Geometric algorithms. More...

Namespaces
	mc
	Marching cubes (MC) algorithm functions and constants.

	primitives

	sdf
	Signed distance functions.

	solid_angle
	Solid angle functions.

Classes
class	brep_attribute_map
	Maps names to B-rep attributes. More...

class	brep_attribute_base
	Abstract base class for B-rep element attributes. More...

class	brep_attribute
	Per-element B-rep data. More...

class	brep_element_container
	Container for B-rep elements. More...

class	brep_edge_loop_list
	List of B-rep loops that share a common edge. More...

class	brep_edge
	Curve segment bounded by two vertices. More...

class	brep_edge_container
	B-rep edge container. More...

class	brep_face_loop_list
	List of B-rep loops that bound a common face. More...

class	brep_face
	Portion of a shell bounded by loops. More...

class	brep_face_container
	B-rep face container. More...

class	brep_loop
	Connected boundary of a single face. More...

class	brep_loop_container
	B-rep loop container. More...

class	brep_mesh
	Boundary representation (B-rep) of a mesh. More...

class	brep_vertex_edge_list
	List of B-rep edges bounded by a common vertex. More...

class	brep_vertex
	A point in space. More...

class	brep_vertex_container
	B-rep vertex container. More...

struct	bvh_node
	Single node in a bounding volume hierarchy. More...

struct	bvh_primitive
	BVH primitive. More...

class	bvh
	Bounding volume hierarchy (BVH). More...

class	hyperoctree
	Hashed linear hyperoctree. More...

struct	rect_pack_node
	Node used in 2D rectangle packing. More...

class	rect_pack
	Packs 2D rectangles. More...

Typedefs
template<std::unsigned_integral T, std::size_t N>
using	unordered_hyperoctree = hyperoctree< T, N, hyperoctree_order::unordered >
	Hyperoctree with unordered node storage and traversal. More...

template<std::unsigned_integral T, hyperoctree_order Order>
using	octree = hyperoctree< T, 3, Order >
	An octree, or 3-dimensional hyperoctree. More...

template<hyperoctree_order Order>
using	octree8 = octree< std::uint8_t, Order >
	Octree with an 8-bit node type (2 depth levels). More...

template<hyperoctree_order Order>
using	octree16 = octree< std::uint16_t, Order >
	Octree with a 16-bit node type (4 depth levels). More...

template<hyperoctree_order Order>
using	octree32 = octree< std::uint32_t, Order >
	Octree with a 32-bit node type (9 depth levels). More...

template<hyperoctree_order Order>
using	octree64 = octree< std::uint64_t, Order >
	Octree with a 64-bit node type (19 depth levels). More...

template<std::unsigned_integral T>
using	unordered_octree = octree< T, hyperoctree_order::unordered >
	Octree with unordered node storage and traversal. More...

typedef unordered_octree< std::uint8_t >	unordered_octree8
	Unordered octree with an 8-bit node type (2 depth levels). More...

typedef unordered_octree< std::uint16_t >	unordered_octree16
	Unordered octree with a 16-bit node type (4 depth levels). More...

typedef unordered_octree< std::uint32_t >	unordered_octree32
	Unordered octree with a 32-bit node type (9 depth levels). More...

typedef unordered_octree< std::uint64_t >	unordered_octree64
	Unordered octree with a 64-bit node type (19 depth levels). More...

template<std::unsigned_integral T, hyperoctree_order Order>
using	quadtree = hyperoctree< T, 2, Order >
	A quadtree, or 2-dimensional hyperoctree. More...

template<hyperoctree_order Order>
using	quadtree8 = quadtree< std::uint8_t, Order >
	Quadtree with an 8-bit node type (2 depth levels). More...

template<hyperoctree_order Order>
using	quadtree16 = quadtree< std::uint16_t, Order >
	Quadtree with a 16-bit node type (6 depth levels). More...

template<hyperoctree_order Order>
using	quadtree32 = quadtree< std::uint32_t, Order >
	Quadtree with a 32-bit node type (13 depth levels). More...

template<hyperoctree_order Order>
using	quadtree64 = quadtree< std::uint64_t, Order >
	Quadtree with a 64-bit node type (29 depth levels). More...

template<std::unsigned_integral T>
using	unordered_quadtree = quadtree< T, hyperoctree_order::unordered >
	Quadtree with unordered node storage and traversal. More...

typedef unordered_quadtree< std::uint8_t >	unordered_quadtree8
	Unordered quadtree with an 8-bit node type (2 depth levels). More...

typedef unordered_quadtree< std::uint16_t >	unordered_quadtree16
	Unordered quadtree with a 16-bit node type (6 depth levels). More...

typedef unordered_quadtree< std::uint32_t >	unordered_quadtree32
	Unordered quadtree with a 32-bit node type (13 depth levels). More...

typedef unordered_quadtree< std::uint64_t >	unordered_quadtree64
	Unordered quadtree with a 64-bit node type (29 depth levels). More...

Enumerations
enum class	triangle_region : std::uint8_t { abc = 0b000 , ab = 0b100 , bc = 0b001 , ca = 0b010 , a = 0b110 , b = 0b101 , c = 0b011 }
	Voronoi regions of a triangle. More...

enum class	hyperoctree_order { unordered , dfs_pre , bfs }
	Orders in which hyperoctree nodes can be stored and traversed. More...

Functions
void	generate_face_normals (brep_mesh &mesh)
	Generates the math::fvec3 face attribute "normal" for a B-rep mesh. More...

void	generate_vertex_normals (brep_mesh &mesh)
	Generates the math::fvec3 vertex attribute "normal" for a B-rep mesh. More...

void	generate_loop_barycentric (brep_mesh &mesh)
	Generates the math::fvec3 loop attribute "barycentric" for a B-rep mesh. More...

std::unique_ptr< render::model >	generate_model (const brep_mesh &mesh, std::shared_ptr< render::material > material=nullptr)
	Generates a model from a B-rep mesh. More...

template<class T , std::size_t N>
constexpr point< T, N >	closest_point (const ray< T, N > &a, const point< T, N > &b) noexcept
	Calculates the closest point on a ray to a point. More...

template<class T , std::size_t N>
constexpr point< T, N >	closest_point (const line_segment< T, N > &ab, const point< T, N > &c) noexcept
	Calculates the closest point on a line segment to a point. More...

template<class T , std::size_t N>
constexpr std::tuple< point< T, N >, point< T, N > >	closest_point (const line_segment< T, N > &ab, const line_segment< T, N > &cd) noexcept
	Calculates the closest points on two line segments. More...

template<class T , std::size_t N>
constexpr point< T, N >	closest_point (const hyperplane< T, N > &a, const point< T, N > &b) noexcept
	Calculates the closest point on a hyperplane to a point. More...

template<class T , std::size_t N>
point< T, N >	closest_point (const hypersphere< T, N > &a, const point< T, N > &b)
	Calculates the closest point on or in a hypersphere to a point. More...

template<class T , std::size_t N>
point< T, N >	closest_point (const hypercapsule< T, N > &a, const point< T, N > &b)
	Calculates the closest point on or in a hypercapsule to a point. More...

template<class T , std::size_t N>
constexpr point< T, N >	closest_point (const hyperrectangle< T, N > &a, const point< T, N > &b) noexcept
	Calculates the closest point on or in a hyperrectangle to a point. More...

constexpr bool	is_face_region (triangle_region region) noexcept
	Checks whether a triangle voronoi region is a face region. More...

constexpr bool	is_edge_region (triangle_region region) noexcept
	Checks whether a triangle voronoi region is an edge region. More...

constexpr bool	is_vertex_region (triangle_region region) noexcept
	Checks whether a triangle voronoi region is a vertex region. More...

constexpr std::uint8_t	edge_index (triangle_region region) noexcept
	Returns the edge index of an edge region. More...

constexpr std::uint8_t	vertex_index (triangle_region region) noexcept
	Returns the vertex index of a vertex region. More...

template<class T >
constexpr triangle_region	barycentric_to_region (const point< T, 3 > &p) noexcept
	Classifies barycentric coordinates according to their Voronoi region. More...

template<class T >
constexpr point< T, 3 >	barycentric_to_cartesian (const point< T, 3 > &p, const point< T, 3 > &a, const point< T, 3 > &b, const point< T, 3 > &c) noexcept
	Converts Cartesian coordinates to barycentric coordinates. More...

template<class T >
constexpr point< T, 3 >	cartesian_to_barycentric (const point< T, 3 > &p, const point< T, 3 > &a, const point< T, 3 > &b, const point< T, 3 > &c) noexcept
	Converts Cartesian coordinates to barycentric coordinates. More...

template<class T >
point< T, 3 >	cartesian_to_spherical (const point< T, 3 > &p)
	Converts Cartesian (rectangular) coordinates to spherical coordinates. More...

template<class T >
point< T, 3 >	spherical_to_cartesian (const point< T, 3 > &p)
	Converts spherical coordinates to Cartesian (rectangular) coordinates. More...

template<class T , std::size_t N>
std::optional< std::tuple< T, T > >	intersection (const ray< T, N > &ray, const hypersphere< T, N > &hypersphere) noexcept
	Ray-hypersphere intersection test. More...

template<class T , std::size_t N>
constexpr bool	intersection (const hyperrectangle< T, N > &a, const hyperrectangle< T, N > &b) noexcept
	Hyperrectangle-hyperrectangle intersection test. More...

template<class T , std::size_t N>
constexpr bool	intersection (const hypersphere< T, N > &a, const hypersphere< T, N > &b) noexcept
	Hypersphere-hypersphere intersection test. More...

template<std::unsigned_integral T>
constexpr T	morton_encode (T x, T y) noexcept
	Encodes 2D coordinates as a Morton location code. More...

template<std::unsigned_integral T>
constexpr T	morton_encode (T x, T y, T z) noexcept
	Encodes 3D coordinates as a Morton location code. More...

template<std::unsigned_integral T>
void	morton_decode (T code, T &x, T &y) noexcept
	Decodes 2D coordinates from a Morton location code. More...

template<std::unsigned_integral T>
void	morton_decode (T code, T &x, T &y, T &z) noexcept
	Decodes 3D coordinates from a Morton location code. More...

template<class T >
math::vec3< T >	project_on_plane (const math::vec3< T > &v, const math::vec3< T > &p, const math::vec3< T > &n)


template<class T >
constexpr std::tuple< point< T, 3 >, triangle_region >	closest_point (const point< T, 3 > &a, const point< T, 3 > &b, const point< T, 3 > &c, const point< T, 3 > &p) noexcept
	Calculates the closest point on a triangle to a point. More...

template<class T >
constexpr std::tuple< point< T, 3 >, triangle_region >	closest_point (const triangle< T, 3 > &tri, const point< T, 3 > &p) noexcept
	Calculates the closest point on a triangle to a point. More...


template<class T , std::size_t N>
constexpr std::optional< T >	intersection (const ray< T, N > &ray, const hyperplane< T, N > &hyperplane) noexcept
	Ray-hyperplane intersection test. More...

template<class T , std::size_t N>
constexpr std::optional< T >	intersection (const hyperplane< T, N > &hyperplane, const ray< T, N > &ray) noexcept
	Ray-hyperplane intersection test. More...


template<class T , std::size_t N>
constexpr std::optional< std::tuple< T, T > >	intersection (const ray< T, N > &ray, const hyperrectangle< T, N > &hyperrectangle) noexcept
	Ray-hyperrectangle intersection test. More...

template<class T , std::size_t N>
constexpr std::optional< std::tuple< T, T > >	intersection (const hyperrectangle< T, N > &hyperrectangle, const ray< T, N > &ray) noexcept
	Ray-hyperrectangle intersection test. More...


template<class T >
constexpr std::optional< std::tuple< T, T, T > >	intersection (const ray< T, 3 > &ray, const math::vec3< T > &a, const math::vec3< T > &b, const math::vec3< T > &c) noexcept
	Ray-triangle intersection test. More...

template<class T >
constexpr std::optional< std::tuple< T, T, T > >	intersection (const math::vec3< T > &a, const math::vec3< T > &b, const math::vec3< T > &c, const ray< T, 3 > &ray) noexcept
	Ray-triangle intersection test. More...


template<class T , std::size_t N>
constexpr bool	intersection (const hyperrectangle< T, N > &hyperrectangle, const hypersphere< T, N > &hypersphere) noexcept
	Hyperrectangle-hypersphere intersection test. More...

template<class T , std::size_t N>
constexpr bool	intersection (const hypersphere< T, N > &hypersphere, const hyperrectangle< T, N > &hyperrectangle) noexcept
	Hyperrectangle-hypersphere intersection test. More...

Detailed Description

Geometric algorithms.

Typedef Documentation

◆ octree

template<std::unsigned_integral T, hyperoctree_order Order>

using geom::octree = typedef hyperoctree<T, 3, Order>

An octree, or 3-dimensional hyperoctree.

Definition at line 30 of file octree.hpp.

◆ octree16

template<hyperoctree_order Order>

using geom::octree16 = typedef octree<std::uint16_t, Order>

Octree with a 16-bit node type (4 depth levels).

Definition at line 38 of file octree.hpp.

◆ octree32

template<hyperoctree_order Order>

using geom::octree32 = typedef octree<std::uint32_t, Order>

Octree with a 32-bit node type (9 depth levels).

Definition at line 42 of file octree.hpp.

◆ octree64

template<hyperoctree_order Order>

using geom::octree64 = typedef octree<std::uint64_t, Order>

Octree with a 64-bit node type (19 depth levels).

Definition at line 46 of file octree.hpp.

◆ octree8

template<hyperoctree_order Order>

using geom::octree8 = typedef octree<std::uint8_t, Order>

Octree with an 8-bit node type (2 depth levels).

Definition at line 34 of file octree.hpp.

◆ quadtree

template<std::unsigned_integral T, hyperoctree_order Order>

using geom::quadtree = typedef hyperoctree<T, 2, Order>

A quadtree, or 2-dimensional hyperoctree.

Definition at line 30 of file quadtree.hpp.

◆ quadtree16

template<hyperoctree_order Order>

using geom::quadtree16 = typedef quadtree<std::uint16_t, Order>

Quadtree with a 16-bit node type (6 depth levels).

Definition at line 38 of file quadtree.hpp.

◆ quadtree32

template<hyperoctree_order Order>

using geom::quadtree32 = typedef quadtree<std::uint32_t, Order>

Quadtree with a 32-bit node type (13 depth levels).

Definition at line 42 of file quadtree.hpp.

◆ quadtree64

template<hyperoctree_order Order>

using geom::quadtree64 = typedef quadtree<std::uint64_t, Order>

Quadtree with a 64-bit node type (29 depth levels).

Definition at line 46 of file quadtree.hpp.

◆ quadtree8

template<hyperoctree_order Order>

using geom::quadtree8 = typedef quadtree<std::uint8_t, Order>

Quadtree with an 8-bit node type (2 depth levels).

Definition at line 34 of file quadtree.hpp.

◆ unordered_hyperoctree

template<std::unsigned_integral T, std::size_t N>

using geom::unordered_hyperoctree = typedef hyperoctree<T, N, hyperoctree_order::unordered>

Hyperoctree with unordered node storage and traversal.

Definition at line 573 of file hyperoctree.hpp.

◆ unordered_octree

template<std::unsigned_integral T>

using geom::unordered_octree = typedef octree<T, hyperoctree_order::unordered>

Octree with unordered node storage and traversal.

Definition at line 50 of file octree.hpp.

◆ unordered_octree16

typedef unordered_octree<std::uint16_t> geom::unordered_octree16

Unordered octree with a 16-bit node type (4 depth levels).

Definition at line 56 of file octree.hpp.

◆ unordered_octree32

typedef unordered_octree<std::uint32_t> geom::unordered_octree32

Unordered octree with a 32-bit node type (9 depth levels).

Definition at line 59 of file octree.hpp.

◆ unordered_octree64

typedef unordered_octree<std::uint64_t> geom::unordered_octree64

Unordered octree with a 64-bit node type (19 depth levels).

Definition at line 62 of file octree.hpp.

◆ unordered_octree8

typedef unordered_octree<std::uint8_t> geom::unordered_octree8

Unordered octree with an 8-bit node type (2 depth levels).

Definition at line 53 of file octree.hpp.

◆ unordered_quadtree

template<std::unsigned_integral T>

using geom::unordered_quadtree = typedef quadtree<T, hyperoctree_order::unordered>

Quadtree with unordered node storage and traversal.

Definition at line 50 of file quadtree.hpp.

◆ unordered_quadtree16

typedef unordered_quadtree<std::uint16_t> geom::unordered_quadtree16

Unordered quadtree with a 16-bit node type (6 depth levels).

Definition at line 56 of file quadtree.hpp.

◆ unordered_quadtree32

typedef unordered_quadtree<std::uint32_t> geom::unordered_quadtree32

Unordered quadtree with a 32-bit node type (13 depth levels).

Definition at line 59 of file quadtree.hpp.

◆ unordered_quadtree64

typedef unordered_quadtree<std::uint64_t> geom::unordered_quadtree64

Unordered quadtree with a 64-bit node type (29 depth levels).

Definition at line 62 of file quadtree.hpp.

◆ unordered_quadtree8

typedef unordered_quadtree<std::uint8_t> geom::unordered_quadtree8

Unordered quadtree with an 8-bit node type (2 depth levels).

Definition at line 53 of file quadtree.hpp.

Enumeration Type Documentation

◆ hyperoctree_order

enum geom::hyperoctree_order

strong

Orders in which hyperoctree nodes can be stored and traversed.

Enumerator
unordered	Hyperoctree nodes are unordered, potentially resulting in faster insertions through the internal use of `std::unordered_set` rather than `std::set`.
dfs_pre	Hyperoctree nodes are stored and traversed in depth-first preorder.
bfs	Hyperoctree nodes are stored and traversed in breadth-first order.

Definition at line 36 of file hyperoctree.hpp.

◆ triangle_region

enum geom::triangle_region : std::uint8_t

strong

Voronoi regions of a triangle.

Enumerator
abc	Face ABC region.
ab	Edge AB region.
bc	Edge BC region.
ca	Edge CA region.
a	Vertex A region.
b	Vertex B region.
c	Vertex C region.

Definition at line 33 of file coordinates.hpp.

Function Documentation

◆ barycentric_to_cartesian()

template<class T >

constexpr point<T, 3> geom::barycentric_to_cartesian	(	const point< T, 3 > &	p,
		const point< T, 3 > &	a,
		const point< T, 3 > &	b,
		const point< T, 3 > &	c
	)

inlineconstexprnoexcept

Converts Cartesian coordinates to barycentric coordinates.

Template Parameters

T	Real type.

Parameters

p	Barycentric coordinates of point to convert.
a	Cartesian coordinates of first point of triangle.
b	Cartesian coordinates of second point of triangle.
c	Cartesian coordinates of third point of triangle.

Returns: Cartesian coordinates of point p.

Definition at line 148 of file coordinates.hpp.

◆ barycentric_to_region()

template<class T >

constexpr triangle_region geom::barycentric_to_region ( const point< T, 3 > & p )

constexprnoexcept

Classifies barycentric coordinates according to their Voronoi region.

Template Parameters

T	Real type.

Parameters

p	Barycentric coordinates of point to classify.

Returns: Voronoi region of point p.

Definition at line 127 of file coordinates.hpp.

◆ cartesian_to_barycentric()

template<class T >

constexpr point<T, 3> geom::cartesian_to_barycentric	(	const point< T, 3 > &	p,
		const point< T, 3 > &	a,
		const point< T, 3 > &	b,
		const point< T, 3 > &	c
	)

constexprnoexcept

Converts Cartesian coordinates to barycentric coordinates.

Template Parameters

T	Real type.

Parameters

p	Cartesian coordinates of point to convert.
a	Cartesian coordinates of first point of triangle.
b	Cartesian coordinates of second point of triangle.
c	Cartesian coordinates of third point of triangle.

Returns: Barycentric coordinates of point p.

Definition at line 166 of file coordinates.hpp.

◆ cartesian_to_spherical()

template<class T >

point<T, 3> geom::cartesian_to_spherical ( const point< T, 3 > & p )

Converts Cartesian (rectangular) coordinates to spherical coordinates.

Template Parameters

T	Real type.

Parameters

p	Cartesian coordinates of point to convert.

Returns: Spherical coordinates of point p, in the ISO order of radial distance, polar angle (radians), and azimuthal angle (radians).

Definition at line 208 of file coordinates.hpp.

◆ closest_point() [1/9]

template<class T , std::size_t N>

point<T, N> geom::closest_point	(	const hypercapsule< T, N > &	a,
		const point< T, N > &	b
	)

Calculates the closest point on or in a hypercapsule to a point.

Template Parameters

T	Real type.
N	Number of dimensions.

Parameters

a	Hypercapsule a.
b	Point b.

Returns: Closest point on or in hypercapsule a to point b.

Definition at line 309 of file closest-point.hpp.

◆ closest_point() [2/9]

template<class T , std::size_t N>

constexpr point<T, N> geom::closest_point	(	const hyperplane< T, N > &	a,
		const point< T, N > &	b
	)

constexprnoexcept

Calculates the closest point on a hyperplane to a point.

Template Parameters

T	Real type.
N	Number of dimensions.

Parameters

a	Hyperplane a.
b	Point b.

Returns: Closest point on hyperplane a to point b.

Definition at line 191 of file closest-point.hpp.

◆ closest_point() [3/9]

template<class T , std::size_t N>

constexpr point<T, N> geom::closest_point	(	const hyperrectangle< T, N > &	a,
		const point< T, N > &	b
	)

constexprnoexcept

Calculates the closest point on or in a hyperrectangle to a point.

Template Parameters

T	Real type.
N	Number of dimensions.

Parameters

a	Hyperrectangle a.
b	Point b.

Returns: Closest point on or in hyperrectangle a to point b.

Definition at line 329 of file closest-point.hpp.

◆ closest_point() [4/9]

template<class T , std::size_t N>

point<T, N> geom::closest_point	(	const hypersphere< T, N > &	a,
		const point< T, N > &	b
	)

Calculates the closest point on or in a hypersphere to a point.

Template Parameters

T	Real type.
N	Number of dimensions.

Parameters

a	Hypersphere a.
b	Point b.

Returns: Closest point on or in hypersphere a to point b.

Definition at line 290 of file closest-point.hpp.

◆ closest_point() [5/9]

template<class T , std::size_t N>

constexpr std::tuple<point<T, N>, point<T, N> > geom::closest_point	(	const line_segment< T, N > &	ab,
		const line_segment< T, N > &	cd
	)

constexprnoexcept

Calculates the closest points on two line segments.

Template Parameters

T	Real type.
N	Number of dimensions.

Parameters

ab	Line segment ab.
cd	Line segment cd.

Returns: Tuple containing the closest point on segment ab to segment cd, followed by the closest point on segment cd to segment ab.

See also: Ericson, C. (2004). Real-time collision detection. Crc Press.

Definition at line 104 of file closest-point.hpp.

◆ closest_point() [6/9]

template<class T , std::size_t N>

constexpr point<T, N> geom::closest_point	(	const line_segment< T, N > &	ab,
		const point< T, N > &	c
	)

constexprnoexcept

Calculates the closest point on a line segment to a point.

Template Parameters

T	Real type.
N	Number of dimensions.

Parameters

ab	Line segment ab.
c	Point c.

Returns: Closest point on line segment ab to point c.

Definition at line 67 of file closest-point.hpp.

◆ closest_point() [7/9]

template<class T >

constexpr std::tuple<point<T, 3>, triangle_region> geom::closest_point	(	const point< T, 3 > &	a,
		const point< T, 3 > &	b,
		const point< T, 3 > &	c,
		const point< T, 3 > &	p
	)

constexprnoexcept

Calculates the closest point on a triangle to a point.

Template Parameters

T	Real type.

Parameters

tri	Triangle.
a	First point of triangle.
b	Second point of triangle.
c	Third point of triangle.
p	Point.

Returns: Closest point on the triangle to point p, followed by the Voronoi region of the point.

See also: Ericson, C. (2004). Real-time collision detection. Crc Press.

Definition at line 213 of file closest-point.hpp.

◆ closest_point() [8/9]

template<class T , std::size_t N>

constexpr point<T, N> geom::closest_point	(	const ray< T, N > &	a,
		const point< T, N > &	b
	)

constexprnoexcept

Calculates the closest point on a ray to a point.

Template Parameters

T	Real type.
N	Number of dimensions.

Parameters

a	Ray a.
b	Point b.

Returns: Closest point on ray a to point b.

Definition at line 50 of file closest-point.hpp.

◆ closest_point() [9/9]

template<class T >

constexpr std::tuple<point<T, 3>, triangle_region> geom::closest_point	(	const triangle< T, 3 > &	tri,
		const point< T, 3 > &	p
	)

inlineconstexprnoexcept

Calculates the closest point on a triangle to a point.

Template Parameters

T	Real type.

Parameters

tri	Triangle.
a	First point of triangle.
b	Second point of triangle.
c	Third point of triangle.
p	Point.

Returns: Closest point on the triangle to point p, followed by the Voronoi region of the point.

See also: Ericson, C. (2004). Real-time collision detection. Crc Press.

Definition at line 272 of file closest-point.hpp.

◆ edge_index()

constexpr std::uint8_t geom::edge_index ( triangle_region region )

inlineconstexprnoexcept

Returns the edge index of an edge region.

Parameters

region Triangle edge region.

Returns: Edge index.

Definition at line 100 of file coordinates.hpp.

◆ generate_face_normals()

void geom::generate_face_normals ( brep_mesh & mesh )

Generates the math::fvec3 face attribute "normal" for a B-rep mesh.

Parameters

mesh	Mesh for which to generate normals.

Warning: Requires the math::fvec3 vertex attribute "position".

Definition at line 29 of file brep-operations.cpp.

◆ generate_loop_barycentric()

void geom::generate_loop_barycentric ( brep_mesh & mesh )

Generates the math::fvec3 loop attribute "barycentric" for a B-rep mesh.

Parameters

mesh	Mesh for which to generate barycentric coordinates.

Definition at line 122 of file brep-operations.cpp.

◆ generate_model()

std::unique_ptr< render::model > geom::generate_model	(	const brep_mesh &	mesh,
		std::shared_ptr< render::material >	material = `nullptr`
	)

Generates a model from a B-rep mesh.

Parameters

mesh	Mesh for which to generate a model. @parma material Material to assign to the model.

Returns: Generated model.

Definition at line 136 of file brep-operations.cpp.

◆ generate_vertex_normals()

void geom::generate_vertex_normals ( brep_mesh & mesh )

Generates the math::fvec3 vertex attribute "normal" for a B-rep mesh.

Parameters

mesh	Mesh for which to generate normals.

Note: The math::fvec3 face attribute "normal" will also be generated if not found.

Warning: Requires the math::fvec3 vertex attribute "position".

Definition at line 45 of file brep-operations.cpp.

◆ intersection() [1/11]

template<class T , std::size_t N>

constexpr std::optional<T> geom::intersection	(	const hyperplane< T, N > &	hyperplane,
		const ray< T, N > &	ray
	)

inlineconstexprnoexcept

Ray-hyperplane intersection test.

Parameters

ray	Ray.
hyperplane	Hyperplane.

Returns: Distance along the ray to the point of intersection, or std::nullopt if no intersection occurred.

Definition at line 58 of file intersection.hpp.

◆ intersection() [2/11]

template<class T , std::size_t N>

constexpr bool geom::intersection	(	const hyperrectangle< T, N > &	a,
		const hyperrectangle< T, N > &	b
	)

inlineconstexprnoexcept

Hyperrectangle-hyperrectangle intersection test.

Parameters

a	First hyperrectangle.
b	Second hyperrectangle.

Returns: true if an intersection occurred, false otherwise.

Definition at line 206 of file intersection.hpp.

◆ intersection() [3/11]

template<class T , std::size_t N>

constexpr bool geom::intersection	(	const hyperrectangle< T, N > &	hyperrectangle,
		const hypersphere< T, N > &	hypersphere
	)

constexprnoexcept

Hyperrectangle-hypersphere intersection test.

Parameters

hyperrectangle	Hyperrectangle.
hypersphere	Hypersphere.

Returns: true if an intersection occurred, false otherwise.

Definition at line 221 of file intersection.hpp.

◆ intersection() [4/11]

template<class T , std::size_t N>

constexpr std::optional<std::tuple<T, T> > geom::intersection	(	const hyperrectangle< T, N > &	hyperrectangle,
		const ray< T, N > &	ray
	)

inlineconstexprnoexcept

Ray-hyperrectangle intersection test.

Parameters

ray	Ray.
hyperrectangle	Hyperrectangle.

Returns: Tuple containing the distances along the ray to the first and second points of intersection, or std::nullopt if no intersection occurred.

Definition at line 106 of file intersection.hpp.

◆ intersection() [5/11]

template<class T , std::size_t N>

constexpr bool geom::intersection	(	const hypersphere< T, N > &	a,
		const hypersphere< T, N > &	b
	)

inlineconstexprnoexcept

Hypersphere-hypersphere intersection test.

Parameters

a	First hypersphere.
b	Second hypersphere.

Returns: true if an intersection occurred, false otherwise.

Definition at line 257 of file intersection.hpp.

◆ intersection() [6/11]

template<class T , std::size_t N>

constexpr bool geom::intersection	(	const hypersphere< T, N > &	hypersphere,
		const hyperrectangle< T, N > &	hyperrectangle
	)

inlineconstexprnoexcept

Hyperrectangle-hypersphere intersection test.

Parameters

hyperrectangle	Hyperrectangle.
hypersphere	Hypersphere.

Returns: true if an intersection occurred, false otherwise.

Definition at line 242 of file intersection.hpp.

◆ intersection() [7/11]

template<class T >

constexpr std::optional<std::tuple<T, T, T> > geom::intersection	(	const math::vec3< T > &	a,
		const math::vec3< T > &	b,
		const math::vec3< T > &	c,
		const ray< T, 3 > &	ray
	)

inlineconstexprnoexcept

Ray-triangle intersection test.

Parameters

ray	Ray.
a,b,c	Triangle points.

Returns: Tuple containing the distance along the ray to the point of intersection, followed by two barycentric coordinates of the point of intersection, or std::nullopt if no intersection occurred.

Definition at line 191 of file intersection.hpp.

◆ intersection() [8/11]

template<class T >

constexpr std::optional<std::tuple<T, T, T> > geom::intersection	(	const ray< T, 3 > &	ray,
		const math::vec3< T > &	a,
		const math::vec3< T > &	b,
		const math::vec3< T > &	c
	)

constexprnoexcept

Ray-triangle intersection test.

Parameters

ray	Ray.
a,b,c	Triangle points.

Returns: Tuple containing the distance along the ray to the point of intersection, followed by two barycentric coordinates of the point of intersection, or std::nullopt if no intersection occurred.

Definition at line 149 of file intersection.hpp.

◆ intersection() [9/11]

template<class T , std::size_t N>

constexpr std::optional<T> geom::intersection	(	const ray< T, N > &	ray,
		const hyperplane< T, N > &	hyperplane
	)

constexprnoexcept

Ray-hyperplane intersection test.

Parameters

ray	Ray.
hyperplane	Hyperplane.

Returns: Distance along the ray to the point of intersection, or std::nullopt if no intersection occurred.

Definition at line 42 of file intersection.hpp.

◆ intersection() [10/11]

template<class T , std::size_t N>

constexpr std::optional<std::tuple<T, T> > geom::intersection	(	const ray< T, N > &	ray,
		const hyperrectangle< T, N > &	hyperrectangle
	)

constexprnoexcept

Ray-hyperrectangle intersection test.

Parameters

ray	Ray.
hyperrectangle	Hyperrectangle.

Returns: Tuple containing the distances along the ray to the first and second points of intersection, or std::nullopt if no intersection occurred.

Definition at line 74 of file intersection.hpp.

◆ intersection() [11/11]

template<class T , std::size_t N>

std::optional<std::tuple<T, T> > geom::intersection	(	const ray< T, N > &	ray,
		const hypersphere< T, N > &	hypersphere
	)

noexcept

Ray-hypersphere intersection test.

Parameters

ray	Ray.
hypersphere	Hypersphere.

Returns: Tuple containing the distances along the ray to the first and second points of intersection, or std::nullopt if no intersection occurred.

See also: Haines, E., Günther, J., & Akenine-Möller, T. (2019). Precision improvements for ray/sphere intersection. Ray Tracing Gems: High-Quality and Real-Time Rendering with DXR and Other APIs, 87-94.

Definition at line 123 of file intersection.hpp.

◆ is_edge_region()

constexpr bool geom::is_edge_region ( triangle_region region )

inlineconstexprnoexcept

Checks whether a triangle voronoi region is an edge region.

Parameters

region Triangle region.

Returns: true if region is an edge region, false otherwise.

Definition at line 76 of file coordinates.hpp.

◆ is_face_region()

constexpr bool geom::is_face_region ( triangle_region region )

inlineconstexprnoexcept

Checks whether a triangle voronoi region is a face region.

Parameters

region Triangle region.

Returns: true if region is a face region, false otherwise.

Definition at line 64 of file coordinates.hpp.

◆ is_vertex_region()

constexpr bool geom::is_vertex_region ( triangle_region region )

inlineconstexprnoexcept

Checks whether a triangle voronoi region is a vertex region.

Parameters

region Triangle region.

Returns: true if region is an vertex region, false otherwise.

Definition at line 88 of file coordinates.hpp.

◆ morton_decode() [1/2]

template<std::unsigned_integral T>

void geom::morton_decode	(	T	code,
		T &	x,
		T &	y
	)

noexcept

Decodes 2D coordinates from a Morton location code.

Parameters

[in]	code	Morton location code to decode.
[out]	x	Decoded x-coordinate.
[out]	y	Decoded y-coordinate.

Definition at line 122 of file morton.hpp.

◆ morton_decode() [2/2]

template<std::unsigned_integral T>

void geom::morton_decode	(	T	code,
		T &	x,
		T &	y,
		T &	z
	)

noexcept

Decodes 3D coordinates from a Morton location code.

Parameters

[in]	code	Morton location code to decode.
[out]	x	Decoded x-coordinate.
[out]	y	Decoded y-coordinate.
[out]	z	Decoded z-coordinate.

Definition at line 159 of file morton.hpp.

◆ morton_encode() [1/2]

template<std::unsigned_integral T>

constexpr T geom::morton_encode	(	T	x,
		T	y
	)

constexprnoexcept

Encodes 2D coordinates as a Morton location code.

Parameters

[in]	x	X-coordinate to encode.
[in]	y	Y-coordinate to encode.

Returns: Morton location code.

Definition at line 36 of file morton.hpp.

◆ morton_encode() [2/2]

template<std::unsigned_integral T>

constexpr T geom::morton_encode	(	T	x,
		T	y,
		T	z
	)

constexprnoexcept

Encodes 3D coordinates as a Morton location code.

Parameters

[in]	x	X-coordinate to encode.
[in]	y	Y-coordinate to encode.
[in]	z	Z-coordinate to encode.

Returns: Morton location code.

Definition at line 74 of file morton.hpp.

◆ project_on_plane()

template<class T >

math::vec3<T> geom::project_on_plane	(	const math::vec3< T > &	v,
		const math::vec3< T > &	p,
		const math::vec3< T > &	n
	)

Definition at line 28 of file geom/projection.hpp.

◆ spherical_to_cartesian()

template<class T >

point<T, 3> geom::spherical_to_cartesian ( const point< T, 3 > & p )

Converts spherical coordinates to Cartesian (rectangular) coordinates.

Template Parameters

T	Real type.

Parameters

p	Spherical coordinates to convert, in the ISO order of radial distance, polar angle (radians), and azimuthal angle (radians).

Returns: Cartesian coordinates of point p.

Definition at line 230 of file coordinates.hpp.

◆ vertex_index()

constexpr std::uint8_t geom::vertex_index ( triangle_region region )

inlineconstexprnoexcept

Returns the vertex index of a vertex region.

Parameters

region Triangle vertex region.

Returns: Vertex index.

Definition at line 112 of file coordinates.hpp.

Namespaces

Classes

Typedefs

Enumerations

Functions

Detailed Description

Typedef Documentation

◆ octree

◆ octree16

◆ octree32

◆ octree64

◆ octree8

◆ quadtree

◆ quadtree16

◆ quadtree32

◆ quadtree64

◆ quadtree8

◆ unordered_hyperoctree

◆ unordered_octree

◆ unordered_octree16

◆ unordered_octree32

◆ unordered_octree64

◆ unordered_octree8

◆ unordered_quadtree

◆ unordered_quadtree16

◆ unordered_quadtree32

◆ unordered_quadtree64

◆ unordered_quadtree8

Enumeration Type Documentation

◆ hyperoctree_order

◆ triangle_region

Function Documentation

◆ barycentric_to_cartesian()

◆ barycentric_to_region()

◆ cartesian_to_barycentric()

◆ cartesian_to_spherical()

◆ closest_point() [1/9]

◆ closest_point() [2/9]

◆ closest_point() [3/9]

◆ closest_point() [4/9]

◆ closest_point() [5/9]

◆ closest_point() [6/9]

◆ closest_point() [7/9]

◆ closest_point() [8/9]

◆ closest_point() [9/9]

◆ edge_index()

◆ generate_face_normals()

◆ generate_loop_barycentric()

◆ generate_model()

◆ generate_vertex_normals()

◆ intersection() [1/11]

◆ intersection() [2/11]

◆ intersection() [3/11]

◆ intersection() [4/11]

◆ intersection() [5/11]

◆ intersection() [6/11]

◆ intersection() [7/11]

◆ intersection() [8/11]

◆ intersection() [9/11]

◆ intersection() [10/11]

◆ intersection() [11/11]

◆ is_edge_region()

◆ is_face_region()

◆ is_vertex_region()

◆ morton_decode() [1/2]

◆ morton_decode() [2/2]

◆ morton_encode() [1/2]

◆ morton_encode() [2/2]

◆ project_on_plane()

◆ spherical_to_cartesian()

◆ vertex_index()