indices then the order of the remaining indices is preserved and the specified indices are appended to the end.

If an index is repeated in permutation the behaviour is unspecified and can change in the future because of implementation changes.

Parameters

mapper
permutation
permMatrix	: if specified, the pointed to matrix is the permutation matrix

Returns

the position of the first specified index

Enumeration Type Documentation

gsGridIteratorMode

enum gsGridIteratorMode

Specifies aliases describing the modes for gismo::gsGridIterator.

Enumerator
CUBE	Cube mode iterates over all lattice points inside a cube.
BDR	Boundary mode iterates over boundary lattice points only.
VERTEX	Vertex mode iterates over cube vertices only.
CWISE	Coordinate-wise mode iterates over a grid given by coordinate vectors.

gsNeedEnum

enum gsNeedEnum

Enumerator
NEED_VALUE	Value of the object.
NEED_DERIV	Gradient of the object.
NEED_JACOBIAN	Jacobian of the object.
NEED_MEASURE	The density of the measure pull back.
NEED_GRAD_TRANSFORM	Gradient transformation matrix.
NEED_DIV	Div operator.
NEED_CURL	Curl operator.
NEED_DERIV2	Second derivatives.
NEED_HESSIAN	Hessian matrix.
NEED_LAPLACIAN	Laplacian.
NEED_ACTIVE	Active function ids.
NEED_NORMAL	Normal vector of the object.
NEED_OUTER_NORMAL	Outward normal on the boundary.
NEED_2ND_FFORM	Second fundamental form.
SAME_ELEMENT	Enable optimizations based on the assumption that all evaluation points are in the same bezier domain.

gsStatus

enum struct gsStatus

strong

Enumerator
Success	Successful.
NotConverged	Step did not converge.
AssemblyError	Assembly problem in step.
SolverError	Assembly problem in step.
NotStarted	ALM has not started yet.
OtherError	Other error.

solver_status

enum solver_status

Specifies the status of the iterative solver.

Enumerator
interrupted	method successfully converged
working	solver was interrupted after exceeding the limit of iterations
bad_solution	solver working

ThinShellAssemblerStatus

enum class ThinShellAssemblerStatus

strong

Enumerator
Success	Assembly is successful.
AssemblyError	Assembly failed due to an error in the expression (e.g. overflow)
DimensionError	Assembly failed due to a dimension error.

Function Documentation

addBCs()

template<class T >

void addBCs	(	gsBoundaryConditions< T > &	bcInfo,
		std::vector< std::pair< int, boxSide > > &	bndIn,
		std::vector< std::pair< int, boxSide > > &	bndWall,
		gsFunctionExpr< T >	Uin,
		gsFunctionExpr< T >	Uwall
	)

Define boundary conditions for the corresponding boundary parts.

Template Parameters

T	real number type

Parameters

[out]	bcInfo	reference to the boundary conditions as gsBoundaryConditions
[in]	bndIn	reference to a container of patch sides corresponding to inflow boundaries
[in]	bndWall	reference to a container of patch sides corresponding to solid walls
[in]	Uin	the inflow velocity as gsFunctionExpr
[in]	Uwall	the wall velocity as gsFunctionExpr

BSplineBlock()

template<class T >

gsTensorBSpline< 3, T > BSplineBlock	(	int	deg,
		const T	llx,
		const T	lly,
		const T	llz,
		const T	a,
		const T	b,
		const T	c,
		int	numSep = 0
	)

Returns a B-spline parametrization of a 3D block of a given degree in all directions.

Template Parameters

T	real number type

Parameters

deg	polynomial degree of the B-spline parametrization
llx	x coordinate of a corner
lly	y coordinate of a corner
llz	z coordinate of a corner
a	width of the block
b	height of the block
c	depth of the block
numSep	number of \f C^0 \f separators in the parametrization (knots of multiplicity deg uniformly distributed in each parametric direction)

BSplineCavity2D()

template<class T >

gsMultiPatch< T > BSplineCavity2D	(	int	deg,
		const T	a,
		const T	b,
		const int	np = 1,
		int	numSep = 0
	)

Returns a B-spline multipatch domain for 2D problems of flow in a cavity.

Template Parameters

T	real number type

Parameters

deg	polynomial degree of the B-spline parametrization
a	width of the cavity
b	height of the cavity
np	number of patches in each direction
numSep	number of \f C^0 \f separators in each patch (knots of multiplicity deg uniformly distributed in each parametric direction)

BSplineCavity3D()

template<class T >

gsMultiPatch< T > BSplineCavity3D	(	int	deg,
		const T	a,
		const T	b,
		const T	c,
		int	numSep = 0
	)

Returns a B-spline multipatch domain for 3D problems of flow in a cavity.

Template Parameters

T	real number type

Parameters

deg	polynomial degree of the B-spline parametrization
a	width of the cavity
b	height of the cavity
c	depth of the cavity
numSep	number of \f C^0 \f separators in each patch (knots of multiplicity deg uniformly distributed in each parametric direction)

BSplineRectangle()

template<class T >

gsTensorBSpline< 2, T > BSplineRectangle	(	int	deg,
		const T	llx,
		const T	lly,
		const T	a,
		const T	b,
		int	numSep = 0
	)

Returns a B-spline parametrization of a rectangle of a given degree in both directions.

Template Parameters

T	real number type

Parameters

deg	polynomial degree of the B-spline parametrization
llx	x coordinate of the lower left corner
lly	y coordinate of the lower left corner
a	width of the rectangle
b	height of the rectangle
numSep	number of \f C^0 \f separators in the parametrization (knots of multiplicity deg uniformly distributed in each parametric direction)

BSplineStep2D()

template<class T >

gsMultiPatch< T > BSplineStep2D	(	int	deg,
		const T	a,
		const T	b,
		const T	a_in,
		T	h = 0,
		bool	periodic = false
	)

Returns a B-spline multipatch domain for 2D problems of flow over a backward facing step.

Template Parameters

T	real number type

Parameters

deg	polynomial degree of the B-spline parametrization
a	length of the domain behind the step
b	total height of the domain
a_in	length of the inflow part (before the step)
h	height of the step
periodic	periodic domain (if true, the bottom and top boundaries of the channel behind step are defined as interface)

BSplineStep3D()

template<class T >

gsMultiPatch< T > BSplineStep3D	(	int	deg,
		const T	a,
		const T	b,
		const T	c,
		const T	a_in,
		T	h = 0,
		bool	periodic = false
	)

Returns a B-spline multipatch domain for 3D problems of flow over a backward facing step.

Template Parameters

T	real number type

Parameters

deg	polynomial degree of the B-spline parametrization
a	length of the domain behind the step
b	total height of the domain
c	width of the domain
a_in	length of the inflow part (before the step)
h	height of the step
periodic	periodic domain (if true, the bottom and top boundaries of the channel behind step are defined as interface)

CalcIntervals()

template<typename T >

gsMatrix< T > CalcIntervals	(	const gsMonomialPoly< T > &	poly,
		T	eps,
		gsMatrix< T >	rootIntervals
	)

calculates the sturm sequence and the boundaries and calls then the function RootIsolation

combineMappers()

template<class T >

gsWeightMapper< T > * combineMappers	(	const std::vector< gsWeightMapper< T > * > &	mappers,
		std::vector< index_t > &	shifts,
		bool	needShifting = true
	)

combineMappers Given a set of mappers it creates a new mapper that combines all. It can be used to construct a global mapper for the cartesian product of spaces or to map both unknown and test space.

Parameters

mappers
shifts,is	a vector containing the shift of source indices for each space applied in the use of this mapper.
shift,if	true the target indices of each spaces are shifted (this is the default). This is the case of representing the cartesian product of spaces. If false the target indices are preserved; this is needed to share the same mapper for both unknown and test spaces.

conditionedAngle()

template<class T >

T conditionedAngle	(	gsVector3d< T >	vec1,
		gsVector3d< T >	vec2,
		gsVector3d< T >	normal
	)

Angle between two vector when viewing from a given normal vector (the angle can be more than pi)

constructCoefsForSlice()

template<short_t d, class T >

void constructCoefsForSlice	(	index_t	dir_fixed,
		const index_t	index,
		const gsMatrix< T > &	fullCoefs,
		const gsVector< index_t, d > &	sizes,
		gsMatrix< T > &	result
	)

Helper function for the slice function selects the row of coefficients from coefficients of geo that are suitable for the isoparametric slice in dir_fixed with par. Note that geo has to have already C^0 continuity at par in direction dir.

createVectorOfUniqueIndices()

template<class T >

gsMatrix< T > createVectorOfUniqueIndices

(

const gsMatrix< T > &

mat

)

Creates a one-column matrix (vector) of unique values from the input matrix (useful for creating a unique list of active basis functions in several quadrature points).

Parameters

[in]

mat

a const reference to the input matrix

criticalPointOfQuadratic() [1/3]

template<class T >

gsVector< T > criticalPointOfQuadratic	(	gsMatrix< T > &	A,
		gsMatrix< T > &	C,
		gsVector< T > &	d
	)

Find a critical point of a quadratic X^T A X subject to a linear constraint C X = d.

criticalPointOfQuadratic() [2/3]

template<class T >

gsMatrix< T > criticalPointOfQuadratic	(	gsMatrix< T > const &	A,
		gsMatrix< T > const &	b,
		gsMatrix< T > const &	C,
		gsMatrix< T > const &	d
	)

Find a critical point of a quadratic X^T A X + bX + c subject to a linear constraint C X = d.

criticalPointOfQuadratic() [3/3]

template<class T >

gsMatrix< T > criticalPointOfQuadratic	(	gsMatrix< T > const &	A,
		gsMatrix< T > const &	C,
		gsMatrix< T > const &	d
	)

Find a critical point of a quadratic X^T A X subject to a linear constraint C X = d.

crossNorm2Mat()

template<class T >

gsMatrix< T > crossNorm2Mat	(	gsMatrix< T > const &	mat1,
		gsMatrix< T > const &	mat2
	)

cross product of each pair of columes of two matrices and normalize each columes

defineBCs_cavity()

template<class T >

void defineBCs_cavity	(	gsBoundaryConditions< T > &	bcInfo,
		std::vector< std::pair< int, boxSide > > &	bndWall,
		int	dim,
		const int	np = 1,
		std::string	lidVel = "1"
	)

Define boundary conditions for the lid-driven cavity problem.

Template Parameters

T	real number type

Parameters

[out]	bcInfo	reference to the boundary conditions as gsBoundaryConditions
[out]	bndWall	reference to a container of patch sides corresponding to solid walls
	dim	space dimension
[in]	np	number of patches in each direction
[in]	lidVel	the x component of the lid velocity

defineBCs_cavity2D()

template<class T >

void defineBCs_cavity2D	(	gsBoundaryConditions< T > &	bcInfo,
		const int	np,
		std::vector< std::pair< int, boxSide > > &	bndWall,
		std::string	lidVel = "1"
	)

Define boundary conditions for the 2D lid-driven cavity problem.

Template Parameters

T	real number type

Parameters

[out]	bcInfo	reference to the boundary conditions as gsBoundaryConditions
[in]	np	number of patches in each direction
[out]	bndWall	reference to a container of patch sides corresponding to solid walls
[in]	lidVel	the x component of the lid velocity

defineBCs_cavity3D()

template<class T >

void defineBCs_cavity3D	(	gsBoundaryConditions< T > &	bcInfo,
		std::vector< std::pair< int, boxSide > > &	bndWall,
		std::string	lidVel = "1"
	)

Define boundary conditions for the 3D lid-driven cavity problem.

Template Parameters

T	real number type

Parameters

[out]	bcInfo	reference to the boundary conditions as gsBoundaryConditions
[out]	bndWall	reference to a container of patch sides corresponding to solid walls
[in]	lidVel	the x component of the lid velocity

defineBCs_profile2D()

template<class T >

void defineBCs_profile2D	(	gsBoundaryConditions< T > &	bcInfo,
		std::vector< std::pair< int, boxSide > > &	bndIn,
		std::vector< std::pair< int, boxSide > > &	bndOut,
		std::vector< std::pair< int, boxSide > > &	bndWall,
		T	inVelX,
		T	inVelY
	)

Define boundary conditions for the 2D blade profile problem.

Template Parameters

T	real number type

Parameters

[out]	bcInfo	reference to the boundary conditions as gsBoundaryConditions
[out]	bndIn	reference to a container of patch sides corresponding to inflow boundaries
[out]	bndOut	reference to a container of patch sides corresponding to outflow boundaries
[out]	bndWall	reference to a container of patch sides corresponding to solid walls
[in]	inVel	the x component of the inflow velocity as string
[in]	inVelX	x-coordinate of inflow velocity
[in]	inVelY	y-coordinate of inflow velocity

defineBCs_step()

template<class T >

void defineBCs_step	(	gsBoundaryConditions< T > &	bcInfo,
		std::vector< std::pair< int, boxSide > > &	bndIn,
		std::vector< std::pair< int, boxSide > > &	bndOut,
		std::vector< std::pair< int, boxSide > > &	bndWall,
		int	dim,
		bool	periodic = false,
		std::string	inVel = "default"
	)

Define boundary conditions for the backward-facing step problem.

Template Parameters

T	real number type

Parameters

[out]	bcInfo	reference to the boundary conditions as gsBoundaryConditions
[out]	bndIn	reference to a container of patch sides corresponding to inflow boundaries
[out]	bndOut	reference to a container of patch sides corresponding to outflow boundaries
[out]	bndWall	reference to a container of patch sides corresponding to solid walls
	dim	space dimension
[in]	periodic	periodic domain (true/false)
[in]	inVel	the x component of the inflow velocity as string

defineBCs_step2D()

template<class T >

void defineBCs_step2D	(	gsBoundaryConditions< T > &	bcInfo,
		std::vector< std::pair< int, boxSide > > &	bndIn,
		std::vector< std::pair< int, boxSide > > &	bndOut,
		std::vector< std::pair< int, boxSide > > &	bndWall,
		bool	periodic = false,
		std::string	inVel = "default"
	)

Define boundary conditions for the 2D backward-facing step problem.

Template Parameters

T	real number type

Parameters

[out]	bcInfo	reference to the boundary conditions as gsBoundaryConditions
[out]	bndIn	reference to a container of patch sides corresponding to inflow boundaries
[out]	bndOut	reference to a container of patch sides corresponding to outflow boundaries
[out]	bndWall	reference to a container of patch sides corresponding to solid walls
[in]	periodic	periodic domain (true/false)
[in]	inVel	the x component of the inflow velocity as string

defineBCs_step3D()

template<class T >

void defineBCs_step3D	(	gsBoundaryConditions< T > &	bcInfo,
		std::vector< std::pair< int, boxSide > > &	bndIn,
		std::vector< std::pair< int, boxSide > > &	bndOut,
		std::vector< std::pair< int, boxSide > > &	bndWall,
		bool	periodic = false,
		std::string	inVel = "default"
	)

Define boundary conditions for the 3D backward-facing step problem.

Template Parameters

T	real number type

Parameters

[out]	bcInfo	reference to the boundary conditions as gsBoundaryConditions
[out]	bndIn	reference to a container of patch sides corresponding to inflow boundaries
[out]	bndOut	reference to a container of patch sides corresponding to outflow boundaries
[out]	bndWall	reference to a container of patch sides corresponding to solid walls
[in]	periodic	periodic domain (true/false)
[in]	inVel	the x component of the inflow velocity as string

diagInvMatrix_into()

template<class T , int MatOrder>

void diagInvMatrix_into	(	const gsSparseMatrix< T, MatOrder > &	mat,
		gsSparseMatrix< T, MatOrder > &	diagInv,
		int	repeat,
		bool	lumping = false
	)

Fill a diagonal approximation of an inverse matrix.

Template Parameters

T	real number type
MatOrder	matrix storage order (RowMajor/ColMajor)

Parameters

[in]	mat	a const reference to the matrix of which the inverse is approximated
[out]	diagInv	a reference to the resulting inverse approximation
[in]	repeat	number of the diagonal block repetition (e.g. for velocity components)
[in]	lumping	use lumping to define the diagonal approximation

direction()

GISMO_DEPRECATED index_t direction ( index_t  s )

inline

Returns the parametric direction that corresponds to side s.

Parameters

[in]

s

integer corresponding to a boundary side

Returns

Integer which says which parameter has to be fixed in order to get the boundary.

Example:
In 2D, let the parameter domain be defined by \((u,v)\in [0,1]^2\). Since the side with index 3 corresponds to "south", i.e. to \( \{ (u,v):\ v = 0 \} \), calling parameter(3) will return 1, because v (i.e., parameter direction with index 1) is fixed/set to zero.
use boxSide struct instead of enumerated values

FindRootIntervals()

template<typename T >

gsMatrix< T > FindRootIntervals	(	gsMonomialPoly< T > &	poly,
		T	eps
	)

entry function needs a polynomial and a boundary eps as an input and returns a sorted matrix, where the intervals of the real roots are stored

genCircle() [1/2]

template<class T >

gsGeometry< T >::uPtr genCircle	(	gsBasis< T > &	basis,
		T	radius = 1.,
		T	x0 = 0.,
		T	y0 = 0.,
		T	angle0 = 0.,
		T	arcAngle = 2*EIGEN_PI
	)

@breif generates a uniformly parametrized circular arc with a given basis; generates a closed circle if <arcAngle> is 2pi

genCircle() [2/2]

template<class T >

gsGeometry< T >::uPtr genCircle	(	index_t	deg,
		index_t	num,
		T	radius = 1.,
		T	x0 = 0.,
		T	y0 = 0.,
		T	angle0 = 0.,
		T	arcAngle = 2*EIGEN_PI
	)

@breif generates a uniformly parametrized circular arc with a B-spline basis; generates a closed circle if <arcAngle> is 2pi

genLine()

template<class T >

gsGeometry< T >::uPtr genLine	(	index_t	deg,
		index_t	num,
		gsMatrix< T > const &	A,
		gsMatrix< T > const &	B,
		index_t	iA = 0,
		index_t	iB = 0
	)

@breif generates a uniformly parametrized straight line with a B-spline basis; end points are given as ROWS of matrices

genPatchInterpolation()

template<class T >

gsGeometry< T >::uPtr genPatchInterpolation	(	gsGeometry< T > const &	A,
		gsGeometry< T > const &	B,
		index_t	deg,
		index_t	num,
		bool	xiDir = false
	)

@grief generates a tensor product B-spline patch by interpolating between the two given B-spline patches of a dimension one lower; in 2D case, interpolates in eta/south-north direction by default; in 3D case, always interpolates in the third direction/front-back

getNnzVectorPerOuter()

template<class T , int MatOrder>

gsVector< index_t > getNnzVectorPerOuter

(

const gsSparseMatrix< T, MatOrder > &

mat

)

Get a vector of nonzero entries per outer index (row or column depending on the matrix storage order).

Template Parameters

T	real number type
MatOrder	matrix storage order (RowMajor/ColMajor)

Parameters

mat[in]

a const reference to the matrix

give()

template<typename S >

S give ( S &  x )

inline

Alias for std::move, to be used instead of std::move for backward c++98 compatibility and MSVC before 2015

Based on swapping and copy elision.

gsAllCloseAbsolute()

template<typename matrix_t1 , typename matrix_t2 >

bool gsAllCloseAbsolute ( const matrix_t1 &  a, const matrix_t2 &  b, const typename matrix_t1::Scalar &  tol  )

inline

tests if the difference between two matrices is bounded by tol in \( L^\infty \) norm

The tolerance is absolute, therefore independent of the matrix entries.

gsAllCloseRelAndAbsWithRef()

template<typename matrix_t1 , typename matrix_t2 >

bool gsAllCloseRelAndAbsWithRef ( const matrix_t1 &  a, const matrix_t2 &  b, const typename matrix_t1::Scalar &  tol, const typename matrix_t1::Scalar &  ref  )

inline

Tests whether the difference between two matrices is bounded by tol in \( L^\infty \) norm.

The tolerance is absolute below the reference, but relative for bigger numbers.

gsAllCloseRelativeToMax()

template<typename matrix_t1 , typename matrix_t2 >

bool gsAllCloseRelativeToMax ( const matrix_t1 &  a, const matrix_t2 &  b, const typename matrix_t1::Scalar &  tol  )

inline

tests if the difference between two matrices is bounded by tol in \( L^\infty \) norm

The tolerance is relative to maximum absolute values of the entries of the matrices.

gsBoehmRefine()

template<class KnotVectorType , class Mat , class ValIt >

void gsBoehmRefine	(	KnotVectorType &	knots,
		Mat &	coefs,
		int	p,
		ValIt	valBegin,
		ValIt	valEnd,
		bool	update_knots = true
	)

Performs knot refinement on "knots" and coefficients "coefs", by adding new knots vals NURBS book p.165 modified

gsBoehmSingle()

template<class T , class iter , class Mat >

void gsBoehmSingle	(	iter	knot,
		Mat &	coefs,
		int	p,
		T	val
	)

Performs knot insertion once on "knots" and coefficients "coefs". Iter points to the first affected knot (ie. knot is the result of findspan)

gsDeboor()

template<class T , class KnotVectorType >

void gsDeboor ( const gsMatrix< T > &  u, const KnotVectorType &  knots, int  deg, const gsMatrix< T > &  coefs, gsMatrix< T > &  result  )

inline

Executes deBoor's algorithm on the absissae (row vector) u, knot vector knots, degree deg and coefficients matrix coefs

gsDeboorDeriv()

template<class T , class KnotVectorType >

void gsDeboorDeriv ( const gsMatrix< T > &  u, const KnotVectorType &  knots, int  deg, const gsMatrix< T > &  coefs, gsMatrix< T > &  result  )

inline

Executes deBoor's algorithm on the absissae (row vector) u, for the derivative of the B-spline defined by knot vector knots, degree deg and coefficients matrix coefs

gsInterpolate()

template<class T >

gsBSpline< T > gsInterpolate	(	gsKnotVector< T > &	kv,
		const gsMatrix< T > &	preImage,
		const gsMatrix< T > &	image,
		const gsMatrix< T > &	preNormal,
		const gsMatrix< T > &	normal,
		const gsMatrix< T > &	preImageApp,
		const gsMatrix< T > &	imageApp,
		T const &	w_reg,
		T const &	w_app,
		gsMatrix< T > &	outPointResiduals,
		gsMatrix< T > &	outNormalResiduals
	)

Interpolation with standard smoothing. TODO1: make the output as gsGeometry, gsBSpline for now; also use gsBasis as input TODO2: there should a different weight for approximating normal: w_nor Size of input matrices: each colummn represents a geometry point.

gsInterpolateSurface()

template<class T >

gsTensorBSpline< 2, T >::Ptr gsInterpolateSurface	(	const gsMatrix< T > &	exactPoints,
		const gsMatrix< T > &	exactValues,
		const gsMatrix< T > &	appxPointsEdges,
		const gsMatrix< T > &	appxValuesEdges,
		const gsMatrix< T > &	appxPointsInt,
		const gsMatrix< T > &	appxValuesInt,
		const gsMatrix< T > &	appxNormalPoints,
		const gsMatrix< T > &	appxNormals,
		T	wEdge,
		T	wInt,
		T	wNormal,
		T	wReg,
		const gsKnotVector< T > &	kv1,
		const gsKnotVector< T > &	kv2,
		bool	force_normal
	)

Create a surface (as a tensor product B-spline) satisfying conditions: The evaluation of the surface at the columns of exactPoints are constrained to equal the columns of exactValues. The evaluation at the columns of appxPointsEdges (resp appxPointsInt) should be approximately equal to the columns of appxValuesEdges (resp appxValuesInt) with weighting wEdge (resp wInt). The normals to the surface, evaluated at the columns of appxNormalPoints, should be approximately equal to the columns of appxNormals with weighting wNormal. Finally you can add a weighting wReg for the regularity of the surface. The parameter force_normal is for a special case; typically it should be set to false.

gsIsfinite()

template<typename T >

bool gsIsfinite

(

T

a

)

Check if a flaoting point number is different than INF

See https://en.wikipedia.org/wiki/Floating_point#Special_values

gsIsnumber()

template<typename T >

bool gsIsnumber

(

T

a

)

Check if a floating point number is different than NAN (not a number)

See https://en.wikipedia.org/wiki/Floating_point#Special_values and https://en.wikipedia.org/wiki/NaN

gsPointGrid() [1/2]

template<class T , class CwiseContainer >

void gsPointGrid ( CwiseContainer const &  cwise, gsMatrix< T > &  res  )

inline

Construct a grid of points by coordinate vectors in the container cwise, use out argument res

gsPointGrid() [2/2]

template<class T >

gsMatrix< T > gsPointGrid ( gsMatrix< T > const &  ab, int  numPoints  )

inline

Returns an approximately uniformly spaced grid in every direction, with approximately numPoints total points.

Each column of the result correspond to a point.

gsTraceCurvePart()

template<class T >

void gsTraceCurvePart	(	std::pair< gsFunction< T > *, gsFunction< T > * > &	map,
		gsMatrix< T > const &	x,
		gsBSpline< T > *	bs,
		T	t0,
		T	t1,
		gsMatrix< T > &	result,
		const int	n_points = 50,
		const T	tolerance = 0.0001
	)

Parameters

map	is a planar map given by two component functions,
x	point in the planar domain, should correspond to pre image (via map) to the middle point of bs.
bs	is the curve you want to trace
t0	and...
t1	parametric values, they represent the interval you want to discretize
result	stores resulting points
n_points	is the number of points you want to trace per curve
tolerance

gsWriteGoTools() [1/3]

template<typename T >

void gsWriteGoTools	(	const gsGeometry< T > &	geom,
		const std::string &	fileName
	)

Writes geometry in GoTools (.g2) format to a file.

Parameters

geom	geometry
fileName	output file name

gsWriteGoTools() [2/3]

template<typename T >

void gsWriteGoTools	(	const gsGeometry< T > &	geom,
		std::ofstream &	out
	)

Writes geometry in GoTools (.g2) format to a file.

Parameters

geom	geometry
out	file stream

gsWriteGoTools() [3/3]

template<typename T >

void gsWriteGoTools	(	const gsMultiPatch< T > &	multiPatch,
		const std::string &	fileName
	)

Writes multi patch in GoTools (.g2) format to a file.

Parameters

multiPatch	multi patch
fileName	output file name

gsWriteGoToolsSpline()

template<short_t d, typename T >

void gsWriteGoToolsSpline	(	const gsTensorBSpline< d, T > &	bspl,
		std::ofstream &	out
	)

Writes bspline in GoTools (.g2) format to a file.

Parameters

bspl	tensor B-Spline
out	file stream

gsWriteOutput()

void gsWriteOutput ( std::ofstream &  file, const std::string  output, bool  fileOutput, bool  dispInTerminal  )

inline

Writes an output into the given file and optionally also into terminal.

Parameters

[out]	file	the output file
[in]	output	the output to write
[in]	fileOutput	write output in file (true/false)
[in]	dispInTerminal	display output in terminal (true/false)

gsWriteOutputLine()

void gsWriteOutputLine ( std::ofstream &  file, const std::string  line, bool  fileOutput, bool  dispInTerminal  )

inline

Writes an output line into the given file and optionally also into terminal.

Parameters

[out]	file	the output file
[in]	line	the line to write
[in]	fileOutput	write output in file (true/false)
[in]	dispInTerminal	display output in terminal (true/false)

gsWriteParaview() [1/24]

template<class T >

void gsWriteParaview	(	const gsField< T > &	field,
		std::string const &	fn,
		unsigned	npts = NS,
		bool	mesh = false,
		const std::string	pDelim = ""
	)

Write a file containing a solution field (as color on its geometry) to paraview file.

Write a file containing a solution field over a geometry.

Parameters

field	a field object
fn	filename where paraview file is written
npts	number of points used for sampling each patch
mesh	if true, the parameter mesh is plotted as well
pDelim	is the delimiter that is used to separate fn from the patch index

gsWriteParaview() [2/24]

template<class T >

void gsWriteParaview	(	const gsGeometrySlice< T > &	Geo,
		std::string const &	fn,
		unsigned	npts = NS
	)

Export a Geometry slice to paraview file.

Export a Geometry without scalar information.

Parameters

Geo	a gsGeometrySlice
fn	filename where paraview file is written
npts	number of points used for sampling each curve

gsWriteParaview() [3/24]

template<class T >

void gsWriteParaview	(	const gsHBox< 2, T > &	box,
		std::string const &	fn
	)

Export gsHBox to paraview files.

Writes a single gsHBox box to a file with name fn.

Parameters

box	a gsHBox
fn	filename where paraview file is written

gsWriteParaview() [4/24]

template<class T >

void gsWriteParaview	(	const gsHBoxContainer< 2, T > &	box,
		std::string const &	fn
	)

Export gsHBox to paraview files.

Writes a container of gsHBox , i.e. a \gsHBoxContainer boxes, to a file with name fn.

Parameters

basis	a basis object
fn	filename where paraview file is written
npts	number of points used for sampling each curve
mesh	if true, the parameter mesh is plotted as well

gsWriteParaview() [5/24]

template<class T >

void gsWriteParaview	(	const gsMatrix< T > &	box,
		const gsVector< T > &	values,
		std::string const &	fn
	)

Export an element box to paraview files.

Writes boxes to a file with name fn.

Parameters

box	an element represented by a bounding box
fn	filename where paraview file is written

gsWriteParaview() [6/24]

template<class T >

void gsWriteParaview	(	const gsMatrix< T > &	box,
		std::string const &	fn,
		T	value = 0.0
	)

Export an element box to paraview files.

Writes boxes to a file with name fn.

Parameters

box	an element represented by a bounding box
fn	filename where paraview file is written
value	to write

gsWriteParaview() [7/24]

template<class T >

void gsWriteParaview	(	const gsMultiPatch< T > &	Geo,
		std::string const &	fn,
		unsigned	npts = NS,
		bool	mesh = false,
		bool	ctrlNet = false,
		const std::string	pDelim = "_"
	)

Export a multipatch Geometry (without scalar information) to paraview file.

Parameters

Geo	a multipatch object
fn	filename where paraview file is written
npts	number of points used for sampling each patch
mesh	if true, the parameter mesh is plotted as well
ctrlNet	if true, the control net is plotted as well

gsWriteParaview() [8/24]

template<typename T >

void gsWriteParaview	(	const gsVolumeBlock< T > &	volBlock,
		std::string const &	fn,
		unsigned	npts = NS
	)

Export a volumeBlock.

Currently: output file shows boundary curves of this block.

Parameters

volBlock	pointer to the volume block
fn	filename where paraview file is written
npts	number of points used for sampling of a curve

gsWriteParaview() [9/24]

template<typename T >

void gsWriteParaview	(	const std::vector< gsMesh< T > > &	meshes,
		std::string const &	fn
	)

Export a vector of meshes, each mesh in its own file.

Parameters

meshes	vector of gsMesh objects
fn	filename

gsWriteParaview() [10/24]

template<class T >

void gsWriteParaview	(	gsBasis< T > const &	basis,
		std::string const &	fn,
		unsigned	npts = NS,
		bool	mesh = false
	)

Export Basis functions to paraview files.

Export Basis functions.

Parameters

basis	a basis object
fn	filename where paraview file is written
npts	number of points used for sampling each curve
mesh	if true, the parameter mesh is plotted as well

gsWriteParaview() [11/24]

template<class T >

void gsWriteParaview	(	gsBasis< T > const &	basis,
		std::vector< index_t > const &	indices,
		std::string const &	fn,
		unsigned	npts = NS,
		bool	mesh = false
	)

Export Basis functions to paraview files.

Export Basis functions.

Parameters

basis	a basis object
fn	filename where paraview file is written
npts	number of points used for sampling each curve
mesh	if true, the parameter mesh is plotted as well

gsWriteParaview() [12/24]

template<class T >

void gsWriteParaview	(	gsCurveLoop< T > const &	cloop,
		std::string const &	fn,
		unsigned	npts
	)

Visualizing a gsCurveLoop.

Parameters

cloop	the curve loop
fn	filename where paraview file is written
npts	number of points used for sampling each curve

gsWriteParaview() [13/24]

template<class T >

void gsWriteParaview	(	gsFunction< T > const &	func,
		gsMatrix< T > const &	supp,
		std::string const &	fn,
		unsigned	npts = NS,
		bool	graph = true
	)

Export a function plot to paraview file.

Export a function.

Parameters

func	a function object
supp	a matrix with two columns defining (lower and upper corner of) a box: this is the domain over which we shall evaluate the function, after sampling
fn	filename where paraview file is written
npts	number of points used for sampling the domain

gsWriteParaview() [14/24]

template<class T >

void gsWriteParaview	(	gsFunctionSet< T > const &	func,
		std::string const &	fn,
		unsigned	npts = NS
	)

Export a functionSet plot to paraview file.

Parameters

func	a functionSet object
fn	filename where paraview file is written
npts	number of points used for sampling the domain

gsWriteParaview() [15/24]

template<class T >

void gsWriteParaview	(	gsFunctionSet< T > const &	geo,
		gsFunctionSet< T > const &	func,
		std::string const &	fn,
		unsigned	npts = NS,
		const std::string	pDelim = ""
	)

Write a file containing a solution func (as color on its geometry geo), defined using functionsets, to paraview file.

Write a file containing a solution field over a geometry.

Parameters

func	a gsFunctionSet representing the function to be plotted
geo	a gsFunctionSet representing the geometry to be plotted
fn	filename where paraview file is written
npts	number of points used for sampling each patch

gsWriteParaview() [16/24]

template<class T >

void gsWriteParaview	(	gsFunctionSet< T > const &	geom,
		gsMappedBasis< 2, T > const &	mbasis,
		std::string const &	fn,
		unsigned	npts = NS,
		const bool	fullsupport = false,
		const std::vector< index_t >	indices = std::vector<index_t>()
	)

Writes a gsMappedBasis over a gsMappedSpline geometry.

Write a file containing a solution field over a geometry.

Parameters

	mspline	The mapped spline
	mbasis	The mapped basis
	fn	The filename
	fullsupport	Plot the basis over the whole domain
	indices	Basis functions to be plotted
[in]	npts	The number of sampling points

gsWriteParaview() [17/24]

template<class T >

void gsWriteParaview	(	gsMappedSpline< 2, T > const &	mspline,
		std::string const &	fn,
		unsigned	npts = NS
	)

Writes a gsMappedSpline geometry.

Write a file containing a solution field over a geometry.

Parameters

	mspline	The mapped spline
	fn	The filename
[in]	npts	The number of sampling points

gsWriteParaview() [18/24]

template<class T >

void gsWriteParaview	(	gsMesh< T > const &	sl,
		std::string const &	fn,
		bool	pvd
	)

Visualizing a mesh.

Number of vertices and number of faces

Coordinates of vertices

Which vertices belong to which faces

gsWriteParaview() [19/24]

template<class T >

void gsWriteParaview	(	gsMesh< T > const &	sl,
		std::string const &	fn,
		const gsMatrix< T > &	params
	)

Export a mesh to paraview file.

Parameters

sl	a gsMesh object
fn	filename where paraview file is written
pvd	if true, a .pvd file is generated (for compatibility)

Exports a parametrized mesh.

gsWriteParaview() [20/24]

template<class T >

void gsWriteParaview	(	gsMultiPatch< T > const &	mp,
		gsMultiBasis< T > const &	mb,
		std::string const &	fn,
		unsigned	npts = NS
	)

Plot the basis functions of a multi-basis.

Export basis functions.

Parameters

	mp	A multi-patch geometry to plot the basis on
	mb	The multi-basis
	fn	The file name
[in]	npts	The number of points

gsWriteParaview() [21/24]

template<class T >

void gsWriteParaview	(	gsMultiPatch< T > const &	patches,
		typename gsBoundaryConditions< T >::bcContainer const &	bcs,
		std::string const &	fn,
		unsigned	npts = NS,
		bool	ctrlNet = false
	)

Visualizing boundary conditions.

Parameters

pdomain	the planar domain
fn	filename where paraview file is written
npts	number of points used for sampling

gsWriteParaview() [22/24]

template<class T >

void gsWriteParaview	(	gsPlanarDomain< T > const &	pdomain,
		std::string const &	fn,
		unsigned	npts = NS
	)

Visualizing a gsPlanarDomain.

Parameters

pdomain	the planar domain
fn	filename where paraview file is written
npts	number of points used for sampling

gsWriteParaview() [23/24]

template<class T >

void gsWriteParaview	(	gsSolid< T > const &	sl,
		std::string const &	fn,
		unsigned	numPoints_for_eachCurve = 50,
		int	vol_Num = 0,
		T	edgeThick = 0.01,
		gsVector3d< T > const &	translate = gsVector3d<T>(0,0,0),
		int	color_convex = 0,
		int	color_nonconvex = 20,
		int	color_eloop = 10,
		std::vector< unsigned > const &	eloop = std::vector<unsigned>()
	)

Export tensor-structured point set with field data to Paraview file.

Parameters

points	matrix that contain 2D or 3D points, points are columns
data
np
fn	filename where paraview file is written

Depicting edge graph of each volume of one gsSolid with a segmenting loop

Parameters

sl	a gsMesh object
fn	filename where paraview file is written
numPoints_for_eachCurve	number of points used for sampling each curve
vol_Num	ID of face(s), that should be written
edgeThick	thickness of edges
translate	"translate" vector, toward the volume is translated
color_convex	Color, if face is convex and not eloop.
color_nonconvex	Color, if face is not convex
color_eloop	Color, if is in heSet and convex
eloop	a vector of ID numbers of vertices, often for representing a segmenting loop

Todo:

please document

Number of vertices and number of faces

Coordinates of vertices

Scalar field attached to each degenerate face on the "edge"

limit: for now, assign all scalars to 0

Which vertices belong to which faces

Space between edges

Number of vertices and number of faces

Coordinates of vertices

Scalar field attached to each degenerate face on the "edge"

limit: for now, assign all scalars to 0

Which vertices belong to which faces

Space between edges

gsWriteParaview() [24/24]

template<class T >

void gsWriteParaview	(	std::vector< gsGeometry< T > * > const &	Geo,
		std::string const &	fn,
		unsigned	npts = NS,
		bool	mesh = false,
		bool	ctrlNet = false,
		const std::string	pDelim = "_"
	)

Export a multipatch Geometry (without scalar information) to paraview file.

Export a multipatch Geometry without scalar information.

Parameters

Geo	a vector of the geometries to be plotted
fn	filename where paraview file is written
npts	number of points used for sampling each geometry
mesh	if true, the parameter mesh is plotted as well
ctrlNet	if true, the control net is plotted as well

gsWriteParaview_basisFnct()

template<class T >

void gsWriteParaview_basisFnct	(	int	i,
		gsBasis< T > const &	basis,
		std::string const &	fn,
		unsigned	npts = NS
	)

Export i-th Basis function to paraview file.

Export i-th Basis function.

Parameters

i	index of a basis function
basis	a basis object
fn	filename where paraview file is written
npts	number of points used for sampling each curve

gsWriteParaviewBdr()

template<class T >

void gsWriteParaviewBdr	(	gsMultiPatch< T > const &	patches,
		std::string const &	fn,
		unsigned	npts,
		bool	ctrlNet
	)

Writes the boundaries of a multipatch to paraview.

Parameters

	patches	The patches
	fn	The filename
[in]	npts	The number of sampling points per boundary
[in]	ctrlNet	Plot the control net

gsWriteParaviewBezier()

template<class T >

void gsWriteParaviewBezier	(	const gsMultiPatch< T > &	mPatch,
		std::string const &	filename,
		bool	ctrlNet = false
	)

Export a multipatch Geometry (without scalar information) to paraview file using Bezier elements.

Export a multipatch Geometry without scalar information using Bezier elements.

Parameters

Geo	a multipatch object
fn	filename where paraview file is written
singleFile	if true, the entire gsMultiPatch is exported in one .vtu file, to reduce clutter
ctrlNet	if true, the control net is plotted as well

gsWriteParaviewIfc()

template<class T >

void gsWriteParaviewIfc	(	gsMultiPatch< T > const &	patches,
		std::string const &	fn,
		unsigned	npts,
		bool	ctrlNet
	)

Writes the interfaces of a multipatch to paraview.

Parameters

	patches	The patches
	fn	The filename
[in]	npts	The number of sampling points per interface
[in]	ctrlNet	Plot the control net

gsWriteParaviewMultiPhysics()

template<class T >

void gsWriteParaviewMultiPhysics	(	std::map< std::string, const gsField< T > * >	fields,
		std::string const &	fn,
		unsigned	npts = NS,
		bool	mesh = false,
		bool	ctrlNet = false
	)

Write a file containing several fields defined on the same geometry to ONE paraview file.

Parameters

fields	a map of field pointers
fn	filename where paraview file is written
npts	number of points used for sampling each patch
mesh	if true, the parameter mesh is plotted as well

gsWriteParaviewMultiPhysicsSinglePatch()

template<class T >

void gsWriteParaviewMultiPhysicsSinglePatch	(	std::map< std::string, const gsField< T > * >	fields,
		const unsigned	patchNum,
		std::string const &	fn,
		unsigned	npts
	)

Extract and evaluate geometry and the fields for a single patch.

Parameters

fields	a map of field pointers
patchNum	a number of patch
fn	filename where paraview file is written
npts	number of points used for sampling each patch

gsWriteParaviewMultiPhysicsTimeStep()

template<class T >

void gsWriteParaviewMultiPhysicsTimeStep	(	std::map< std::string, const gsField< T > * >	fields,
		std::string const &	fn,
		gsParaviewCollection &	collection,
		int	time,
		unsigned	npts = NS
	)

Write a file containing several fields defined on the same geometry to ONE paraview file and adds it as a timestep to a Paraview collection.

Parameters

fields	a map of field pointers
fn	filename where paraview file is written
npts	number of points used for sampling each patch
mesh	if true, the parameter mesh is plotted as well

gsWriteParaviewMultiTPgrid()

template<class T >

void gsWriteParaviewMultiTPgrid	(	gsMatrix< T > const &	points,
		std::map< std::string, gsMatrix< T > > &	data,
		const gsVector< index_t > &	np,
		std::string const &	fn
	)

Utility function to actually write prepaired matrices with data into Paraview file.

Parameters

points	a matrix with space-points to plot
data	a map of matrices with field evaluations to plotfilename where paraview file is written
np	a vector containg the data range info
fn	filename where paraview file is written

gsWriteParaviewPoints() [1/4]

template<class T >

void gsWriteParaviewPoints	(	gsMatrix< T > const &	points,
		std::string const &	fn
	)

Export Point set to Paraview file.

Parameters

points	matrix that contain 2D or 3D points, points are columns
fn	filename where paraview file is written

gsWriteParaviewPoints() [2/4]

template<class T >

void gsWriteParaviewPoints	(	gsMatrix< T > const &	X,
		gsMatrix< T > const &	Y,
		gsMatrix< T > const &	Z,
		gsMatrix< T > const &	V,
		std::string const &	fn
	)

Export 3D Point set to Paraview file.

Parameters

X	1 times n matrix of values for x direction
Y	1 times n matrix of values for y direction
Z	1 times n matrix of values for z-direction
V	1 times n matrix of values for values
fn	filename where paraview file is written

gsWriteParaviewPoints() [3/4]

template<class T >

void gsWriteParaviewPoints	(	gsMatrix< T > const &	X,
		gsMatrix< T > const &	Y,
		gsMatrix< T > const &	Z,
		std::string const &	fn
	)

Export 3D Point set to Paraview file.

Parameters

X	1 times n matrix of values for x direction
Y	1 times n matrix of values for y direction
Z	1 times n matrix of values for z-direction
fn	filename where paraview file is written

gsWriteParaviewPoints() [4/4]

template<class T >

void gsWriteParaviewPoints	(	gsMatrix< T > const &	X,
		gsMatrix< T > const &	Y,
		std::string const &	fn
	)

Export 2D Point set to Paraview file.

Export Point set to Paraview.

Parameters

X	1 times n matrix of values for x direction
Y	1 times n matrix of values for y direction
fn	filename where paraview file is written

gsWriteParaviewTrimmedCurve()

template<typename T >

void gsWriteParaviewTrimmedCurve	(	const gsTrimSurface< T > &	surf,
		const unsigned	idLoop,
		const unsigned	idCurve,
		const std::string	fn,
		unsigned	npts = NS
	)

Export a boundary/hole curve in trimmed surface.

Parameters

surf	trimmed surface
idLoop	curve loop number of a curve (0 - boundary, > 0 - hole)
idCurve	curve number in a curve loop
fn	filename (output paraview file)
npts	number of points used for sampling a curve

HornerEval()

template<typename T >

gsVector< T > HornerEval	(	gsMatrix< T > &	mat,
		T	num
	)

in the input gsMatrix the polynomials are stored row by row with their coefficiens HornerEval returns a vector where the matrix is evaluated at position num

isfinite()

template<typename Derived >

bool isfinite ( const gsEigen::MatrixBase< Derived > &  x )

inline

Check if all the entires if the matrix x are not INF (infinite)

See https://en.wikipedia.org/wiki/Floating_point#Special_values

isnumber()

template<typename Derived >

bool() isnumber ( const gsEigen::MatrixBase< Derived > &  x )

inline

Check if all the entires if the matrix x are not NAN (not a number)

See https://en.wikipedia.org/wiki/Floating_point#Special_values and https://en.wikipedia.org/wiki/NaN

makeCollection()

void makeCollection ( std::string const &  fn, std::string const &  ext, int  n = 0  )

inline

Fast creation of a collection using base filename fn, extension ext. The collection will contain the files fn_0.ext, fn_1.ext,...,fn_{n-1}.ext In the special case of n=0, the collection is just fn.pvd and contains only the file fn.ext

makeHierarchicalMesh()

template<typename T >

bool makeHierarchicalMesh	(	const gsBasis< T > &	basis,
		std::vector< gsMesh< T > > &	meshes,
		int	n = 0
	)

Constructs a series of meshes, each mesh presents on level in hierarchical basis.

Parameters

basis	hierarchocal tensor basis
meshes	we return meshes via reference to std::vector
n	how many vertices is used in presentation of one element

Returns

success of the function

makeMesh()

template<class T >

void makeMesh	(	const gsBasis< T > &	basis,
		gsMesh< T > &	mesh,
		int	n = 0
	)

Returns the computational mesh of basis.

Parameters

[in]	basis
	mesh
[in]	n	number of samples per element side

operator!=()

template<class T >

bool operator!=	(	gsVertex< T > const &	lhs,
		gsVertex< T > const &	rhs
	)

Compares to gsVertex

Parameters

lhs	LHS gsVertex
rhs	RHS gsVertex

Returns

true if LHS != RHS, false if LHS == RHS

operator<<()

std::ostream & operator<< ( std::ostream &  os, const boundaryInterface &  i  )

inline

Print (as string) an interface.

TODO: the information could be stored in a single vector of signed integers: the sign gives the orientation the problem is that it is necessary to shift the indices as there is no -0

operator==()

template<class T >

bool operator==	(	gsVertex< T > const &	lhs,
		gsVertex< T > const &	rhs
	)

Compare LHS == RHS

Template Parameters

T

Parameters

lhs
rhs

Returns

operator>()

template<class T >

bool operator>	(	gsVertex< T > const &	lhs,
		gsVertex< T > const &	rhs
	)

Compares LHS.x < RHS.X Compares first x, if equal y, if equal z.

Template Parameters

T

Parameters

lhs
rhs

Returns

true if lhs.x < rhs.x; lhs.x==rhs.x and lhs.y < rhs.y; lhs.x==rhs.x, lhs.y==rhs.y and lhs.z < rhs.z; false if lhs.x >= rhs.x and lhs.y >= rhs.y and lhs.z >= rhs.y

optQuadratic()

template<class T >

gsMatrix< T > optQuadratic	(	gsMatrix< T > const &	A1,
		gsMatrix< T > const &	b1,
		T const &	w1,
		gsMatrix< T > const &	A2,
		gsMatrix< T > const &	b2,
		T const &	w2,
		gsMatrix< T > const &	C,
		gsMatrix< T > const &	d,
		T const &	w3,
		gsMatrix< T > const &	Q
	)

Find X which solves: min w_1 (A_1 X-b_1)^T (A_1 X-b_1) + w_2 (A_2 X-b_2)^T (A_2 X-b_2) + w3 X'QX, s.t. CX=d

parameter()

GISMO_DEPRECATED bool parameter ( int  s )

inline

Returns the parameter value (false=0=start, true=1=end) that corresponds to side s.

Parameters

[in]

s

integer corresponding to a boundary side

Returns

false, if side s is defined by setting the corresponding parameter to 0, and
true, if it is defined by setting the corresponding parameter to 1.

Example:
In 2D, let the parameter domain be defined by \((u,v)\in [0,1]^2\). Since the side with index 3 corresponds to "south", i.e. to \( \{ (u,v):\ v = 0 \} \), calling parameter(3) will return 0=false.

use boxSide struct instead of enumerated values

plotDeformation()

template<class T >

void plotDeformation	(	const gsMultiPatch< T > &	initDomain,
		const std::vector< gsMultiPatch< T > > &	displacements,
		std::string	fileName,
		index_t	numSamplingPoints = 10000
	)

use all saved displacement fields to plot the all intermediate deformed configurations of the computational domain; always plots the deformed isoparametric mesh; plots the Jacobian determinant of the deformed configuration if numSamplingPoints > 0

PolyDerivWithSameDegree()

template<typename T >

gsMonomialPoly< T > PolyDerivWithSameDegree

(

const gsMonomialPoly< T > &

poly

)

Returns the derivation of the input polynomial including a leading 0, s.t. the output polynomial is of the same degree as the input polynomial

PolyDivision()

template<typename T >

gsMonomialPoly< T > PolyDivision	(	const gsMonomialPoly< T > &	dividendPoly,
		const gsMonomialPoly< T > &	divisorPoly,
		int	num
	)

Polynomial Division the input num dedicates if the quotient or the remainder is returned num = 1 returns the qoutient num = 2 returns the remainder

refineBasis_cavity()

template<class T >

void refineBasis_cavity	(	gsMultiBasis< T > &	basis,
		int	numRefine,
		int	numRefineLocal,
		int	dim,
		int	numSep = 0
	)

Refine basis for the 2D lid-driven cavity problem.

Template Parameters

T	real number type

Parameters

basis	reference to the basis to be refined
numRefine	number of uniform refinements
numRefineLocal	number of near-wall refinements
dim	space dimension
numSep	number of \f C^0 \f separators in each patch (knots of multiplicity deg uniformly distributed in each parametric direction)

refineBasis_profile2D()

template<class T >

void refineBasis_profile2D	(	gsMultiBasis< T > &	basis,
		int	numRefine,
		int	numRefineBlade,
		int	numRefineLead
	)

Refine basis for the 2D profile problem.

Template Parameters

T	real number type

Parameters

[in,out]	basis	reference to the basis to be refined
[in]	numRefine	number of uniform refinements
[in]	numRefineBlade	number of refinements near the blade
[in]	numRefineLead	number of refinements near the beginning of the blade

refineBasis_step()

template<class T >

void refineBasis_step	(	gsMultiBasis< T > &	basis,
		int	numRefine,
		int	numRefineWalls,
		int	numRefineCorner,
		int	numRefineU,
		real_t	addRefPart,
		int	dim,
		real_t	a,
		real_t	b,
		real_t	c = 0.0
	)

Refine basis for the backward-facing step problem.

Template Parameters

T	real number type

Parameters

basis	reference to the basis to be refined
numRefine	number of uniform refinements
numRefineWalls	number of refinements near top and bottom walls
numRefineCorner	number of refinements near the step corner
numRefineU	number of uniform refinements of patches 0 and 1 in u direction
addRefPart	a value of the u parameter for additional refinement behind the step
dim	space dimension
a	length of the domain behind the step
b	total height of the domain
c	width of the domain (3D case)

refineFirstKnotSpan()

template<int d, class T >

void refineFirstKnotSpan	(	gsMultiBasis< T > &	basis,
		int	numRefine,
		int	patch,
		int	dir
	)

Refine basis near wall (the first knot span).

Template Parameters

T	real number type
d	space dimension

Parameters

basis	reference to the basis to be refined
numRefine	number of recursive refinements
patch	patch number
dir	direction in which the basis will be refined

refineLastKnotSpan()

template<int d, class T >

void refineLastKnotSpan	(	gsMultiBasis< T > &	basis,
		int	numRefine,
		int	patch,
		int	dir
	)

Refine basis near wall (the last knot span).

Template Parameters

T	real number type
d	space dimension

Parameters

basis	reference to the basis to be refined
numRefine	number of recursive refinements
patch	patch number
dir	direction in which the basis will be refined

refineLocal_step()

template<int d, class T >

void refineLocal_step	(	gsMultiBasis< T > &	basis,
		int	numRefineWalls,
		int	numRefineCorner
	)

Refine basis for the backward-facing step problem near walls.

Template Parameters

T	real number type
d	space dimension

Parameters

basis	reference to the basis to be refined
numRefineWalls	number of refinements near top and bottom walls
numRefineCorner	number of refinements near the step corner

sampleGridGeometry()

template<class T >

void sampleGridGeometry	(	const gsMultiPatch< T > &	mp,
		const index_t &	numPatch,
		const index_t &	numSamples,
		gsMatrix< T > &	params,
		gsMatrix< T > &	points
	)

sampleGridGeometry: samples a grid point cloud from a given geometry

Parameters

mp	: input multi-patch
numPatch	: patch number
numSamples	: number of samples in each direction
params	: output parameters
points	: output points

sampleScatteredGeometry()

template<class T >

void sampleScatteredGeometry	(	const gsMultiPatch< T > &	mp,
		const index_t &	numPatch,
		const index_t &	numSamples,
		index_t &	numBdr,
		gsMatrix< T > &	params,
		gsMatrix< T > &	points
	)

sampleScatteredGeometry: samples a scattered point cloud from a given geometry

Parameters

mp	: input multi-patch
numPatch	: patch number
numSamples	: number of interior samples
numBdr	: number of boundary samples
params	: output parameters
points	: output points

ShiftRight()

template<typename T >

gsVector< T > ShiftRight	(	const gsVector< T > &	vec,
		int	num
	)

returns a gsVector where the elements are shifted "num"-spaces to the right the left side is filled with zeros

sideOrientation()

int sideOrientation ( short_t  s )

inline

Computes the orientation of the boundary side s with respect to the interior of the parameter domain. The result is either +1 (counter-clockwise) or -1 (clock-wise).

Parameters

s	integer corresponding to a boundary side

sortPointCloud()

template<class T >

void sortPointCloud	(	gsMatrix< T > &	parameters,
		gsMatrix< T > &	points,
		std::vector< index_t > &	corners
	)

sortPointCloud: sorts the point cloud into interior and boundary points. parameters and points ordered by : interior (parameters/points) and boundary (parameters/points) ordered anticlockwise south-east-north-west edges, plus the 4 corner domains stored in a vector [c1, c2, c3, c4].

Parameters

parameters	: matrix of parameters
points	: matrix of points
corners	: vector of corner domains indeces [c1, c2, c3, c4]

SortRoots()

template<typename T >

gsMatrix< T > SortRoots

(

gsMatrix< T > &

unsort

)

sorts the Matrix, where the roots are stored by their left bound and consolidates equal intervals

threeOnDiag()

template<class T >

void threeOnDiag	(	const gsSparseMatrix< T > &	block,
		gsSparseMatrix< T > &	result
	)

Constructs a gsSparseMatrix<T> with with block block repeated three times along the diagonal and saves it to result. TODO: Make more general.

toDataArray() [1/2]

template<class MatrixType >

std::string toDataArray	(	const MatrixType &	matrix,
		std::map< std::string, std::string >	attributes = {{"",""}},
		unsigned	precision = 5,
		const bool &	export_base64 = false
	)

Formats the coordinates of points as a <DataArray> xml tag for ParaView export.

Template Parameters

T	Arithmetic type

Parameters

points	A gsMatrix<T> with the coordinates of the points, stored column-wise. Its size is (numDims, numPoints)
label	A string with the label of the data
precision	Number of decimal points in xml output
export_base64	(defaults true) export as base63 encoded string - ignore precision

Returns

The raw xml string

toDataArray() [2/2]

std::string toDataArray	(	index_t	num,
		std::map< std::string, std::string >	attributes
	)

Converts an integer to a 'DataArray' xml tag, which is returned as a string.

Parameters

num	The integer to be formatted
attributes	Optional, map of strings, with attribute name mapping to attribute value.

Returns

Parameters

num	The integer to be formatted
attributes	Optional, map of strings, with attribute name mapping to attribute value.
ind	Optional, indentation level for the resulting string.

Returns

toVTK() [1/2]

template<class E >

std::vector< std::string > toVTK	(	const expr::_expr< E > &	expr,
		gsExprEvaluator<> *	evaltr,
		unsigned	nPts = 1000,
		unsigned	precision = 5,
		std::string	label = "SolutionField",
		const bool &	export_base64 = false
	)

Evaluates one expression over all patches and returns all <DataArray> xml tags as a vector of strings, as no points are exported, no need to enforce 1:3D fields.

Template Parameters

T

Parameters

expr	Expression to be evaluated
label	The label with which the expression will appear in Paraview
export_base64	export as base64 encoded string

Returns

Vector of strings of all <DataArrays>

toVTK() [2/2]

template<class T >

std::vector< std::string > toVTK	(	const gsFunctionSet< T > &	funSet,
		unsigned	nPts = 1000,
		unsigned	precision = 5,
		std::string	label = "",
		const bool &	export_base64 = false
	)

Evaluates gsFunctionSet over all pieces( patches ) and returns all <DataArray> xml tags as a vector of strings.

Template Parameters

T

Parameters

funSet	gsFunctionSet to be evaluated
nPts	Number of evaluation points, per patch.
precision	Number of decimal points in xml output
label
export_base64	export as base64 encoded string

Returns

Vector of strings of all <DataArrays>

uniformPointGrid()

template<typename T >

gsMatrix< T > uniformPointGrid	(	const gsVector< T > &	lower,
		const gsVector< T > &	upper,
		int	numPoints = 1000
	)

Approximately uniformly spaced grid in every direction, with approximately numPoints total points

verboseLog()

void verboseLog ( const std::string &  message, const index_t &  verbose  )

inline

helper function to set optimizer options

helper function to verbose log

vtkIDTransform()

gsMatrix< real_t > vtkIDTransform	(	index_t	nU,
		index_t	nV
	)

ID transformation between G+Smo and vtk control point IDs.

Parameters

nU	Number of control points in u parametric direction
nV	Number of control points in u parametric direction

Returns

writeSingleBox()

template<class T >

void writeSingleBox	(	const gsMatrix< T > &	box,
		std::string const &	fn,
		T	value
	)

Export an element box.

Writes a single gsHBox box to a file with name fn.

writeSingleHBox()

template<class T >

void writeSingleHBox	(	const gsHBox< 2, T > &	box,
		std::string const &	fn
	)

Export a gsHBox.

Writes a single gsHBox box to a file with name fn.