Geogram
Version 1.9.1-rc
A programming library of geometric algorithms
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Exact predicates and constructs. More...
#include <geogram/basic/common.h>
#include <geogram/basic/geometry.h>
#include <geogram/basic/vechg.h>
#include <geogram/numerics/expansion_nt.h>
#include <geogram/numerics/interval_nt.h>
#include <geogram/numerics/predicates.h>
#include <geogram/numerics/exact_geometry.h>
Go to the source code of this file.
Namespaces | |
GEO | |
Global Vorpaline 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). | |
GEO::exact | |
Exact geometric types. | |
Typedefs | |
typedef vecng< 2, expansion_nt > | GEO::vec2E |
vec2 with coordinates as expansions More... | |
typedef vecng< 3, expansion_nt > | GEO::vec3E |
vec3 with coordinates as expansions More... | |
typedef vecng< 2, interval_nt > | GEO::vec2I |
vec2 with coordinates as interval_nt More... | |
typedef vecng< 3, interval_nt > | GEO::vec3I |
vec3 with coordinates as interval_nt More... | |
typedef vec2Hg< expansion_nt > | GEO::vec2HE |
2D vector in homogeneous coordinates with coordinates as expansions More... | |
typedef vec3Hg< expansion_nt > | GEO::vec3HE |
3D vector in homogeneous coordinates with coordinates as expansions More... | |
typedef vec2Hg< interval_nt > | GEO::vec2HI |
2D vector in homogeneous coordinates with coordinates as intervals. More... | |
typedef vec3Hg< interval_nt > | GEO::vec3HI |
3D vector in homogeneous coordinates with coordinates as intervals. More... | |
typedef expansion_nt | GEO::exact::scalar |
typedef vecng< 2, scalar > | GEO::exact::vec2 |
typedef vecng< 3, scalar > | GEO::exact::vec3 |
typedef vec2Hg< scalar > | GEO::exact::vec2h |
2d vector with exact homogeneous coordinates | |
typedef vec3Hg< scalar > | GEO::exact::vec3h |
3d vector with exact homogeneous coordinates | |
typedef rationalg< scalar > | GEO::exact::rational |
rational with exact numerator and denominator | |
Functions | |
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. More... | |
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. More... | |
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. More... | |
Sign | GEO::PCK::orient_2d (const vec2HE &p0, const vec2HE &p1, const vec2HE &p2) |
Computes the orientation predicate in 2d. More... | |
Sign | GEO::PCK::orient_2d_projected (const vec3HE &p0, const vec3HE &p1, const vec3HE &p2, coord_index_t axis) |
Computes the orientation predicate in 2d projected along an axis. More... | |
Sign | GEO::PCK::orient_3d (const vec3HE &p0, const vec3HE &p1, const vec3HE &p2, const vec3HE &p3) |
Computes the orientation predicate in 3d. More... | |
Sign | GEO::PCK::dot_2d (const vec2HE &p0, const vec2HE &p1, const vec2HE &p2) |
Computes the sign of the dot product between two vectors defined by three points. More... | |
Sign | GEO::PCK::incircle_2d_SOS_with_lengths (const vec2HE &p0, const vec2HE &p1, const vec2HE &p2, const vec2HE &p3, double l0, double l1, double l2, double l3) |
Tests whether a point is in the circumscribed circle of three other points. More... | |
Sign | GEO::PCK::incircle_2d_SOS (const vec2HE &p0, const vec2HE &p1, const vec2HE &p2, const vec2HE &p3) |
Tests whether a point is in the circumscribed circle of three other points. More... | |
coord_index_t | GEO::PCK::triangle_normal_axis (const vec3 &p1, const vec3 &p2, const vec3 &p3) |
Gets the axis that is most normal to a triangle. More... | |
bool | GEO::PCK::aligned_3d (const vec3HE &p0, const vec3HE &p1, const vec3HE &p2) |
Tests whether three 3d points are aligned. More... | |
bool | GEO::PCK::on_segment_3d (const vec3HE &p, const vec3HE &q1, const vec3HE &q2) |
Tests whether a point is on a segment. More... | |
vec3 | GEO::PCK::approximate (const vec3HE &p) |
Gets a 3D floating-point approximation of a 3D point with exact coordinates. More... | |
vec2 | GEO::PCK::approximate (const vec2HE &p) |
Gets a 2D floating-point approximation of a 2D point with exact coordinates. More... | |
template<> | |
vec2E | GEO::make_vec2< vec2E > (const vec2 &p1, const vec2 &p2) |
Specialization of make_vec2() for vec2E. | |
template<> | |
vec3E | GEO::make_vec3< vec3E > (const vec3 &p1, const vec3 &p2) |
Specialization of make_vec3() for vec3E. | |
Exact predicates and constructs.
Implements vector types with expansion coordinates (vec2E, vec3E), vector types with homogeneous expansion coordinates (vec2HE, vec3HE), 2d orientation predicate, incircle predicate and constructions for intersections.
Definition in file exact_geometry.h.