exact_geometry.h File Reference

Exact predicates and constructs. More...

#include <geogram/basic/common.h>
#include <geogram/basic/geometry.h>
#include <geogram/numerics/expansion_nt.h>

Go to the source code of this file.

Classes
struct	GEO::vec2HE
	2D vector in homogeneous coordinates with coordinates as arithmetic expansions More...
struct	GEO::vec3HE
	3D vector in homogeneous coordinates with coordinates as arithmetic expansions. More...
class	GEO::vec2HELexicoCompare
	Comparator class for vec3HE \detail Used to create maps indexed by vec3HE. More...
class	GEO::vec3HELexicoCompare
	Comparator class for vec3HE \detail Used to create maps indexed by vec3HE. More...
class	GEO::vec3HEProjectedLexicoCompare
	Comparator class for projected vec3HE. More...

Namespaces
namespace	GEO
	Global Vorpaline namespace.
namespace	GEO::PCK
	PCK (Predicate Construction Kit) implements a set of geometric predicates. PCK uses arithmetic filters (Meyer and Pion), expansion arithmetics (Shewchuk) and simulation of simplicity (Edelsbrunner).

Typedefs
typedef vecng< 2, expansion_nt >	GEO::vec2E
	vec2 with coordinates as expansions
typedef vecng< 3, expansion_nt >	GEO::vec3E
	vec3 with coordinates as expansions

Functions
vec2HE	GEO::operator- (const vec2HE &p1, const vec2HE &p2)
vec3HE	GEO::operator- (const vec3HE &p1, const vec3HE &p2)
vec3HE	GEO::mix (const rational_nt &t, const vec3 &p1, const vec3 &p2)
vec2HE	GEO::mix (const rational_nt &t, const vec2HE &p1, const vec2HE &p2)
vec3HE	GEO::mix (const rational_nt &t, const vec3HE &p1, const vec3HE &p2)
template<>
expansion_nt	GEO::det (const vec2E &v1, const vec2E &v2)
	Specialization optimized using low-level API.
template<>
expansion_nt	GEO::dot (const vec2E &v1, const vec2E &v2)
	Specialization optimized using low-level API.
template<>
expansion_nt	GEO::dot (const vec3E &v1, const vec3E &v2)
	Specialization optimized using low-level API.
template<class T >
bool	GEO::PCK::same_point (const vecng< 3, T > &v1, const vecng< 3, T > &v2)
template<class T >
bool	GEO::PCK::same_point (const vecng< 2, T > &v1, const vecng< 2, T > &v2)
bool	GEO::PCK::same_point (const vec2HE &v1, const vec2HE &v2)
bool	GEO::PCK::same_point (const vec3HE &v1, const vec3HE &v2)
Sign	GEO::PCK::orient_2d (const vec2HE &p0, const vec2HE &p1, const vec2HE &p2)
Sign	GEO::PCK::orient_2d_projected (const vec3HE &p0, const vec3HE &p1, const vec3HE &p2, coord_index_t axis)
Sign	GEO::PCK::orient_3d (const vec3HE &p0, const vec3HE &p1, const vec3HE &p2, const vec3HE &p3)
Sign	GEO::PCK::dot_2d (const vec2HE &p0, const vec2HE &p1, const vec2HE &p2)
Sign	GEO::PCK::orient_2dlifted_SOS (const vec2HE &p0, const vec2HE &p1, const vec2HE &p2, const vec2HE &p3, double h0, double h1, double h2, double h3)
	Computes the 3d orientation test with lifted points.
Sign	GEO::PCK::orient_2dlifted_SOS_projected (const vec3HE &p0, const vec3HE &p1, const vec3HE &p2, const vec3HE &p3, double h0, double h1, double h2, double h3, coord_index_t axis)
template<class VEC3 >
VEC3	GEO::make_vec3 (const vec3 &p)
	Converts a 3d vector with double coordinates into a 3d vector with coordinates of arbitrary type.
template<class VEC3 = vec3>
VEC3	GEO::make_vec3 (const vec3 &p1, const vec3 &p2)
	Creates a vector with coordinates of arbitrary type from two points with double coordinates.
template<>
vec3E	GEO::make_vec3< vec3E > (const vec3 &p1, const vec3 &p2)
	Specialization for vec3E.
template<class VEC2 >
VEC2	GEO::make_vec2 (const vec2 &p1, const vec2 &p2)
	Creates a vector with coordinates of arbitrary type from two points with double coordinates.
template<>
vec2E	GEO::make_vec2< vec2E > (const vec2 &p1, const vec2 &p2)
	Specialization for vec2E.
template<class VEC3 >
VEC3	GEO::triangle_normal (const vec3 &p1, const vec3 &p2, const vec3 &p3)
	Computes the normal to a triangle from its three vertices.
template<>
vec3E	GEO::triangle_normal< vec3E > (const vec3 &p1, const vec3 &p2, const vec3 &p3)
	Specialization for vec3E.
bool	GEO::get_three_planes_intersection (vec3HE &result, const vec3 &p1, const vec3 &p2, const vec3 &p3, const vec3 &q1, const vec3 &q2, const vec3 &q3, const vec3 &r1, const vec3 &r2, const vec3 &r3)
	Computes the exact intersection between the support planes of three triangles.
vec3HE	GEO::plane_line_intersection (const vec3 &p1, const vec3 &p2, const vec3 &p3, const vec3 &q1, const vec3 &q2)
	Computes the exact intersection between the support plane of a triangle and the support line of a segment.
coord_index_t	GEO::triangle_normal_axis_exact (const vec3 &p1, const vec3 &p2, const vec3 &p3)
	Finds an axis along which a triangle can be projected without degeneracy.

Detailed Description

Exact predicates and constructs.

Implements vector types with expansion coordinates (vec2E, vec3E), vector types with homogeneous expansion coordinates (vec2HE, vec3HE), 2d orientation predicate, 3d-lifted orientation predicate (can be used to implement incircle), and constructions for intersections.

Definition in file exact_geometry.h.