easy3d::geom Namespace Reference

Functions for basic geometric computations. More...

Classes
struct	VertexCurvature
	Discrete curvature information for a vertex. More...

Functions
float	triangle_area (const SurfaceMesh *mesh, SurfaceMesh::Face f)
	Compute the area of a triangle face in a mesh.
float	surface_area (const SurfaceMesh *mesh)
	Compute the surface area of the mesh.
float	volume (const SurfaceMesh *mesh)
	Compute the volume of a mesh.
vec3	centroid (const SurfaceMesh *mesh, SurfaceMesh::Face f)
	Compute the barycenter/centroid of a face.
vec3	centroid (const SurfaceMesh *mesh)
	Compute the barycenter/centroid of the mesh.
void	dual (SurfaceMesh *mesh)
	Compute the dual of a mesh.
double	cotan_weight (const SurfaceMesh *mesh, SurfaceMesh::Edge e)
	Compute the cotangent weight for an edge.
double	voronoi_area (const SurfaceMesh *mesh, SurfaceMesh::Vertex v)
	Compute the (mixed) Voronoi area of a vertex.
double	voronoi_area_barycentric (const SurfaceMesh *mesh, SurfaceMesh::Vertex v)
	Compute the barycentric Voronoi area of a vertex.
vec3	laplace (const SurfaceMesh *mesh, SurfaceMesh::Vertex v)
	Compute the Laplace vector for a vertex.
double	angle_sum (const SurfaceMesh *mesh, SurfaceMesh::Vertex v)
	Compute the sum of angles around a vertex.
VertexCurvature	vertex_curvature (const SurfaceMesh *mesh, SurfaceMesh::Vertex v)
	Compute min, max, mean, and Gaussian curvature for a vertex.
template<int DIM, typename FT>
GenericBox< DIM, FT >	box_union (GenericBox< DIM, FT > const &a, GenericBox< DIM, FT > const &b)
	Compute the union of two boxes.
template<int DIM, typename FT>
GenericBox< DIM, FT >	box_intersection (GenericBox< DIM, FT > const &a, GenericBox< DIM, FT > const &b)
	Compute the intersection of two boxes.
template<typename FT>
bool	intersect (const GenericPlane< FT > &plane1, const GenericPlane< FT > &plane2, const GenericPlane< FT > &plane3, typename GenericPlane< FT >::Point3 &point)
vec3	orthogonal (const vec3 &v)
	Returns a vector orthogonal to v. Its norm() depends on v, but is zero only for a null v.
template<typename Box, typename Container>
Box	bounding_box (const Container &points)
	Computes the bounding box of a set of points.
template<typename Vec, typename Container>
Vec	centroid (const Container &points)
	Computes the centroid of a set of points.
template<typename Vec>
Vec	barycenter (const Vec &p1, const Vec &p2)
	Computes the barycenter of two points.
template<typename Vec>
Vec	barycenter (const Vec &p1, const Vec &p2, const Vec &p3)
	Computes the barycenter of three points.
template<typename Vec>
Vec	barycenter (const Vec &p1, const Vec &p2, const Vec &p3, const Vec &p4)
	Computes the barycenter of four points.
template<typename FT>
Vec< 3, FT >	barycentric_coordinates (const Vec< 3, FT > &p, const Vec< 3, FT > &u, const Vec< 3, FT > &v, const Vec< 3, FT > &w)
	Computes the barycentric coordinates of a point p with respect to three points u, v, and w.
bool	point_in_polygon (const vec2 &p, const std::vector< vec2 > &polygon)
	Tests if a point p lies inside or outside of a polygon. This function is robust to handle general polygons (no matter convex or concave).
double	clamp_cot (const double v)
	Clamps cotangent values as if angles are in [1, 179].
double	clamp_cos (const double v)
	Clamps cosine values as if angles are in [1, 179].
template<typename Vec>
double	cos_angle (const Vec &a, const Vec &b)
	Computes cosine of angle between two (un-normalized) vectors.
template<typename Vec>
double	sin_angle (const Vec &a, const Vec &b)
	Computes sine of angle between two (un-normalized) vectors.
template<typename Vec>
Vec::FT	cotan_angle (const Vec &a, const Vec &b)
	Computes cotangent of angle between two (un-normalized) vectors.
template<typename Vec>
double	angle (const Vec &a, const Vec &b)
	Computes angle between two (un-normalized) vectors.
template<typename FT>
FT	to_radians (FT degrees)
	Converts an angle from degrees to radians.
template<typename FT>
FT	to_degrees (FT radians)
	Converts an angle from radians to degrees.
float	triangle_area (const vec3 &p1, const vec3 &p2, const vec3 &p3)
	Computes area of a triangle given by three points.
float	triangle_signed_area (const vec2 &p1, const vec2 &p2, const vec2 &p3)
	Computes signed area of a triangle given by three points.
vec3	triangle_normal (const vec3 &p1, const vec3 &p2, const vec3 &p3)
	Computes the normal vector of a triangle given by three points.
float	dist_point_line_segment (const vec3 &p, const vec3 &v0, const vec3 &v1, vec3 &nearest_point)
	Computes the distance of a point p to a line segment given by vec3s (v0,v1).
float	dist_point_triangle (const vec3 &p, const vec3 &v0, const vec3 &v1, const vec3 &v2, vec3 &nearest_point)
	Computes the distance of a point p to the triangle given by vec3s (v0, v1, v2).
vec3	tetra_circum_center (const vec3 &p, const vec3 &q, const vec3 &r, const vec3 &s)
	Computes the circum center of a tetrahedron.

Detailed Description

Functions for basic geometric computations.

Function Documentation

angle_sum()

double angle_sum	(	const SurfaceMesh *	mesh,
		SurfaceMesh::Vertex	v )

Compute the sum of angles around a vertex.

Used for Gaussian curvature.

Parameters

mesh	The surface mesh containing the vertex.
v	The vertex for which to compute the angle sum.

Returns

The sum of angles around the vertex.

box_intersection()

template<int DIM, typename FT>

GenericBox< DIM, FT > box_intersection	(	GenericBox< DIM, FT > const &	a,
		GenericBox< DIM, FT > const &	b )

Compute the intersection of two boxes.

Template Parameters

DIM	The dimension.
FT	The floating point type.

Parameters

a	The first box.
b	The second box.

Returns

The resulting intersection box.

box_union()

template<int DIM, typename FT>

GenericBox< DIM, FT > box_union	(	GenericBox< DIM, FT > const &	a,
		GenericBox< DIM, FT > const &	b )

Compute the union of two boxes.

Template Parameters

DIM	The dimension.
FT	The floating point type.

Parameters

a	The first box.
b	The second box.

Returns

The resulting union box.

centroid() [1/2]

vec3 centroid

(

const SurfaceMesh *

mesh

)

Compute the barycenter/centroid of the mesh.

Computed as the area-weighted mean of vertices. Assumes triangular faces.

Parameters

mesh	The surface mesh for which to compute the centroid.

Returns

The centroid of the mesh.

centroid() [2/2]

vec3 centroid	(	const SurfaceMesh *	mesh,
		SurfaceMesh::Face	f )

Compute the barycenter/centroid of a face.

Parameters

mesh	The surface mesh containing the face.
f	The face for which to compute the centroid.

Returns

The centroid of the face.

cotan_weight()

double cotan_weight	(	const SurfaceMesh *	mesh,
		SurfaceMesh::Edge	e )

Compute the cotangent weight for an edge.

Parameters

mesh	The surface mesh containing the edge.
e	The edge for which to compute the cotangent weight.

Returns

The cotangent weight of the edge.

dual()

void dual

(

SurfaceMesh *

mesh

)

Compute the dual of a mesh.

Warning

Changes the mesh in place. All properties are cleared.

Parameters

mesh	The surface mesh for which to compute the dual.

intersect()

template<typename FT>

bool intersect	(	const GenericPlane< FT > &	plane1,
		const GenericPlane< FT > &	plane2,
		const GenericPlane< FT > &	plane3,
		typename GenericPlane< FT >::Point3 &	point )

Check if three planes intersect. Returns false if one of the planes is parallel to any of the others.

Parameters

plane1	The first plane.
plane2	The second plane.
plane3	The third plane.
point	The intersecting point.

Note

The intersecting point is valid only if the function returns true.

Returns

true if the three planes intersect at a point.

laplace()

vec3 laplace	(	const SurfaceMesh *	mesh,
		SurfaceMesh::Vertex	v )

Compute the Laplace vector for a vertex.

Normalized by the Voronoi area.

Parameters

mesh	The surface mesh containing the vertex.
v	The vertex for which to compute the Laplace vector.

Returns

The Laplace vector of the vertex.

surface_area()

float surface_area

(

const SurfaceMesh *

mesh

)

Compute the surface area of the mesh.

Precondition

The input mesh needs to be a pure triangle mesh.

Parameters

mesh	The surface mesh for which to compute the surface area.

Returns

The surface area of the mesh.

triangle_area()

float triangle_area	(	const SurfaceMesh *	mesh,
		SurfaceMesh::Face	f )

Compute the area of a triangle face in a mesh.

Parameters

mesh	The surface mesh containing the face.
f	The face for which to compute the area.

Returns

The area of the triangle face.

vertex_curvature()

VertexCurvature vertex_curvature	(	const SurfaceMesh *	mesh,
		SurfaceMesh::Vertex	v )

Compute min, max, mean, and Gaussian curvature for a vertex.

Attention

This will not give reliable values for boundary vertices.

Parameters

mesh	The surface mesh containing the vertex.
v	The vertex for which to compute the curvature.

Returns

The curvature information of the vertex.

volume()

float volume

(

const SurfaceMesh *

mesh

)

Compute the volume of a mesh.

See "Zhang and Chen. Efficient feature extraction for 2D/3D objects in mesh representation. 2021".

Precondition

The input mesh needs to be a pure triangle mesh and must be closed.

Parameters

mesh	The surface mesh for which to compute the volume.

Returns

The volume of the mesh.

voronoi_area()

double voronoi_area	(	const SurfaceMesh *	mesh,
		SurfaceMesh::Vertex	v )

Compute the (mixed) Voronoi area of a vertex.

Parameters

mesh	The surface mesh containing the vertex.
v	The vertex for which to compute the Voronoi area.

Returns

The Voronoi area of the vertex.

voronoi_area_barycentric()

double voronoi_area_barycentric	(	const SurfaceMesh *	mesh,
		SurfaceMesh::Vertex	v )

Compute the barycentric Voronoi area of a vertex.

Parameters

mesh	The surface mesh containing the vertex.
v	The vertex for which to compute the barycentric Voronoi area.

Returns

The barycentric Voronoi area of the vertex.