Functions for basic geometric computations. More...

Classes
struct	VertexCurvature
	discrete curvature information for a vertex. used for vertex_curvature() More...

Functions
float	triangle_area (const SurfaceMesh *mesh, SurfaceMesh::Face f)
	compute area of triangle f

float	surface_area (const SurfaceMesh *mesh)
	surface area of the mesh (assumes triangular faces)

float	volume (const SurfaceMesh &mesh)

vec3	centroid (const SurfaceMesh *mesh, SurfaceMesh::Face f)
	barycenter/centroid of a face

vec3	centroid (const SurfaceMesh *mesh)
	barycenter/centroid of mesh, computed as area-weighted mean of vertices. More...

void	dual (SurfaceMesh *mesh)
	Compute dual of a mesh. More...

double	cotan_weight (const SurfaceMesh *mesh, SurfaceMesh::Edge e)
	compute the cotangent weight for edge e

double	voronoi_area (const SurfaceMesh *mesh, SurfaceMesh::Vertex v)
	compute (mixed) Voronoi area of vertex v

double	voronoi_area_barycentric (const SurfaceMesh *mesh, SurfaceMesh::Vertex v)
	compute barycentric Voronoi area of vertex v

vec3	laplace (const SurfaceMesh *mesh, SurfaceMesh::Vertex v)
	compute Laplace vector for vertex v (normalized by Voronoi area)

double	angle_sum (const SurfaceMesh *mesh, SurfaceMesh::Vertex v)
	compute the sum of angles around vertex v (used for Gaussian curvature)

VertexCurvature	vertex_curvature (const SurfaceMesh *mesh, SurfaceMesh::Vertex v)
	compute min, max, mean, and Gaussian curvature for vertex v. More...

float	volume (const SurfaceMesh *mesh)
	Compute the volume of a mesh. More...

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

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

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

◆ centroid()

vec3 centroid ( const SurfaceMesh * mesh )

barycenter/centroid of mesh, computed as area-weighted mean of vertices.

Note: assumes triangular faces.

◆ dual()

void dual ( SurfaceMesh * mesh )

Compute dual of a mesh.

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

◆ intersect()

bool easy3d::geom::intersect	(	const GenericPlane< FT > &	plane1,
		const GenericPlane< FT > &	plane2,
		const GenericPlane< FT > &	plane3,
		typename GenericPlane< FT >::Point3 &	point
	)

inline

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.

◆ vertex_curvature()

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

compute min, max, mean, and Gaussian curvature for vertex v.

Attention: This will not give reliable values for boundary vertices.

◆ volume()

float easy3d::geom::volume ( const SurfaceMesh * mesh )

Compute the volume of a mesh.

See [zhang_2002_efficient] for details.

Precondition: Input mesh needs to be a pure triangle mesh.

Classes