Detailed Description

template<class T>
class gismo::gsTrimSurface< T >

Class for a trim surface.

Public Member Functions
gsCurveLoop< T > &	boundaryLoop ()
	Get a boundary curve loop.

const gsCurveLoop< T > &	boundaryLoop () const
	Look at (non-const) boundaryLoop.

gsTrimSurface< T > *	clone () const
	Clone function. Used to make a copy of the (derived) geometry.

gsVector3d< T >	cornerNormal (int const &sourceID) const
	Compute the surface normal at a corner.

void	cuttingAngles (int const &sourceID, int const &targetID, T angle, T angle1, T *angle2, bool const &isCCWviewFromNormal=true) const
	Compute angle discrepancy between the angles defined by the edge source-target with the sides of the angle wrt source

gsBSpline< T >	cuttingCurve (int const &sourceID, int const &targetID) const
	Define a spline curve connecting source-target

gsMatrix< T >	derivatives (int sourceID) const

gsMatrix< T >	evalCurve (int loopNumber, int curveNumber, const gsMatrix< T > &u) const
	Look at evalCurve_into.

void	evalCurve_into (int loopNumber, int curveNumber, const gsMatrix< T > &u, gsMatrix< T > &result) const

gsMatrix< T >	evalSurface (const gsMatrix< T > &u) const

void	evalSurface_into (const gsMatrix< T > &u, gsMatrix< T > &result) const

gsCurve< T > &	getCurve (int loopNumber, int curveNumber) const
	Returns curveNumber-th curve in loopNumber-th loop.

T	getLengthOfCurve (const int loopNumber, const int curveNumber, const T eps=1e-6, const int nmbSegments=50) const
	Computes length of curveNumber-th curve in loopNumber-th loop.

void	getPhysicalyUniformCurveParameters (const int loopNumber, const int curveNumber, const int nmbParams, gsVector< T > &parameters, const T eps=1e-6)

	gsTrimSurface ()
	Default empty constructor.

	gsTrimSurface (typename gsSurface< T >::Ptr g, gsPlanarDomain< T > *d)
	Constructor by a shared pointer.

	gsTrimSurface (gsMatrix< T > const &corner, int patchDeg1, int patchDeg2, int curveDeg)

T	nearestPoint (int loopNumber, int curveNumber, int nTrialPoints, int nIterations, const gsMatrix< T > &spacePoint)
	find the parameter of the nearest point on a curve to a given point in space

std::ostream &	print (std::ostream &os) const
	Prints the object as a string.

gsMatrix< T >	sampleNormal (int loopNumber, int curveNumber, size_t npoints) const
	sample standard unit normals along a trimming curve

gsMatrix< T >	splitCurve (size_t loopId, size_t curveId, T lengthRatio=.5)

gsVector< T >	TangentCoefs_bisect (int const &sourceID) const
	Compute the (scale of) tangent of the curve emanateing from a vertex in the parameter whose image bisects the corresponding angle.

gsVector< T >	TangentCoefs_bisect (int const &sourceID, gsVector3d< T > normal) const

gsMatrix< T >	TangentCoefs_next (int const &sourceID) const
	Return the coefficients of the representation of the unit tangent of the edge ENAMATING from vertex sourceID in terms of the standard basis of the tangent space.

gsMatrix< T >	TangentCoefs_prev (int const &sourceID) const
	Return the coefficients of the representation of the unit tangent of the edge COMING to vertex sourceID in terms of the standard basis of the tangent space.

memory::unique_ptr< gsMesh< T > >	toMesh (int npoints=50) const
	Return a triangulation of the trimmed surface.

gsMatrix< T >	trimCurTangents (int loopN, int curveN, size_t npoints) const
	Return the tangent vectors of the trimming curve curveNumber in trimming loop loopNumber.

gsMatrix< T >	unitNormal (gsMatrix< T > point) const
	Compute the unit normal vector of the trimmed surface at a point in the parameter domain.

gsMatrix< T >	UnitTangentCoefs_next (int const &sourceID, gsMatrix< T > const &corJacobian) const
	Return the coefficients of the representation of the unit tangent of the edge ENAMATING from vertex sourceID in terms of the standard basis of the tangent space.

gsMatrix< T >	UnitTangentCoefs_prev (int const &sourceID, gsMatrix< T > const &corJacobian) const
	Return the coefficients of the representation of the unit tangent of the edge COMING to vertex sourceID in terms of the standard basis of the tangent space.

Private Member Functions
T	arcLength (const gsCurve< T > &curve, const T a, const T b, const int quadPoints=4) const

void	evalCurve_into (const gsCurve< T > &curve, const gsMatrix< T > &u, gsMatrix< T > &result) const

T	findParameter (const gsCurve< T > &curve, const T arc, T curArc, T lowParam, T uppParam, const T eps)

void	fromArcsToParams (const int loopNumber, const int curveNumber, const gsVector< T > &arcs, gsVector< T > &parameters, const T eps)

T	getLengthOfCurve (const gsCurve< T > &curve, gsMatrix< T > &params, bool linear=false) const

Constructor & Destructor Documentation

gsTrimSurface	(	gsMatrix< T > const &	corner,
		int	patchDeg1,
		int	patchDeg2,
		int	curveDeg
	)

Construct a trivial trimmed surface from 4 vertices Inputs: corner (the 4 corner vertices), patchDeg1 and patchDeg2 (spline degree in dim 1 and 2), curveDeg (spline degree of all trimming curves)

Member Function Documentation

T arcLength	(	const gsCurve< T > &	curve,
		const T	a,
		const T	b,
		const int	quadPoints = `4`
	)		const

private

Computes the arc length between surface( curve(a) ) and surface( curve(b) ).

Integral is evaluated with the number of quadPoints.

gsMatrix< T > derivatives ( int sourceID ) const

Compute the partial derivatives of the surface parametrization at a corner point of a trimmed patch specified by the index of the trimming curve sourceID emanating from the corner point

void evalCurve_into	(	int	loopNumber,
		int	curveNumber,
		const gsMatrix< T > &	u,
		gsMatrix< T > &	result
	)		const

inline

Evaluates curveNumber-th curve from loopNumber-th loop.

Curve is evaluated at parameter u. Parameter u is in curve domain and resulting points are in physical space ( result = surf(curve(u)) ).

void evalCurve_into	(	const gsCurve< T > &	curve,
		const gsMatrix< T > &	u,
		gsMatrix< T > &	result
	)		const

private

Evaluates curve (in physical space) at parameter u.

result = surface( curve(u) )

gsMatrix<T> evalSurface ( const gsMatrix< T > & u ) const

inline

Look at evalSurface_into

Parameters

u	parameters

Returns: points on surface at parameter u

void evalSurface_into	(	const gsMatrix< T > &	u,
		gsMatrix< T > &	result
	)		const

inline

Evaluates surface.

Note that this is NOT trimmed surface. (You can evaluate at parameter which is trimmed away.)

Parameters

u	parameters
result	points on surface at parameter u

T findParameter	(	const gsCurve< T > &	curve,
		const T	arc,
		T	curArc,
		T	lowParam,
		T	uppParam,
		const T	eps
	)

private

Let be C( t ) = surface( curve( t ) ). Function finds a parameter t0 of the curve C, where C( t0 ) lies arc away from the C( 0 ).

Let P1 lies curArc away from C( 0 ) on the curve C. Let P2 lies less than arc away from C( 0 ) on the curve.

uppParam corresponds to P1 lowParam corresponts to P2

void fromArcsToParams	(	const int	loopNumber,
		const int	curveNumber,
		const gsVector< T > &	arcs,
		gsVector< T > &	parameters,
		const T	eps
	)

private

Let curve be a curveNumber-th curve in loopNumber-th loop. Let be C( t ) = surface( curve( t ) ), t in [parameter domain] Function returns parameters t_i such that C( t_i ) = P_i and L( C( 0 ), C( t_i ) ) = arcs( i ) where L( x, y ) is an arc length of a curve C between x and y.

We return t_i in a vector parameters.

T getLengthOfCurve	(	const gsCurve< T > &	curve,
		gsMatrix< T > &	params,
		bool	linear = `false`
	)		const

private

Computes the length of curve: surface( curve(t) ).

Parameters

curve
params	precomputed parameters (we evaluate length of the curve from the begining till the end of params values)
linear	true - we do linear approximation false - we compute integral of derivative surface( curve(t) )'

void getPhysicalyUniformCurveParameters	(	const int	loopNumber,
		const int	curveNumber,
		const int	nmbParams,
		gsVector< T > &	parameters,
		const T	eps = `1e-6`
	)

inline

Returns parameters t_i, i = 1, 2, ..., nmbParams, such that arc between surface( curve (t_i) ) and surface( curve (t_{i + 1}) ) is equal for all i.

With other words: Parameters are maped into points that are uniform in physical space.

curve is the curveNumber-th curve in loopNumber-th loop.

gsMatrix<T> splitCurve	(	size_t	loopId,
		size_t	curveId,
		T	lengthRatio = `.5`
	)

inline

split the curveId^th curve in the loopId^th loop of the planar domain into two curves

Parameters

loopId	specifies the loop
curveId	specifies the curve in the loop
lengthRatio	the ratio of the lengths of the first new curve and of the original curve

gsVector< T > TangentCoefs_bisect	(	int const &	sourceID,
		gsVector3d< T >	normal
	)		const

Compute the (scale of) tangent of the curve emanateing from a vertex in the parameter whose image bisects the corresponding angle In addition, accounting for the bisecting vector defined according to the normal

Detailed Description

template<class T> class gismo::gsTrimSurface< T >

Public Member Functions

Private Member Functions

Constructor & Destructor Documentation

Member Function Documentation

template<class T>
class gismo::gsTrimSurface< T >