Geogram
Version 1.9.1
A programming library of geometric algorithms
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Geometric functions in 2d and 3d. More...
Go to the source code of this file.
Classes | |
struct | GEO::Plane |
A 3D Plane. More... | |
class | GEO::Box |
Axis-aligned bounding box. More... | |
class | GEO::Box2d |
Axis-aligned bounding box. More... | |
struct | GEO::Ray |
A Ray, in parametric form. More... | |
Namespaces | |
GEO | |
Global Vorpaline namespace. | |
GEO::Geom | |
Geometric functions and utilities. | |
Typedefs | |
typedef vecng< 2, Numeric::float64 > | GEO::vec2 |
Represents points and vectors in 2d. More... | |
typedef vecng< 3, Numeric::float64 > | GEO::vec3 |
Represents points and vectors in 3d. More... | |
typedef vecng< 4, Numeric::float64 > | GEO::vec4 |
Represents points and vectors in 4d. More... | |
typedef vecng< 2, Numeric::float32 > | GEO::vec2f |
Represents points and vectors in 2d with single-precision coordinates. More... | |
typedef vecng< 3, Numeric::float32 > | GEO::vec3f |
Represents points and vectors in 3d with single-precision coordinates. More... | |
typedef vecng< 4, Numeric::float32 > | GEO::vec4f |
Represents points and vectors in 4d with single-precision coordinates. More... | |
typedef vecng< 2, Numeric::int32 > | GEO::vec2i |
Represents points and vectors in 2d with integer coordinates. More... | |
typedef vecng< 4, Numeric::int32 > | GEO::vec4i |
Represents points and vectors in 4d with integer coordinates. More... | |
typedef Matrix< 2, Numeric::float64 > | GEO::mat2 |
Represents a 2x2 matrix. More... | |
typedef Matrix< 3, Numeric::float64 > | GEO::mat3 |
Represents a 3x3 matrix. More... | |
typedef Matrix< 4, Numeric::float64 > | GEO::mat4 |
Represents a 4x4 matrix. More... | |
typedef Box | GEO::Box3d |
Functions | |
double | GEO::det (const mat2 &M) |
Computes the determinant of a 2x2 matrix. More... | |
vec3 | GEO::Geom::barycenter (const vec3 &p1, const vec3 &p2) |
Computes the barycenter of two points in 3d. More... | |
vec3 | GEO::Geom::barycenter (const vec3 &p1, const vec3 &p2, const vec3 &p3) |
Computes the barycenter of three points in 3d. More... | |
double | GEO::Geom::cos_angle (const vec3 &a, const vec3 &b) |
Computes the cosine of the angle between two 3d vectors. More... | |
double | GEO::Geom::angle (const vec3 &a, const vec3 &b) |
Computes the angle between two 3d vectors. More... | |
double | GEO::Geom::det (const vec2 &a, const vec2 &b) |
Computes the determinant of two vectors. More... | |
vec3 | GEO::Geom::triangle_normal (const vec3 &p1, const vec3 &p2, const vec3 &p3) |
Computes the normal of a 3d triangle. More... | |
double | GEO::Geom::triangle_area_3d (const double *p1, const double *p2, const double *p3) |
Computes the area of a 3d triangle. More... | |
double | GEO::Geom::triangle_area (const vec3 &p1, const vec3 &p2, const vec3 &p3) |
Computes the area of a 3d triangle. More... | |
double | GEO::Geom::triangle_signed_area_2d (const double *p1, const double *p2, const double *p3) |
Computes the area of a 2d triangle. More... | |
double | GEO::Geom::triangle_signed_area (const vec2 &p1, const vec2 &p2, const vec2 &p3) |
Computes the area of a 2d triangle. More... | |
double | GEO::Geom::triangle_area_2d (const double *p1, const double *p2, const double *p3) |
Computes the area of a 2d triangle. More... | |
vec2 | GEO::Geom::triangle_circumcenter (const vec2 &p1, const vec2 &p2, const vec2 &p3) |
Computes the center of the circumscribed circle of a 2d triangle. More... | |
bool | GEO::Geom::has_nan (const vec3 &v) |
Tests whether a 3d vector has a NaN (not a number) coordinate. More... | |
vec3 | GEO::Geom::perpendicular (const vec3 &V) |
Computes a 3d vector orthogonal to another one. More... | |
double | GEO::Geom::tetra_signed_volume (const vec3 &p1, const vec3 &p2, const vec3 &p3, const vec3 &p4) |
Computes the signed volume of a 3d tetrahedron. More... | |
double | GEO::Geom::tetra_signed_volume (const double *p1, const double *p2, const double *p3, const double *p4) |
Computes the signed volume of a 3d tetrahedron. More... | |
double | GEO::Geom::tetra_volume (const vec3 &p1, const vec3 &p2, const vec3 &p3, const vec3 &p4) |
Computes the volume of a 3d tetrahedron. More... | |
vec3 | GEO::Geom::tetra_circum_center (const vec3 &p1, const vec3 &p2, const vec3 &p3, const vec3 &p4) |
Computes the center of the circumscribed sphere of 3d tetrahedron. More... | |
void | GEO::Geom::triangle_centroid (const vec3 &p, const vec3 &q, const vec3 &r, double a, double b, double c, vec3 &Vg, double &V) |
Computes the centroid of a 3d triangle with weighted points. More... | |
double | GEO::Geom::triangle_mass (const vec3 &p, const vec3 &q, const vec3 &r, double a, double b, double c) |
Computes the mass of a 3d triangle with weighted points. More... | |
vec3 | GEO::Geom::random_point_in_triangle (const vec3 &p1, const vec3 &p2, const vec3 &p3) |
Generates a random point in a 3d triangle. More... | |
bool | GEO::bboxes_overlap (const Box &B1, const Box &B2) |
Tests whether two Boxes have a non-empty intersection. More... | |
void | GEO::bbox_union (Box &target, const Box &B1, const Box &B2) |
Computes the smallest Box that encloses two Boxes. More... | |
bool | GEO::bboxes_overlap (const Box2d &B1, const Box2d &B2) |
Tests whether two Box2d have a non-empty intersection. More... | |
void | GEO::bbox_union (Box2d &target, const Box2d &B1, const Box2d &B2) |
Computes the smallest Box2d that encloses two Box2d. More... | |
template<class FT > | |
vecng< 3, FT > | GEO::transform_vector (const vecng< 3, FT > &v, const Matrix< 4, FT > &m) |
Applies a 3d transform to a 3d vector. More... | |
template<class FT > | |
vecng< 3, FT > | GEO::transform_point (const vecng< 3, FT > &v, const Matrix< 4, FT > &m) |
Applies a 3d transform to a 3d point. More... | |
template<class FT > | |
vecng< 3, FT > | GEO::transform_point (const Matrix< 4, FT > &m, const vecng< 3, FT > &v) |
Applies a 3d transform to a 3d point. More... | |
template<class FT > | |
vecng< 4, FT > | GEO::transform_vector (const vecng< 4, FT > &v, const Matrix< 4, FT > &m) |
Applies a 4d transform to a 4d point. More... | |
mat4 | GEO::create_translation_matrix (const vec3 &T) |
Creates a translation matrix from a vector. More... | |
mat4 | GEO::create_scaling_matrix (double s) |
Creates a scaling matrix. More... | |
Geometric functions in 2d and 3d.
Definition in file geometry.h.