gsGeoUtils.hpp File Reference

Provides isogeometric meshing and modelling routines. More...

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

Functions
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<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	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 >
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 >
gsVector< unsigned >	distributePoints (const gsGeometry< T > &geo, unsigned numPoints)
	distributes sampling points according to the length of the patch in each parametric direction
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 >
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	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	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 (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	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	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<class T >
T	normL2 (gsMultiPatch< T > const &domain, gsMultiPatch< T > const &solution)
	@ Compute norm of the isogeometric solution
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<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	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	plotGeometry (gsMultiPatch< T > const &domain, std::string fileName, index_t numSamples)
	Plots the mesh and the jacobian (if <numSamples> > 0) to Paraview.
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 >
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

Detailed Description

Provides isogeometric meshing and modelling routines.

This file is part of the G+Smo library.

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/.

Author(s): A.Shamanskiy (2016 - ...., TU Kaiserslautern)