pmp Namespace Reference

The pmp-library namespace. More...

Classes
class	AllocationException
	Exception indicating failure to allocate a new resource. More...
class	BoundingBox
	Simple class for representing a bounding box. More...
class	Edge
	this type represents an edge (internally it is basically an index) More...
class	EdgeProperty
	Edge property of type T. More...
class	Face
	this type represents a face (internally it is basically an index) More...
class	FaceProperty
	Face property of type T. More...
class	GLException
	Exception indicating an OpenGL error. More...
class	Halfedge
	this type represents a halfedge (internally it is basically an index) More...
class	HalfedgeProperty
	Halfedge property of type T. More...
class	Handle
	Base class for all entity handles types. More...
class	InvalidInputException
	Exception indicating invalid input passed to a function. More...
class	IOException
	Exception indicating an error occurred while performing IO. More...
struct	IOFlags
	Flags to control reading and writing. More...
class	Matrix
	Generic class for \( M \times N \) matrices. More...
class	MemoryUsage
	A simple class to retrieve memory usage information. More...
class	MeshViewer
	Simple viewer for a SurfaceMesh. More...
class	Renderer
	Class for rendering surface meshes using OpenGL. More...
class	Shader
	Class for handling shaders. More...
class	SolverException
	Exception indicating failure so solve an equation system. More...
class	StopWatch
	A simple stop watch class. More...
class	SurfaceMesh
	A class for representing polygon surface meshes. More...
class	TopologyException
	Exception indicating a topological error has occurred. More...
class	TrackballViewer
	A simple GLFW viewer with trackball user interface. More...
class	Vertex
	this type represents a vertex (internally it is basically an index) More...
class	VertexProperty
	Vertex property of type T. More...
class	Window
	A window provided by GLFW. More...

Typedefs
using	SparseMatrix = Eigen::SparseMatrix< double >
	PMP uses Eigen's double-precision sparse matrices.
using	DiagonalMatrix = Eigen::DiagonalMatrix< double, Eigen::Dynamic >
	PMP uses Eigen's double-precision diagonal matrices.
using	DenseMatrix = Eigen::MatrixXd
	PMP uses Eigen's double-precision dense matrices.
using	Triplet = Eigen::Triplet< double >
	PMP uses Eigen's double-precision triplets.
template<typename Scalar , int M>
using	Vector = Matrix< Scalar, M, 1 >
	template specialization for Vector as Nx1 matrix
template<typename Scalar >
using	Mat4 = Matrix< Scalar, 4, 4 >
	template specialization for 4x4 matrices
template<typename Scalar >
using	Mat3 = Matrix< Scalar, 3, 3 >
	template specialization for 3x3 matrices
template<typename Scalar >
using	Mat2 = Matrix< Scalar, 2, 2 >
	template specialization for 2x2 matrices
using	vec2 = Vector< float, 2 >
	template specialization for a vector of two float values
using	dvec2 = Vector< double, 2 >
	template specialization for a vector of two double values
using	bvec2 = Vector< bool, 2 >
	template specialization for a vector of two bool values
using	ivec2 = Vector< int, 2 >
	template specialization for a vector of two int values
using	uvec2 = Vector< unsigned int, 2 >
	template specialization for a vector of two unsigned int values
using	vec3 = Vector< float, 3 >
	template specialization for a vector of three float values
using	dvec3 = Vector< double, 3 >
	template specialization for a vector of three double values
using	bvec3 = Vector< bool, 3 >
	template specialization for a vector of three bool values
using	ivec3 = Vector< int, 3 >
	template specialization for a vector of three int values
using	uvec3 = Vector< unsigned int, 3 >
	template specialization for a vector of three unsigned int values
using	vec4 = Vector< float, 4 >
	template specialization for a vector of four float values
using	dvec4 = Vector< double, 4 >
	template specialization for a vector of four double values
using	bvec4 = Vector< bool, 4 >
	template specialization for a vector of four bool values
using	ivec4 = Vector< int, 4 >
	template specialization for a vector of four int values
using	uvec4 = Vector< unsigned int, 4 >
	template specialization for a vector of four unsigned int values
using	mat2 = Mat2< float >
	template specialization for a 2x2 matrix of float values
using	dmat2 = Mat2< double >
	template specialization for a 2x2 matrix of double values
using	mat3 = Mat3< float >
	template specialization for a 3x3 matrix of float values
using	dmat3 = Mat3< double >
	template specialization for a 3x3 matrix of double values
using	mat4 = Mat4< float >
	template specialization for a 4x4 matrix of float values
using	dmat4 = Mat4< double >
	template specialization for a 4x4 matrix of double values
using	Scalar = float
	Scalar type.
using	Point = Vector< Scalar, 3 >
	Point type.
using	Normal = Vector< Scalar, 3 >
	Normal type.
using	Color = Vector< Scalar, 3 >
	Color type.
using	TexCoord = Vector< Scalar, 2 >
	Texture coordinate type.

Enumerations
enum class	Curvature {   Min , Max , Mean , Gauss ,   MaxAbs }
	Type of curvature to be computed. More...

Functions
void	curvature_to_texture_coordinates (SurfaceMesh &mesh)
	convert curvature values "v:curv" to 1D texture coordinates stored in vertex property "v:tex"
void	curvature (SurfaceMesh &mesh, Curvature c=Curvature::Mean, int smoothing_steps=0, bool use_tensor=false, bool use_two_ring=false)
	Compute per-vertex curvature (min,max,mean,Gaussian).
void	decimate (SurfaceMesh &mesh, unsigned int n_vertices, Scalar aspect_ratio=0.0, Scalar edge_length=0.0, unsigned int max_valence=0, Scalar normal_deviation=0.0, Scalar hausdorff_error=0.0, Scalar seam_threshold=1e-2, Scalar seam_angle_deviation=1)
	Mesh decimation based on approximation error and fairness criteria.
Scalar	triangle_area (const Point &p0, const Point &p1, const Point &p2)
	Compute the area of a triangle given by three points.
Scalar	face_area (const SurfaceMesh &mesh, Face f)
	Compute area of face f.
Scalar	surface_area (const SurfaceMesh &mesh)
	Compute the surface area of mesh as the sum of face areas.
Scalar	edge_area (const SurfaceMesh &mesh, Edge e)
	Compute the area assigned to edge e.
Scalar	voronoi_area (const SurfaceMesh &mesh, Vertex v)
	Compute the (barycentric) Voronoi area of vertex v.
Scalar	voronoi_area_mixed (const SurfaceMesh &mesh, Vertex v)
	Compute mixed Voronoi area of a vertex.
Scalar	volume (const SurfaceMesh &mesh)
	Compute the volume of a mesh.
Point	centroid (const SurfaceMesh &mesh, Face f)
	Compute the barycenter/centroid of face f.
Point	centroid (const SurfaceMesh &mesh)
	Compute the barycenter (centroid) of the mesh.
void	dual (SurfaceMesh &mesh)
	Compute dual of a mesh.
double	cotan_weight (const SurfaceMesh &mesh, Edge e)
	Compute the cotangent weight for edge e.
Point	laplace (const SurfaceMesh &mesh, Vertex v)
	Compute the Laplace vector for vertex v, normalized by Voronoi area.
Scalar	clamp_cot (const Scalar v)
	Clamp cotangent values as if angles are in [3, 177].
Scalar	clamp_cos (const Scalar v)
	Clamp cosine values as if angles are in [3, 177].
Scalar	angle (const Point &v0, const Point &v1)
	Compute the angle between two (un-normalized) vectors.
Scalar	sin (const Point &v0, const Point &v1)
	Compute the sine of angle between two (un-normalized) vectors.
Scalar	cos (const Point &v0, const Point &v1)
	Compute the cosine of angle between two (un-normalized) vectors.
Scalar	cotan (const Point &v0, const Point &v1)
	Compute the cotangent of angle between two (un-normalized) vectors.
Scalar	dist_point_line_segment (const Point &p, const Point &v0, const Point &v1, Point &nearest_point)
	Compute the distance of a point p to a line segment given by points v0 and v1.
Scalar	dist_point_triangle (const Point &p, const Point &v0, const Point &v1, const Point &v2, Point &nearest_point)
	Compute the distance of a point p to the triangle given by points v0, v1, v2.
void	minimize_area (SurfaceMesh &mesh)
	Minimize surface area.
void	minimize_curvature (SurfaceMesh &mesh)
	Minimize surface curvature.
void	fair (SurfaceMesh &mesh, unsigned int k=2)
	Implicit surface fairing.
size_t	detect_features (SurfaceMesh &mesh, Scalar angle)
	Mark edges with dihedral angle larger than angle as feature.
size_t	detect_boundary (SurfaceMesh &mesh)
	Mark all boundary edges as features.
void	clear_features (SurfaceMesh &mesh)
	Clear feature and boundary edges.
void	distance_to_texture_coordinates (SurfaceMesh &mesh)
	Use the normalized distances as texture coordinates.
unsigned int	geodesics (SurfaceMesh &mesh, const std::vector< Vertex > &seeds, Scalar maxdist=std::numeric_limits< Scalar >::max(), unsigned int maxnum=std::numeric_limits< unsigned int >::max(), std::vector< Vertex > *neighbors=nullptr)
	Compute geodesic distance from a set of seed vertices.
void	geodesics_heat (SurfaceMesh &mesh, const std::vector< Vertex > &seeds)
	Compute geodesic distance from a set of seed vertices.
void	fill_hole (SurfaceMesh &mesh, Halfedge h)
	Fill the hole specified by halfedge h.
void	uniform_mass_matrix (const SurfaceMesh &mesh, DiagonalMatrix &M)
	Construct the mass matrix for the uniform Laplacian.
void	mass_matrix (const SurfaceMesh &mesh, DiagonalMatrix &M)
	Construct the (lumped) mass matrix for the cotangent Laplacian.
void	uniform_laplace_matrix (const SurfaceMesh &mesh, SparseMatrix &L)
	Construct the uniform Laplace matrix.
void	laplace_matrix (const SurfaceMesh &mesh, SparseMatrix &L, bool clamp=false)
	Construct the cotan Laplace matrix.
void	gradient_matrix (const SurfaceMesh &mesh, SparseMatrix &G)
	Construct the cotan gradient matrix.
void	divergence_matrix (const SurfaceMesh &mesh, SparseMatrix &D)
	Construct the cotan divergence matrix.
void	coordinates_to_matrix (const SurfaceMesh &mesh, DenseMatrix &X)
	For a mesh with N vertices, construct an Nx3 matrix containing the vertex coordinates in its rows.
void	matrix_to_coordinates (const DenseMatrix &X, SurfaceMesh &mesh)
	For a mesh with N vertices, set the vertex coordinates from the rows of an Nx3 matrix.
Normal	face_normal (const SurfaceMesh &mesh, Face f)
	Compute the normal vector of face f.
Normal	vertex_normal (const SurfaceMesh &mesh, Vertex v)
	Compute the normal vector of vertex v.
Normal	corner_normal (const SurfaceMesh &mesh, Halfedge h, Scalar crease_angle)
	Compute the normal vector of the polygon corner specified by the target vertex of halfedge h.
void	vertex_normals (SurfaceMesh &mesh)
	Compute vertex normals for the whole mesh.
void	face_normals (SurfaceMesh &mesh)
	Compute face normals for the whole mesh.
DenseMatrix	cholesky_solve (const SparseMatrix &A, const DenseMatrix &B)
	Solve the linear system A*X=B using sparse Cholesky decomposition.
DenseMatrix	cholesky_solve (const SparseMatrix &A, const DenseMatrix &B, const std::function< bool(unsigned int)> &is_constrained, const DenseMatrix &C)
	Solve the linear system A*X=B with given hard constraints using sparse Cholesky decomposition.
void	selector_matrix (const SurfaceMesh &mesh, const std::function< bool(Vertex)> &is_selected, SparseMatrix &S)
	Constructs a selector matrix for a mesh with N vertices.
void	matrices_to_mesh (const Eigen::MatrixXd &V, const Eigen::MatrixXi &F, SurfaceMesh &mesh)
	Build SurfaceMesh from Eigen matrices containing vertex coordinates and triangle indices.
void	mesh_to_matrices (const SurfaceMesh &mesh, Eigen::MatrixXd &V, Eigen::MatrixXi &F)
	Convert SurfaceMesh to Eigen matrices of vertex coordinates and triangle indices.
void	harmonic_parameterization (SurfaceMesh &mesh, bool use_uniform_weights=false)
	Compute discrete harmonic parameterization.
void	lscm_parameterization (SurfaceMesh &mesh)
	Compute parameterization based on least squares conformal mapping.
void	uniform_remeshing (SurfaceMesh &mesh, Scalar edge_length, unsigned int iterations=10, bool use_projection=true)
	Perform uniform remeshing.
void	adaptive_remeshing (SurfaceMesh &mesh, Scalar min_edge_length, Scalar max_edge_length, Scalar approx_error, unsigned int iterations=10, bool use_projection=true)
	Perform adaptive remeshing.
SurfaceMesh	tetrahedron ()
	Generate tetrahedron.
SurfaceMesh	hexahedron ()
	Generate hexahedron.
SurfaceMesh	octahedron ()
	Generate octahedron.
SurfaceMesh	dodecahedron ()
	Generate dodecahedron.
SurfaceMesh	icosahedron ()
	Generate icosahedron.
SurfaceMesh	icosphere (size_t n_subdivisions=3)
	Generate icosphere refined by n_subdivisions .
SurfaceMesh	quad_sphere (size_t n_subdivisions=3)
	Generate quad sphere refined by n_subdivisions .
SurfaceMesh	uv_sphere (const Point &center=Point(0, 0, 0), Scalar radius=1.0, size_t n_slices=15, size_t n_stacks=15)
	Generate UV sphere with given center, radius, n_slices, and n_stacks.
SurfaceMesh	plane (size_t resolution=4)
	Generate a plane mesh.
SurfaceMesh	cone (size_t n_subdivisions=30, Scalar radius=1.0, Scalar height=2.5)
	Generate a cone mesh.
SurfaceMesh	cylinder (size_t n_subdivisions=30, Scalar radius=1.0, Scalar height=2.5)
	Generate a cylinder mesh.
SurfaceMesh	torus (size_t radial_resolution=20, size_t tubular_resolution=40, Scalar radius=1.0, Scalar thickness=0.4)
	Generate a torus mesh.
void	explicit_smoothing (SurfaceMesh &mesh, unsigned int iterations=10, bool use_uniform_laplace=false)
	Perform explicit Laplacian smoothing.
void	implicit_smoothing (SurfaceMesh &mesh, Scalar timestep=0.001, unsigned int iterations=1, bool use_uniform_laplace=false, bool rescale=true)
	Perform implicit Laplacian smoothing.
void	catmull_clark_subdivision (SurfaceMesh &mesh, BoundaryHandling boundary_handling=BoundaryHandling::Interpolate)
	Perform one step of Catmull-Clark subdivision.
void	loop_subdivision (SurfaceMesh &mesh, BoundaryHandling boundary_handling=BoundaryHandling::Interpolate)
	Perform one step of Loop subdivision.
void	quad_tri_subdivision (SurfaceMesh &mesh, BoundaryHandling boundary_handling=BoundaryHandling::Interpolate)
	Perform one step of quad-tri subdivision.
void	linear_subdivision (SurfaceMesh &mesh)
	Perform one step of linear quad-tri subdivision.
void	triangulate (SurfaceMesh &mesh)
	Triangulate all faces in mesh by applying triangulate().
void	triangulate (SurfaceMesh &mesh, Face f)
	Triangulate the Face f .
BoundingBox	bounds (const SurfaceMesh &mesh)
	Compute the bounding box of mesh .
void	flip_faces (SurfaceMesh &mesh)
	Flip the orientation of all faces in mesh .
Scalar	min_face_area (const SurfaceMesh &mesh)
	Compute the minimum area of all faces in mesh .
Scalar	mean_edge_length (const SurfaceMesh &mesh)
	Compute mean edge length of mesh .
int	connected_components (SurfaceMesh &mesh)
	Compute connected components in mesh .
Scalar	edge_length (const SurfaceMesh &mesh, Edge e)
	Compute length of an edge e in mesh .
void	read (SurfaceMesh &mesh, const std::filesystem::path &file)
	Read into mesh from file.
void	write (const SurfaceMesh &mesh, const std::filesystem::path &file, const IOFlags &flags=IOFlags())
	Write mesh to file controlled by flags.
template<typename Scalar , int M, int N>
std::ostream &	operator<< (std::ostream &os, const Matrix< Scalar, M, N > &m)
	output a matrix by printing its space-separated components
template<typename Scalar , int M, int N, int K>
Matrix< Scalar, M, N >	operator* (const Matrix< Scalar, M, K > &m1, const Matrix< Scalar, K, N > &m2)
	matrix-matrix multiplication
template<typename Scalar , int M, int N>
Matrix< Scalar, M, N >	cmult (const Matrix< Scalar, M, N > &m1, const Matrix< Scalar, M, N > &m2)
	component-wise multiplication
template<typename Scalar , int M, int N>
Matrix< Scalar, N, M >	transpose (const Matrix< Scalar, M, N > &m)
	transpose MxN matrix to NxM matrix
template<typename Scalar , int M, int N>
Matrix< Scalar, M, N >	operator+ (const Matrix< Scalar, M, N > &m1, const Matrix< Scalar, M, N > &m2)
	matrix addition: m1 + m2
template<typename Scalar , int M, int N>
Matrix< Scalar, M, N >	operator- (const Matrix< Scalar, M, N > &m1, const Matrix< Scalar, M, N > &m2)
	matrix subtraction: m1 - m2
template<typename Scalar , int M, int N>
Matrix< Scalar, M, N >	operator- (const Matrix< Scalar, M, N > &m)
	matrix negation: -m
template<typename Scalar , typename Scalar2 , int M, int N>
Matrix< Scalar, M, N >	operator* (const Scalar2 s, const Matrix< Scalar, M, N > &m)
	scalar multiplication of matrix: s*m
template<typename Scalar , typename Scalar2 , int M, int N>
Matrix< Scalar, M, N >	operator* (const Matrix< Scalar, M, N > &m, const Scalar2 s)
	scalar multiplication of matrix: m*s
template<typename Scalar , typename Scalar2 , int M, int N>
Matrix< Scalar, M, N >	operator/ (const Matrix< Scalar, M, N > &m, const Scalar2 s)
	divide matrix by scalar: m/s
template<typename Scalar , int M, int N>
Scalar	norm (const Matrix< Scalar, M, N > &m)
	compute the Frobenius norm of a matrix (or Euclidean norm of a vector)
template<typename Scalar , int M, int N>
Scalar	sqrnorm (const Matrix< Scalar, M, N > &m)
	compute the squared Frobenius norm of a matrix (or squared Euclidean norm of a vector)
template<typename Scalar , int M, int N>
Matrix< Scalar, M, N >	normalize (const Matrix< Scalar, M, N > &m)
	return a normalized copy of a matrix or a vector
template<typename Scalar , int M, int N>
Matrix< Scalar, M, N >	min (const Matrix< Scalar, M, N > &m1, const Matrix< Scalar, M, N > &m2)
	return component-wise minimum
template<typename Scalar , int M, int N>
Matrix< Scalar, M, N >	max (const Matrix< Scalar, M, N > &m1, const Matrix< Scalar, M, N > &m2)
	return component-wise maximum
template<typename Scalar >
Mat4< Scalar >	viewport_matrix (Scalar l, Scalar b, Scalar w, Scalar h)
	OpenGL viewport matrix with parameters left, bottom, width, height.
template<typename Scalar >
Mat4< Scalar >	inverse_viewport_matrix (Scalar l, Scalar b, Scalar w, Scalar h)
	inverse of OpenGL viewport matrix with parameters left, bottom, width, height
template<typename Scalar >
Mat4< Scalar >	frustum_matrix (Scalar l, Scalar r, Scalar b, Scalar t, Scalar n, Scalar f)
	OpenGL frustum matrix with parameters left, right, bottom, top, near, far.
template<typename Scalar >
Mat4< Scalar >	inverse_frustum_matrix (Scalar l, Scalar r, Scalar b, Scalar t, Scalar n, Scalar f)
	inverse of OpenGL frustum matrix with parameters left, right, bottom, top, near, far
template<typename Scalar >
Mat4< Scalar >	perspective_matrix (Scalar fovy, Scalar aspect, Scalar zNear, Scalar zFar)
	OpenGL perspective matrix with parameters field of view in y-direction, aspect ratio, and distance of near and far planes.
template<typename Scalar >
Mat4< Scalar >	inverse_perspective_matrix (Scalar fovy, Scalar aspect, Scalar zNear, Scalar zFar)
	inverse of perspective matrix
template<typename Scalar >
Mat4< Scalar >	ortho_matrix (Scalar left, Scalar right, Scalar bottom, Scalar top, Scalar zNear=-1, Scalar zFar=1)
	OpenGL orthogonal projection matrix with parameters left, right, bottom, top, near, far.
template<typename Scalar >
Mat4< Scalar >	look_at_matrix (const Vector< Scalar, 3 > &eye, const Vector< Scalar, 3 > &center, const Vector< Scalar, 3 > &up)
	OpenGL look-at camera matrix with parameters eye position, scene center, up-direction.
template<typename Scalar >
Mat4< Scalar >	translation_matrix (const Vector< Scalar, 3 > &t)
	OpenGL matrix for translation by vector t.
template<typename Scalar >
Mat4< Scalar >	scaling_matrix (const Scalar s)
	OpenGL matrix for scaling x/y/z by s.
template<typename Scalar >
Mat4< Scalar >	scaling_matrix (const Vector< Scalar, 3 > &s)
	OpenGL matrix for scaling x/y/z by the components of s.
template<typename Scalar >
Mat4< Scalar >	rotation_matrix_x (Scalar angle)
	OpenGL matrix for rotation around x-axis by given angle (in degrees)
template<typename Scalar >
Mat4< Scalar >	rotation_matrix_y (Scalar angle)
	OpenGL matrix for rotation around y-axis by given angle (in degrees)
template<typename Scalar >
Mat4< Scalar >	rotation_matrix_z (Scalar angle)
	OpenGL matrix for rotation around z-axis by given angle (in degrees)
template<typename Scalar >
Mat4< Scalar >	rotation_matrix (const Vector< Scalar, 3 > &axis, Scalar angle)
	OpenGL matrix for rotation around given axis by given angle (in degrees)
template<typename Scalar >
Mat4< Scalar >	rotation_matrix (const Vector< Scalar, 4 > &quat)
	OpenGL matrix for rotation specified by unit quaternion.
template<typename Scalar >
Mat3< Scalar >	linear_part (const Mat4< Scalar > &m)
	return upper 3x3 matrix from given 4x4 matrix, corresponding to the linear part of an affine transformation
template<typename Scalar >
Vector< Scalar, 3 >	projective_transform (const Mat4< Scalar > &m, const Vector< Scalar, 3 > &v)
	projective transformation of 3D vector v by a 4x4 matrix m: add 1 as 4th component of v, multiply m*v, divide by 4th component
template<typename Scalar >
Vector< Scalar, 3 >	affine_transform (const Mat4< Scalar > &m, const Vector< Scalar, 3 > &v)
	affine transformation of 3D vector v by a 4x4 matrix m: add 1 as 4th component of v, multiply m*v, do NOT divide by 4th component
template<typename Scalar >
Vector< Scalar, 3 >	linear_transform (const Mat4< Scalar > &m, const Vector< Scalar, 3 > &v)
	linear transformation of 3D vector v by a 4x4 matrix m: transform vector by upper-left 3x3 submatrix of m
template<typename Scalar >
Mat4< Scalar >	inverse (const Mat4< Scalar > &m)
	return the inverse of a 4x4 matrix
template<typename Scalar >
Scalar	determinant (const Mat3< Scalar > &m)
	return determinant of 3x3 matrix
template<typename Scalar >
Mat3< Scalar >	inverse (const Mat3< Scalar > &m)
	return the inverse of a 3x3 matrix
template<typename Scalar >
bool	symmetric_eigendecomposition (const Mat3< Scalar > &m, Scalar &eval1, Scalar &eval2, Scalar &eval3, Vector< Scalar, 3 > &evec1, Vector< Scalar, 3 > &evec2, Vector< Scalar, 3 > &evec3)
	compute eigenvector/eigenvalue decomposition of a 3x3 matrix
template<typename Scalar , int N>
std::istream &	operator>> (std::istream &is, Vector< Scalar, N > &vec)
	read the space-separated components of a vector from a stream
template<typename Scalar , int N>
std::ostream &	operator<< (std::ostream &os, const Vector< Scalar, N > &vec)
	output a vector by printing its space-separated components
template<typename Scalar , int N>
Scalar	dot (const Vector< Scalar, N > &v0, const Vector< Scalar, N > &v1)
	compute the dot product of two vectors
template<typename Scalar , int N>
Scalar	distance (const Vector< Scalar, N > &v0, const Vector< Scalar, N > &v1)
	compute the Euclidean distance between two points
template<typename Scalar >
Vector< Scalar, 2 >	perp (const Vector< Scalar, 2 > &v)
	compute perpendicular vector (rotate vector counter-clockwise by 90 degrees)
template<typename Scalar >
Vector< Scalar, 3 >	cross (const Vector< Scalar, 3 > &v0, const Vector< Scalar, 3 > &v1)
	compute the cross product of two vectors (only valid for 3D vectors)
std::ostream &	operator<< (std::ostream &os, const StopWatch &watch)
	output a elapsed time to a stream
std::ostream &	operator<< (std::ostream &os, Vertex v)
	output a Vertex to a stream
std::ostream &	operator<< (std::ostream &os, Halfedge h)
	output a Halfedge to a stream
std::ostream &	operator<< (std::ostream &os, Edge e)
	output an Edge to a stream
std::ostream &	operator<< (std::ostream &os, Face f)
	output a Face to a stream

Detailed Description

The pmp-library namespace.

Function Documentation

cholesky_solve() [1/2]

DenseMatrix cholesky_solve	(	const SparseMatrix &	A,
		const DenseMatrix &	B
	)

Solve the linear system A*X=B using sparse Cholesky decomposition.

Returns the solution vector/matrix X.

Precondition

The matrix A has to be sparse, symmetric, and positive definite.

Parameters

A	The system matrix.
B	The right hand side.

cholesky_solve() [2/2]

DenseMatrix cholesky_solve	(	const SparseMatrix &	A,
		const DenseMatrix &	B,
		const std::function< bool(unsigned int)> &	is_constrained,
		const DenseMatrix &	C
	)

Solve the linear system A*X=B with given hard constraints using sparse Cholesky decomposition.

Returns the solution vector or matrix X.

Precondition

The matrix A has to be sparse, symmetric, and positive definite.

Parameters

A	The system matrix.
B	The right hand side.
is_constrained	A function returning whether or not X(i) is constrained or not.
C	A matrix storing the Dirichlet constraints: X(i) should be C(i) is entry i is constrained.

distance_to_texture_coordinates()

void distance_to_texture_coordinates

(

SurfaceMesh &

mesh

)

Use the normalized distances as texture coordinates.

Stores the normalized distances in a vertex property of type TexCoord named "v:tex". Reuses any existing vertex property of the same type and name.

matrices_to_mesh()

void matrices_to_mesh	(	const Eigen::MatrixXd &	V,
		const Eigen::MatrixXi &	F,
		SurfaceMesh &	mesh
	)

Build SurfaceMesh from Eigen matrices containing vertex coordinates and triangle indices.

Parameters

V	\(n\times 3\) matrix of double precision vertex coordinates.
F	\(m\times 3\) matrix of integer triangle indices.
mesh	The mesh to be build from V and F . The mesh will be cleared.

mesh_to_matrices()

void mesh_to_matrices	(	const SurfaceMesh &	mesh,
		Eigen::MatrixXd &	V,
		Eigen::MatrixXi &	F
	)

Convert SurfaceMesh to Eigen matrices of vertex coordinates and triangle indices.

Parameters

mesh	The mesh used to fill V and F .
V	The resulting \(n\times 3\) matrix of double precision vertex coordinates.
F	The resulting \(m\times 3\) matrix of integer triangle indices.

selector_matrix()

void selector_matrix	(	const SurfaceMesh &	mesh,
		const std::function< bool(Vertex)> &	is_selected,
		SparseMatrix &	S
	)

Constructs a selector matrix for a mesh with N vertices.

Returns a matrix built from the rows of the NxN identity matrix that belong to selected vertices.

Parameters

mesh	The input mesh.
is_selected	A function returning whether or not vertex i is selected or not.
S	The output matrix.