Functions
void	frame_field (const Eigen::MatrixXd &V, const Eigen::MatrixXi &F, const Eigen::VectorXi &b, const Eigen::MatrixXd &bc1, const Eigen::MatrixXd &bc2, Eigen::MatrixXd &FF1, Eigen::MatrixXd &FF2)
	Generate a piecewise-constant frame-field field from a sparse set of constraints on faces using the algorithm proposed in: Frame Fields: Anisotropic and Non-Orthogonal Cross Fields Daniele Panozzo, Enrico Puppo, Marco Tarini, Olga Sorkine-Hornung, ACM Transactions on Graphics (SIGGRAPH, 2014)

template<typename DerivedV , typename DerivedF , typename DerivedU >
void	miq (const Eigen::PlainObjectBase< DerivedV > &V, const Eigen::PlainObjectBase< DerivedF > &F, const Eigen::PlainObjectBase< DerivedV > &PD1, const Eigen::PlainObjectBase< DerivedV > &PD2, Eigen::PlainObjectBase< DerivedU > &UV, Eigen::PlainObjectBase< DerivedF > &FUV, double gradientSize=30.0, double stiffness=5.0, bool directRound=false, unsigned int iter=5, unsigned int localIter=5, bool doRound=true, bool singularityRound=true, const std::vector< int > &roundVertices=std::vector< int >(), const std::vector< std::vector< int > > &hardFeatures=std::vector< std::vector< int > >())
	Global seamless parametrization aligned with a given per-face Jacobian (PD1, PD2).

template<typename DerivedV , typename DerivedF , typename DerivedU >
void	miq (const Eigen::PlainObjectBase< DerivedV > &V, const Eigen::PlainObjectBase< DerivedF > &F, const Eigen::PlainObjectBase< DerivedV > &PD1_combed, const Eigen::PlainObjectBase< DerivedV > &PD2_combed, const Eigen::Matrix< int, Eigen::Dynamic, 3 > &mismatch, const Eigen::Matrix< int, Eigen::Dynamic, 1 > &singular, const Eigen::Matrix< int, Eigen::Dynamic, 3 > &seams, Eigen::PlainObjectBase< DerivedU > &UV, Eigen::PlainObjectBase< DerivedF > &FUV, double gradientSize=30.0, double stiffness=5.0, bool directRound=false, unsigned int iter=5, unsigned int localIter=5, bool doRound=true, bool singularityRound=true, const std::vector< int > &roundVertices=std::vector< int >(), const std::vector< std::vector< int > > &hardFeatures=std::vector< std::vector< int > >())
	miq Helper function that allows to directly provided pre-combed bisectors for an already cut mesh

void	nrosy (const Eigen::MatrixXd &V, const Eigen::MatrixXi &F, const Eigen::VectorXi &b, const Eigen::MatrixXd &bc, const Eigen::VectorXi &b_soft, const Eigen::VectorXd &w_soft, const Eigen::MatrixXd &bc_soft, int N, double soft, Eigen::MatrixXd &R, Eigen::VectorXd &S)
	Generate a N-RoSy field from a sparse set of constraints.

void	nrosy (const Eigen::MatrixXd &V, const Eigen::MatrixXi &F, const Eigen::VectorXi &b, const Eigen::MatrixXd &bc, int N, Eigen::MatrixXd &R, Eigen::VectorXd &S)
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Function Documentation

◆ frame_field()

void igl::copyleft::comiso::frame_field	(	const Eigen::MatrixXd &	V,
		const Eigen::MatrixXi &	F,
		const Eigen::VectorXi &	b,
		const Eigen::MatrixXd &	bc1,
		const Eigen::MatrixXd &	bc2,
		Eigen::MatrixXd &	FF1,
		Eigen::MatrixXd &	FF2
	)

Generate a piecewise-constant frame-field field from a sparse set of constraints on faces using the algorithm proposed in: Frame Fields: Anisotropic and Non-Orthogonal Cross Fields Daniele Panozzo, Enrico Puppo, Marco Tarini, Olga Sorkine-Hornung, ACM Transactions on Graphics (SIGGRAPH, 2014)

Parameters

[in]	V	#V by 3 list of mesh vertex coordinates
[in]	F	#F by 3 list of mesh faces (must be triangles)
[in]	b	#B by 1 list of constrained face indices
[in]	bc1	#B by 3 list of the constrained first representative vector of the frame field (up to permutation and sign)
[in]	bc2	#B by 3 list of the constrained second representative vector of the frame field (up to permutation and sign)
[out]	FF1	#F by 3 the first representative vector of the frame field (up to permutation and sign)
[out]	FF2	#F by 3 the second representative vector of the frame field (up to permutation and sign)

Note: it now supports only soft constraints, should be extended to support both hard and soft constraints

◆ miq() [1/2]

template<typename DerivedV , typename DerivedF , typename DerivedU >

void igl::copyleft::comiso::miq	(	const Eigen::PlainObjectBase< DerivedV > &	V,
		const Eigen::PlainObjectBase< DerivedF > &	F,
		const Eigen::PlainObjectBase< DerivedV > &	PD1,
		const Eigen::PlainObjectBase< DerivedV > &	PD2,
		Eigen::PlainObjectBase< DerivedU > &	UV,
		Eigen::PlainObjectBase< DerivedF > &	FUV,
		double	gradientSize = `30.0`,
		double	stiffness = `5.0`,
		bool	directRound = `false`,
		unsigned int	iter = `5`,
		unsigned int	localIter = `5`,
		bool	doRound = `true`,
		bool	singularityRound = `true`,
		const std::vector< int > &	roundVertices = `std::vector< int >()`,
		const std::vector< std::vector< int > > &	hardFeatures = `std::vector< std::vector< int > >()`
	)

Global seamless parametrization aligned with a given per-face Jacobian (PD1, PD2).

The algorithm is based on "Mixed-Integer Quadrangulation" by D. Bommes, H. Zimmer, L. Kobbelt ACM SIGGRAPH 2009, Article No. 77 (http://dl.acm.org/citation.cfm?id=1531383) We thank Nico Pietroni for providing a reference implementation of MIQ on which our code is based.

Parameters

[in]	V	#V by 3 list of mesh vertex 3D positions
[in]	F	#F by 3 list of faces indices in V
[in]	PD1	#V by 3 first line of the Jacobian per triangle
[in]	PD2	#V by 3 second line of the Jacobian per triangle (optional, if empty it will be a vector in the tangent plane orthogonal to PD1)
[in]	gradientSize	global scaling for the gradient (controls the quads resolution)
[in]	stiffness	weight for the stiffness iterations (Reserved but not used!)
[in]	directRound	greedily round all integer variables at once (greatly improves optimization speed but lowers quality)
[in]	iter	stiffness iterations (0 = no stiffness)
[in]	localIter	number of local iterations for the integer rounding
[in]	doRound	enables the integer rounding (disabling it could be useful for debugging)
[in]	singularityRound	set true/false to decide if the singularities' coordinates should be rounded to the nearest integers
[in]	roundVertices	id of additional vertices that should be snapped to integer coordinates
[in]	hardFeatures	#H by 2 list of pairs of vertices that belongs to edges that should be snapped to integer coordinates
[out]	UV	#UV by 2 list of vertices in 2D
[out]	FUV	#FUV by 3 list of face indices in UV

◆ miq() [2/2]

template<typename DerivedV , typename DerivedF , typename DerivedU >

void igl::copyleft::comiso::miq	(	const Eigen::PlainObjectBase< DerivedV > &	V,
		const Eigen::PlainObjectBase< DerivedF > &	F,
		const Eigen::PlainObjectBase< DerivedV > &	PD1_combed,
		const Eigen::PlainObjectBase< DerivedV > &	PD2_combed,
		const Eigen::Matrix< int, Eigen::Dynamic, 3 > &	mismatch,
		const Eigen::Matrix< int, Eigen::Dynamic, 1 > &	singular,
		const Eigen::Matrix< int, Eigen::Dynamic, 3 > &	seams,
		Eigen::PlainObjectBase< DerivedU > &	UV,
		Eigen::PlainObjectBase< DerivedF > &	FUV,
		double	gradientSize = `30.0`,
		double	stiffness = `5.0`,
		bool	directRound = `false`,
		unsigned int	iter = `5`,
		unsigned int	localIter = `5`,
		bool	doRound = `true`,
		bool	singularityRound = `true`,
		const std::vector< int > &	roundVertices = `std::vector< int >()`,
		const std::vector< std::vector< int > > &	hardFeatures = `std::vector< std::vector< int > >()`
	)

miq Helper function that allows to directly provided pre-combed bisectors for an already cut mesh

Parameters

[in]	V	#V by 3 list of mesh vertex 3D positions
[in]	F	#F by 3 list of faces indices in V
[in]	Additional	Input:
[in]	PD1_combed	#F by 3 first combed Jacobian
[in]	PD2_combed	#F by 3 second combed Jacobian
[in]	mismatch	#F by 3 list of per-corner integer PI/2 rotations
[in]	singular	#V list of flag that denotes if a vertex is singular or not
[in]	seams	#F by 3 list of per-corner flag that denotes seams
[out]	UV	#UV by 2 list of vertices in 2D
[out]	FUV	#FUV by 3 list of face indices in UV
[in]	gradientSize	global scaling for the gradient (controls the quads resolution)
[in]	stiffness	weight for the stiffness iterations (Reserved but not used!)
[in]	directRound	greedily round all integer variables at once (greatly improves optimization speed but lowers quality)
[in]	iter	stiffness iterations (0 = no stiffness)
[in]	localIter	number of local iterations for the integer rounding
[in]	doRound	enables the integer rounding (disabling it could be useful for debugging)
[in]	singularityRound	set true/false to decide if the singularities' coordinates should be rounded to the nearest integers
[in]	roundVertices	id of additional vertices that should be snapped to integer coordinates
[in]	hardFeatures	#H by 2 list of pairs of vertices that belongs to edges that should be snapped to integer coordinates

◆ nrosy() [1/2]

void igl::copyleft::comiso::nrosy	(	const Eigen::MatrixXd &	V,
		const Eigen::MatrixXi &	F,
		const Eigen::VectorXi &	b,
		const Eigen::MatrixXd &	bc,
		const Eigen::VectorXi &	b_soft,
		const Eigen::VectorXd &	w_soft,
		const Eigen::MatrixXd &	bc_soft,
		int	N,
		double	soft,
		Eigen::MatrixXd &	R,
		Eigen::VectorXd &	S
	)

Generate a N-RoSy field from a sparse set of constraints.

Parameters

[in]	V	#V by 3 list of mesh vertex coordinates
[in]	F	#F by 3 list of mesh faces (must be triangles)
[in]	b	#B by 1 list of constrained face indices
[in]	bc	#B by 3 list of representative vectors for the constrained faces
[in]	b_soft	#S by 1 b for soft constraints
[in]	w_soft	#S by 1 weight for the soft constraints (0-1)
[in]	bc_soft	#S by 3 bc for soft constraints
[in]	N	the degree of the N-RoSy vector field
[in]	soft	the strength of the soft constraints w.r.t. smoothness (0 -> smoothness only, 1->constraints only)
[out]	R	#F by 3 the representative vectors of the interpolated field
[out]	S	#V by 1 the singularity index for each vertex (0 = regular)

◆ nrosy() [2/2]

void igl::copyleft::comiso::nrosy	(	const Eigen::MatrixXd &	V,
		const Eigen::MatrixXi &	F,
		const Eigen::VectorXi &	b,
		const Eigen::MatrixXd &	bc,
		int	N,
		Eigen::MatrixXd &	R,
		Eigen::VectorXd &	S
	)

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Functions

Function Documentation

◆ frame_field()

◆ miq() [1/2]

◆ miq() [2/2]

◆ nrosy() [1/2]

◆ nrosy() [2/2]