Mesh processing algorithms. More...

Enumerations
enum class	Curvature { min , max , mean , gauss , max_abs }
	Type of curvature to be computed. More...

Functions
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	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 angle between two (un-normalized) vectors

Scalar	sin (const Point &v0, const Point &v1)
	compute sine of angle between two (un-normalized) vectors

Scalar	cos (const Point &v0, const Point &v1)
	compute cosine of angle between two (un-normalized) vectors

Scalar	cotan (const Point &v0, const Point &v1)
	compute cotangent of angle between two (un-normalized) vectors

Scalar	triangle_area (const Point &p0, const Point &p1, const Point &p2)
	compute 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 sum of face areas).

Scalar	voronoi_area (const SurfaceMesh &mesh, Vertex v)
	compute (barycentric) Voronoi area of vertex v

Scalar	voronoi_area_mixed (const SurfaceMesh &mesh, Vertex v)
	Compute mixed Voronoi area of a vertex.

Scalar	edge_area (const SurfaceMesh &mesh, Edge e)
	compute area assigned to edge e (a face with n edges assigns 1/n of its area to each edge)

Scalar	volume (const SurfaceMesh &mesh)
	Compute the volume of a mesh.

Point	centroid (const SurfaceMesh &mesh, Face f)
	compute barycenter/centroid of a face

Point	centroid (const SurfaceMesh &mesh)
	barycenter/centroid of mesh, computed as area-weighted mean of vertices.

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 Laplace vector for vertex v (normalized by Voronoi area)

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,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.

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	uniform_laplace_matrix (const SurfaceMesh &mesh, SparseMatrix &L)
	Construct the uniform Laplace matrix.

void	mass_matrix (const SurfaceMesh &mesh, DiagonalMatrix &M)
	Construct the (lumped) mass matrix for the cotangent Laplacian.

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.

void	vertex_normals (SurfaceMesh &mesh)
	Compute vertex normals for the whole `mesh`.

void	face_normals (SurfaceMesh &mesh)
	Compute face normals for the whole `mesh`.

Normal	vertex_normal (const SurfaceMesh &mesh, Vertex v)
	Compute the normal vector of vertex `v`.

Normal	face_normal (const SurfaceMesh &mesh, Face f)
	Compute the normal vector of face `f`.

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	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	edge_length (const SurfaceMesh &mesh, Edge e)
	Compute length of an edge `e` in `mesh` .

Scalar	mean_edge_length (const SurfaceMesh &mesh)
	Compute mean edge length of `mesh` .

Detailed Description

Mesh processing algorithms.

Enumeration Type Documentation

◆ Curvature

enum class Curvature

strong

Type of curvature to be computed.

Enumerator
min	minimum curvature
max	maximum curvature
mean	mean curvature
gauss	Gauss curvature.
max_abs	maximum absolute curvature

Function Documentation

◆ adaptive_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.

Performs incremental remeshing based on edge collapse, split, flip, and tangential relaxation. See [2] and [10] for details.

Parameters

mesh	The input mesh, modified in place.
min_edge_length	The minimum edge length.
max_edge_length	The maximum edge length.
approx_error	The maximum approximation error.
iterations	The number of iterations.
use_projection	Use back-projection to the input surface.

Precondition: Input mesh needs to be a triangle mesh.

Exceptions

InvalidInputException if the input precondition is violated.

◆ catmull_clark_subdivision()

void catmull_clark_subdivision	(	SurfaceMesh &	mesh,
		BoundaryHandling	boundary_handling = `BoundaryHandling::Interpolate`
	)

Perform one step of Catmull-Clark subdivision.

See [5] for details.

Parameters

mesh	The input mesh, modified in place.
boundary_handling	Specify to interpolate or preserve boundary edges.

◆ clear_features()

void clear_features ( SurfaceMesh & mesh )

Clear feature and boundary edges.

Sets all "e:feature" and "v:feature" properties to false.

Note: This does not remove the corresponding property arrays.

◆ cone()

SurfaceMesh cone	(	size_t	n_subdivisions = `30`,
		Scalar	radius = `1.0`,
		Scalar	height = `2.5`
	)

Generate a cone mesh.

Generates a polygonal mesh of a cone. The circular base lies in the x-y-plane and the tip points in positive z-direction.

Parameters

n_subdivisions	Number of subdivisions of the base circle. Needs to be >= 3. Default: 30.
radius	Radius of the base circle. Default: 1.
height	Height of the the cone. Default: 2.5.

◆ coordinates_to_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.

Parameters

mesh	The input mesh.
X	The output matrix.

◆ corner_normal()

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.

Averages incident corner normals if they are within crease_angle of the face normal. crease_angle is in radians, not degrees.

Note: This algorithm works on general polygon meshes.

◆ cotan_weight()

double cotan_weight	(	const SurfaceMesh &	mesh,
		Edge	e
	)

compute the cotangent weight for edge e

Precondition: Input mesh needs to be a triangle mesh.

◆ curvature()

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).

Curvature values for boundary vertices are interpolated from their interior neighbors. Curvature values can be smoothed. See [18] and [6] for details.

Note: This algorithm works on general polygon meshes.

◆ cylinder()

SurfaceMesh cylinder	(	size_t	n_subdivisions = `30`,
		Scalar	radius = `1.0`,
		Scalar	height = `2.5`
	)

Generate a cylinder mesh.

Generates a polygonal mesh of a cylinder. The cylinder is oriented in z-direction.

Parameters

n_subdivisions	Number of subdivisions of the cylinder. Needs to be >= 3. Default: 30.
radius	Radius of the cylinder. Default: 1.
height	Height of the cylinder. Default: 2.5.

◆ decimate()

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.

Performs incremental greedy mesh decimation based on halfedge collapses. See [14] and [11] for details.

Parameters

mesh	Target mesh. Modified in place.
n_vertices	Target number of vertices.
aspect_ratio	Minimum aspect ratio of the triangles.
edge_length	Minimum target edge length.
max_valence	Maximum number of incident edges per vertex.
normal_deviation	Maximum deviation of face normals.
hausdorff_error	Maximum deviation from the original surface.
seam_threshold	Threshold for texture seams.
seam_angle_deviation	Maximum texture seam deviation.

Precondition: Input mesh needs to be a triangle mesh.

Exceptions

InvalidInputException if the input precondition is violated.

◆ detect_boundary()

size_t detect_boundary ( SurfaceMesh & mesh )

Mark all boundary edges as features.

Returns: The number of boundary edges detected.

◆ detect_features()

size_t detect_features	(	SurfaceMesh &	mesh,
		Scalar	angle
	)

Mark edges with dihedral angle larger than angle as feature.

Returns: The number of feature edges detected.

◆ divergence_matrix()

void divergence_matrix	(	const SurfaceMesh &	mesh,
		SparseMatrix &	D
	)

Construct the cotan divergence matrix.

Matrix is sparse and maps constant gradient vectors at non-boundary halfedges to values at vertices. The discrete operators are consistent, such that Laplacian is divergence of gradient. See [18] for details on triangle meshes and [4] for details on polygon meshes.

Parameters

mesh	The input mesh.
D	The output matrix.

See also: laplace_matrix; gradient_matrix

◆ dual()

void dual ( SurfaceMesh & mesh )

Compute dual of a mesh.

Warning: Changes the mesh in place. All properties are cleared.

◆ explicit_smoothing()

void explicit_smoothing	(	SurfaceMesh &	mesh,
		unsigned int	iterations = `10`,
		bool	use_uniform_laplace = `false`
	)

Perform explicit Laplacian smoothing.

See [8] for details

Note: This algorithm works on general polygon meshes.

Parameters

mesh	The input mesh, modified in place.
iterations	The number of iterations performed.
use_uniform_laplace	Use uniform or cotan Laplacian. Default: cotan.

◆ face_area()

Scalar face_area	(	const SurfaceMesh &	mesh,
		Face	f
	)

Compute area of face f.

Computes standard area for triangles and norm of vector area for other polygons.

◆ face_normal()

Normal face_normal	(	const SurfaceMesh &	mesh,
		Face	f
	)

Compute the normal vector of face f.

Normal is computed as (normalized) sum of per-corner cross products of the two incident edges. This corresponds to the normalized vector area in [1]

Note: This algorithm works on general polygon meshes.

◆ face_normals()

void face_normals ( SurfaceMesh & mesh )

Compute face normals for the whole mesh.

Calls face_normal() for each face and adds a new face property of type Normal named "f:normal".

Note: This algorithm works on general polygon meshes.

◆ fair()

void fair	(	SurfaceMesh &	mesh,
		unsigned int	k = `2`
	)

Implicit surface fairing.

Computes a surface by solving k-harmonic equation. See also [8] .

Note: This algorithm works on general polygon meshes.

Exceptions

SolverException	in case of failure to solve the linear system
InvalidInputException	in case of missing boundary constraints

◆ fill_hole()

void fill_hole	(	SurfaceMesh &	mesh,
		Halfedge	h
	)

Fill the hole specified by halfedge h.

Close simple holes (boundary loops of manifold vertices) by first filling the hole with an angle/area-minimizing triangulation, followed by isometric remeshing, and finished by curvature-minimizing fairing of the filled-in patch. See [15] for details.

Precondition: The specified halfedge is valid.; The specified halfedge is a boundary halfedge.; The specified halfedge is not adjacent to a non-manifold hole.

Exceptions

InvalidInputException in case on of the input preconditions is violated

Note: This algorithm works on general polygon meshes.

◆ geodesics()

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.

The method works by a Dijkstra-like breadth first traversal from the seed vertices, implemented by a heap structure. See [13] for details.

Parameters

	mesh	The input mesh, modified in place.
[in]	seeds	The vector of seed vertices.
[in]	maxdist	The maximum distance up to which to compute the geodesic distances.
[in]	maxnum	The maximum number of neighbors up to which to compute the geodesic distances.
[out]	neighbors	The vector of neighbor vertices.

Returns: The number of neighbors that have been found.

Precondition: Input mesh needs to be a triangle mesh.

◆ geodesics_heat()

void geodesics_heat	(	SurfaceMesh &	mesh,
		const std::vector< Vertex > &	seeds
	)

Compute geodesic distance from a set of seed vertices.

Compute geodesic distances based on the heat method, by solving two Poisson systems. Works on general polygon meshes. See [7] for details.

Parameters

mesh	The input mesh, modified in place.
seeds	The vector of seed vertices.

Note: This algorithm works on general polygon meshes.

◆ gradient_matrix()

void gradient_matrix	(	const SurfaceMesh &	mesh,
		SparseMatrix &	G
	)

Construct the cotan gradient matrix.

Matrix is sparse and maps values at vertices to constant gradient 3D-vectors at non-boundary halfedges. The discrete operators are consistent, such that Laplacian is divergence of gradient. See [18] for details on triangle meshes and [4] for details on polygon meshes.

Parameters

mesh	The input mesh.
G	The output matrix.

See also: laplace_matrix; divergence_matrix

◆ harmonic_parameterization()

void harmonic_parameterization	(	SurfaceMesh &	mesh,
		bool	use_uniform_weights = `false`
	)

Compute discrete harmonic parameterization.

See [9] for details.

Note: This algorithm works on general polygon meshes.

Precondition: The mesh has a boundary.

Exceptions

InvalidInputException	if the input precondition is violated.
SolverException	in case of failure to solve the linear system.

Note: This algorithm works on general polygon meshes.

◆ icosphere()

SurfaceMesh icosphere ( size_t n_subdivisions = 3 )

Generate icosphere refined by n_subdivisions .

Uses Loop subdivision to refine the initial icosahedron.

◆ implicit_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.

See [8] and [12] .

Note: This algorithm works on general polygon meshes.

Parameters

mesh	The input mesh, modified in place.
timestep	The time step taken.
iterations	The number of iterations performed.
use_uniform_laplace	Use uniform or cotan Laplacian. Default: cotan.
rescale	Re-center and re-scale model after smoothing. Default: true.

Exceptions

SolverException in case of a failure to solve the linear system.

◆ laplace()

Point laplace	(	const SurfaceMesh &	mesh,
		Vertex	v
	)

compute Laplace vector for vertex v (normalized by Voronoi area)

Precondition: Input mesh needs to be a triangle mesh.

◆ laplace_matrix()

void laplace_matrix	(	const SurfaceMesh &	mesh,
		SparseMatrix &	L,
		bool	clamp = `false`
	)

Construct the cotan Laplace matrix.

Matrix is sparse, symmetric and negative semi-definite. M(i,i) is the negative valence of vertex i. M(i,j) is cotangent weight of edge (i,j). M(i,i) is negative sum of off-diagonals. The discrete operators are consistent, such that Laplacian is divergence of gradient. See [18] for details on triangle meshes and [4] for details on polygon meshes.

Parameters

mesh	The input mesh.
L	The output matrix.
clamp	Whether or not negative off-diagonal entries should be clamped to zero.

See also: gradient_matrix; divergence_matrix

◆ linear_subdivision()

void linear_subdivision ( SurfaceMesh & mesh )

Perform one step of linear quad-tri subdivision.

Suitable for mixed quad/triangle meshes.

Parameters

mesh	The input mesh, modified in place.

◆ loop_subdivision()

void loop_subdivision	(	SurfaceMesh &	mesh,
		BoundaryHandling	boundary_handling = `BoundaryHandling::Interpolate`
	)

Perform one step of Loop subdivision.

See [16] for details.

Parameters

mesh	The input mesh, modified in place.
boundary_handling	Specify to interpolate or preserve boundary edges.

Precondition: Requires a triangle mesh as input.

Exceptions

InvalidInputException in case the input violates the precondition.

◆ lscm_parameterization()

void lscm_parameterization ( SurfaceMesh & mesh )

Compute parameterization based on least squares conformal mapping.

See [17] for details.

Precondition: The mesh has a boundary.; Input mesh needs to be a triangle mesh.

Exceptions

InvalidInputException	if the input precondition is violated.
SolverException	in case of failure to solve the linear system.

◆ mass_matrix()

void mass_matrix	(	const SurfaceMesh &	mesh,
		DiagonalMatrix &	M
	)

Construct the (lumped) mass matrix for the cotangent Laplacian.

Matrix is diagonal and positive definite. M(i,i) is the (mixed) Voronoi area of vertex i. See [18] for details on triangle meshes and [4] for details on polygon meshes.

Parameters

mesh	The input mesh.
M	The output matrix.

◆ matrix_to_coordinates()

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.

Parameters

X	The input matrix.
mesh	The mesh.

◆ minimize_area()

void minimize_area ( SurfaceMesh & mesh )

Minimize surface area.

Note: This algorithm works on general polygon meshes.

See also: fair()

◆ minimize_curvature()

void minimize_curvature ( SurfaceMesh & mesh )

Minimize surface curvature.

Note: This algorithm works on general polygon meshes.

See also: fair()

◆ plane()

SurfaceMesh plane ( size_t resolution = 4 )

Generate a plane mesh.

Generates a pure quad mesh in the x-y plane with origin (0,0,0) and side length 1.

Parameters

resolution Number of faces in each direction. Needs to be >= 1. Default: 4.

◆ quad_sphere()

SurfaceMesh quad_sphere ( size_t n_subdivisions = 3 )

Generate quad sphere refined by n_subdivisions .

Uses Catmull-Clark subdivision to refine the initial hexahedron.

◆ quad_tri_subdivision()

void quad_tri_subdivision	(	SurfaceMesh &	mesh,
		BoundaryHandling	boundary_handling = `BoundaryHandling::Interpolate`
	)

Perform one step of quad-tri subdivision.

Suitable for mixed quad/triangle meshes. See [22] for details.

Parameters

mesh	The input mesh, modified in place.
boundary_handling	Specify to interpolate or preserve boundary edges.

◆ torus()

SurfaceMesh torus	(	size_t	radial_resolution = `20`,
		size_t	tubular_resolution = `40`,
		Scalar	radius = `1.0`,
		Scalar	thickness = `0.4`
	)

Generate a torus mesh.

Generates a quad mesh of a torus with its major circle in the x-y plane.

Parameters

radial_resolution	Number of subdivisions of the major circle. Needs to be >= 3. Default: 20.
tubular_resolution	Number of subdivisions of along the tube. Needs to be >= 3. Default: 40.
radius	Radius of the major circle. Default: 1.
thickness	Thickness of the tube. Default: 0.4.

◆ triangulate()

void triangulate	(	SurfaceMesh &	mesh,
		Face	f
	)

Triangulate the Face f .

Triangulate n-gons into n-2 triangles. Finds the triangulation that minimizes the sum of squared triangle areas. See [15] for details.

Precondition: The input face is manifold

Note: This algorithm works on general polygon meshes.

Exceptions

InvalidInputException in case the input precondition is violated

◆ uniform_laplace_matrix()

void uniform_laplace_matrix	(	const SurfaceMesh &	mesh,
		SparseMatrix &	L
	)

Construct the uniform Laplace matrix.

Matrix is sparse, symmetric and negative semi-definite. M(i,i) is the negative valence of vertex i. M(i,j) is +1 if vertex i and vertex j are neighbors.

Parameters

mesh	The input mesh.
L	The output matrix.

◆ uniform_mass_matrix()

void uniform_mass_matrix	(	const SurfaceMesh &	mesh,
		DiagonalMatrix &	M
	)

Construct the mass matrix for the uniform Laplacian.

Matrix is diagonal and positive definite. M(i,i) is the valence of vertex i.

Parameters

mesh	The input mesh.
M	The output matrix.

◆ uniform_remeshing()

void uniform_remeshing	(	SurfaceMesh &	mesh,
		Scalar	edge_length,
		unsigned int	iterations = `10`,
		bool	use_projection = `true`
	)

Perform uniform remeshing.

Performs incremental remeshing based on edge collapse, split, flip, and tangential relaxation. See [2] and [10] for details.

Parameters

mesh	The input mesh, modified in place.
edge_length	The target edge length.
iterations	The number of iterations
use_projection	Use back-projection to the input surface.

Precondition: Input mesh needs to be a triangle mesh.

Exceptions

InvalidInputException if the input precondition is violated.

◆ vertex_normal()

Normal vertex_normal	(	const SurfaceMesh &	mesh,
		Vertex	v
	)

Compute the normal vector of vertex v.

Note: This algorithm works on general polygon meshes.

◆ vertex_normals()

void vertex_normals ( SurfaceMesh & mesh )

Compute vertex normals for the whole mesh.

Calls vertex_normal() for each vertex and adds a new vertex property of type Normal named "v:normal".

Note: This algorithm works on general polygon meshes.

◆ volume()

Scalar volume ( const SurfaceMesh & mesh )

Compute the volume of a mesh.

See [24] for details.

Precondition: Input mesh needs to be a triangle mesh.

Exceptions

InvalidInputException if the input precondition is violated.

◆ voronoi_area_mixed()

Scalar voronoi_area_mixed	(	const SurfaceMesh &	mesh,
		Vertex	v
	)

Compute mixed Voronoi area of a vertex.

This version is preferred for irregular triangles with obtuse angles. See [18] for details.

Precondition: Input mesh needs to be a triangle mesh.

Enumerations

Functions

Detailed Description

Enumeration Type Documentation

◆ Curvature

Function Documentation

◆ adaptive_remeshing()

◆ catmull_clark_subdivision()

◆ clear_features()

◆ cone()

◆ coordinates_to_matrix()

◆ corner_normal()

◆ cotan_weight()

◆ curvature()

◆ cylinder()

◆ decimate()

◆ detect_boundary()

◆ detect_features()

◆ divergence_matrix()

◆ dual()

◆ explicit_smoothing()

◆ face_area()

◆ face_normal()

◆ face_normals()

◆ fair()

◆ fill_hole()

◆ geodesics()

◆ geodesics_heat()

◆ gradient_matrix()

◆ harmonic_parameterization()

◆ icosphere()

◆ implicit_smoothing()

◆ laplace()

◆ laplace_matrix()

◆ linear_subdivision()

◆ loop_subdivision()

◆ lscm_parameterization()

◆ mass_matrix()

◆ matrix_to_coordinates()

◆ minimize_area()

◆ minimize_curvature()

◆ plane()

◆ quad_sphere()

◆ quad_tri_subdivision()

◆ torus()

◆ triangulate()

◆ uniform_laplace_matrix()

◆ uniform_mass_matrix()

◆ uniform_remeshing()

◆ vertex_normal()

◆ vertex_normals()

◆ volume()

◆ voronoi_area_mixed()