geometry.h File Reference

Geometric functions in 2d and 3d. More...

#include <geogram/basic/common.h>
#include <geogram/basic/matrix.h>

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
namespace	GEO
	Global Vorpaline namespace.
namespace	GEO::Geom
	Geometric functions and utilities.

Typedefs
typedef vecng< 2, Numeric::float64 >	GEO::vec2
	Represents points and vectors in 2d.
typedef vecng< 3, Numeric::float64 >	GEO::vec3
	Represents points and vectors in 3d.
typedef vecng< 4, Numeric::float64 >	GEO::vec4
	Represents points and vectors in 4d.
typedef vecng< 2, Numeric::float32 >	GEO::vec2f
	Represents points and vectors in 2d with single-precision coordinates.
typedef vecng< 3, Numeric::float32 >	GEO::vec3f
	Represents points and vectors in 3d with single-precision coordinates.
typedef vecng< 4, Numeric::float32 >	GEO::vec4f
	Represents points and vectors in 4d with single-precision coordinates.
typedef vecng< 2, Numeric::int32 >	GEO::vec2i
	Represents points and vectors in 2d with integer coordinates.
typedef vecng< 3, Numeric::int32 >	GEO::vec3i
	Represents points and vectors in 3d with integer coordinates.
typedef vecng< 4, Numeric::int32 >	GEO::vec4i
	Represents points and vectors in 4d with integer coordinates.
typedef vecng< 2, Numeric::uint32 >	GEO::vec2u
	Represents points and vectors in 2d with unsigned integer coordinates.
typedef vecng< 3, Numeric::uint32 >	GEO::vec3u
	Represents points and vectors in 3d with unsigned integer coordinates.
typedef vecng< 4, Numeric::uint32 >	GEO::vec4u
	Represents points and vectors in 4d with unsigned integer coordinates.
typedef Matrix< 2, Numeric::float64 >	GEO::mat2
	Represents a 2x2 matrix.
typedef Matrix< 3, Numeric::float64 >	GEO::mat3
	Represents a 3x3 matrix.
typedef Matrix< 4, Numeric::float64 >	GEO::mat4
	Represents a 4x4 matrix.
typedef Box	GEO::Box3d

Functions
double	GEO::det (const mat2 &M)
	Computes the determinant of a 2x2 matrix.
vec3	GEO::Geom::barycenter (const vec3 &p1, const vec3 &p2)
	Computes the barycenter of two points in 3d.
vec3	GEO::Geom::barycenter (const vec3 &p1, const vec3 &p2, const vec3 &p3)
	Computes the barycenter of three points in 3d.
double	GEO::Geom::cos_angle (const vec3 &a, const vec3 &b)
	Computes the cosine of the angle between two 3d vectors.
double	GEO::Geom::angle (const vec3 &a, const vec3 &b)
	Computes the angle between two 3d vectors.
double	GEO::Geom::det (const vec2 &a, const vec2 &b)
	Computes the determinant of two vectors.
vec3	GEO::Geom::triangle_normal (const vec3 &p1, const vec3 &p2, const vec3 &p3)
	Computes the normal of a 3d triangle.
double	GEO::Geom::triangle_area_3d (const double *p1, const double *p2, const double *p3)
	Computes the area of a 3d triangle.
double	GEO::Geom::triangle_area (const vec3 &p1, const vec3 &p2, const vec3 &p3)
	Computes the area of a 3d triangle.
double	GEO::Geom::triangle_signed_area_2d (const double *p1, const double *p2, const double *p3)
	Computes the area of a 2d triangle.
double	GEO::Geom::triangle_signed_area (const vec2 &p1, const vec2 &p2, const vec2 &p3)
	Computes the area of a 2d triangle.
double	GEO::Geom::triangle_area_2d (const double *p1, const double *p2, const double *p3)
	Computes the area of a 2d triangle.
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.
bool	GEO::Geom::has_nan (const vec3 &v)
	Tests whether a 3d vector has a NaN (not a number) coordinate.
vec3	GEO::Geom::perpendicular (const vec3 &V)
	Computes a 3d vector orthogonal to another one.
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.
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.
double	GEO::Geom::tetra_volume (const vec3 &p1, const vec3 &p2, const vec3 &p3, const vec3 &p4)
	Computes the volume of a 3d tetrahedron.
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.
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.
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.
vec3	GEO::Geom::random_point_in_triangle (const vec3 &p1, const vec3 &p2, const vec3 &p3)
	Generates a random point in a 3d triangle.
bool	GEO::bboxes_overlap (const Box &B1, const Box &B2)
	Tests whether two Boxes have a non-empty intersection.
void	GEO::bbox_union (Box &target, const Box &B1, const Box &B2)
	Computes the smallest Box that encloses two Boxes.
bool	GEO::bboxes_overlap (const Box2d &B1, const Box2d &B2)
	Tests whether two Box2d have a non-empty intersection.
void	GEO::bbox_union (Box2d &target, const Box2d &B1, const Box2d &B2)
	Computes the smallest Box2d that encloses two Box2d.
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.
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.
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.
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.
mat4	GEO::create_translation_matrix (const vec3 &T)
	Creates a translation matrix from a vector.
mat4	GEO::create_scaling_matrix (double s)
	Creates a scaling matrix.

Detailed Description

Geometric functions in 2d and 3d.

Definition in file geometry.h.