Computational geometry.

Types

• template <class T>
using Array = std::vector< T >
• template <int N>
using Face_array = Array< Face< N > >
• template <class T, int N>
using Matrix = blitz::TinyMatrix< T, N, N >
• template <class T, int N>
using Ray_array = Array< Ray< T, N > >
• template <class T, int N>
using Vertex = blitz::TinyVector< T, N >
• template <class T, int N>
using Vertex_array = Array< Vertex< T, N > >
• template <class T, int N>
using Vertex_matrix = Array< Vertex_array< T, N > >
• using bstream = ::vtb::base::bstream

Enumerations

• enum Plane_position: unsigned char
• enum Segments

Classes

• template <class T>
class vtb::geometry::BSP_node_iterator
• template <class T, int N>
class vtb::geometry::BSP_tree
• template <class T, int N>
class vtb::geometry::Basis
• template <class T, int N>
class vtb::geometry::Basis_spline

  Non-uniform rational basis spline (NURBS).
• template <class T, int N>
class vtb::geometry::Basis_spline_curve
• template <class T>
class vtb::geometry::Basis_spline_surface
• template <class T, int N>
class vtb::geometry::Bezier_curve
• template <class T>
class vtb::geometry::Bounds
• template <class T, int N>
class vtb::geometry::Closed_basis_spline

  Closed non-uniform rational basis spline (NURBS).
• template <class T, class Curve>
class vtb::geometry::Coons_surface
• template <class T, int N>
class vtb::geometry::Coordinate_system
• template <class T, int N = 3>
class vtb::geometry::Cubic_spline
• template <class T, int N>
class vtb::geometry::Curve_segments
• template <class T, class Curve_u, class Curve_v>
class vtb::geometry::Curved_surface
• template <int N>
class vtb::geometry::Face
• template <class T, int N>
class vtb::geometry::Line_segment
• template <class T, int N = 3, Segments seg = Segments::Chord_length>
class vtb::geometry::Linear_interpolation
• template <class T, int N>
class vtb::geometry::Plane

  Three- and two-dimensional plane.
• template <class T, int N>
class vtb::geometry::Polygon
• template <class T, int N = 3>
class vtb::geometry::Polyhedron

  Three-dimensional polyhedron.
• template <class T, int N>
class vtb::geometry::Polyline

  A polygon composed of line segments.
• template <class T>
class vtb::geometry::Quaternion
• template <class T>
class vtb::geometry::Quaternion_coordinate_system
• template <class T, int N>
class vtb::geometry::Ray
• template <class T, int N>
class vtb::geometry::Rectangle
• template <class T, int N>
class vtb::geometry::Rotation_matrix
• template <class T, class Curve>
class vtb::geometry::Ruled_surface
• template <class T, class Curve>
class vtb::geometry::Spline_surface
• template <class T, int N>
class vtb::geometry::Tetrahedron
• template <class T, int N>
class vtb::geometry::Triangle
• template <class T>
class vtb::geometry::Unit_quaternion

Structs

• template <class T, int N>
struct vtb::geometry::Compare_vertex
• template <class T, int N>
struct vtb::geometry::Equal_vertex
• template <class T, int N>
struct vtb::geometry::Inertia_tensor
• template <class T>
struct vtb::geometry::Inertia_tensor< T, 2 >
• template <class T>
struct vtb::geometry::Inertia_tensor< T, 3 >
• template <class T, int N>
struct vtb::geometry::Mass_moments
• template <class T>
struct vtb::geometry::Mass_moments< T, 2 >
• template <class T>
struct vtb::geometry::Mass_moments< T, 3 >
• template <class T>
struct vtb::geometry::is_figure
• template <class T, int N>
struct vtb::geometry::is_figure< Line_segment< T, N > >
• template <class T, int N>
struct vtb::geometry::is_figure< Polygon< T, N > >
• template <class T, int N>
struct vtb::geometry::is_figure< Polyline< T, N > >
• template <class T, int N>
struct vtb::geometry::is_figure< Tetrahedron< T, N > >
• template <class T, int N>
struct vtb::geometry::is_figure< Triangle< T, N > >

Functions

• template <class T, int N>
area(const Triangle< T, N > & t) -> T
• template <class T, int N>
area(const Rectangle< T, N > & r) -> Vertex< T, N >
• template <class T, int N>
area(const Polyhedron< T, N > & polyhedron) -> T
• template <class Figure>
border_contains(const Figure & figure, const typename Figure::value_type & vertex, const typename Figure::scalar_type eps) -> bool
• template <class Figure>
bounding_box(const Figure & figure) -> auto
• template <class T, int N>
centroid(const Triangle< T, N > & t) -> Vertex< T, N >
• template <class T, int N>
centroid(const Tetrahedron< T, N > & t) -> Vertex< T, N >
• template <class T, int N>
centroid(const Rectangle< T, N > & r) -> Vertex< T, N >
• template <class T, int N>
centroid(const Polyhedron< T, N > & geometry) -> Vertex< T, N >
• template <class T>
centroid(const Polygon< T, 2 > & p) -> Vertex< T, 2 >
• template <class Figure>
centroid(const Figure & figure) -> Figure::value_type
• template <class T, int N>
centroid(const Line_segment< T, N > & s) -> Vertex< T, N >
• template <class T>
clockwise(const Vertex< T, 2 > & origin, const Vertex< T, 2 > & a, const Vertex< T, 2 > & b) -> bool
• template <class T, int N>
compare(const Plane< T, N > plane, const Triangle< T, N > & triangle, T eps) -> Vertex< Plane_position, 3 >
• template <class T, int N>
compare(const Plane< T, N > lhs, const Plane< T, N > & rhs, T eps) -> Plane_position
• template <class T, int N>
compare(const Plane< T, N > plane, const Vertex< T, N > & point, T eps) -> Plane_position
• template <class T, int N>
compare(const Plane< T, N > plane, const Line_segment< T, N > & s, T eps) -> Vertex< Plane_position, 2 >
• template <class T>
conj(const Quaternion< T > & q) -> Quaternion< T >
• template <class Figure>
contains(const Figure & figure, const typename Figure::value_type & vertex, const typename Figure::scalar_type eps) -> bool
• template <class T, int N>
cosine(const Vertex< T, N > & a, const Vertex< T, N > & b) -> T
• template <class T, int N>
cuboid(const Vertex< T, N > & a, const Vertex< T, N > & b) -> Polyhedron< T >
• template <class T>
cylinder(T radius, T height, int resolution_u, int resolution_v) -> Polyhedron< T >

  Generate cylinder using NURBS.
• template <class T>
det(const Vertex< T, 3 > & a, const Vertex< T, 3 > & b, const Vertex< T, 3 > & c) -> T
• template <class T>
det(const Vertex< T, 2 > & origin, const Vertex< T, 2 > & a, const Vertex< T, 2 > & b) -> T
• template <class T>
det(const Vertex< T, 2 > & a, const Vertex< T, 2 > & b) -> T
• template <class V>
difference(const V & a, const V & b) -> V
• template <class V, class T>
difference(const V & a, const V & b, T delta) -> V
• template <class T, int N>
from(const Rotation_matrix< T, N > & rot, const Vertex< T, N > & v) -> Vertex< T, N >
• template <class T>
from(const Quaternion_coordinate_system< T > & cs, const Vertex< T, 3 > & v) -> Vertex< T, 3 >
• template <class T, int N>
from(const Coordinate_system< T, N > & cs, const Vertex< T, N > & v) -> Vertex< T, N >
• template <class T, int N>
from(const Basis< T, N > & basis, const Vertex< T, N > & origin, const Vertex< T, N > & v) -> Vertex< T, N >
• template <class T>
from_euler_angles(const Vertex< T, 3 > & angles) -> Quaternion< T >
• template <class T>
from_vector(const Quaternion< T > & q) -> Quaternion< T >
• template <class T>
imag(const Quaternion< T > & q) -> Vertex< T, 3 >
• template <class T, int N>
inertia_tensor(const Polyhedron< T, N > & body) -> Inertia_tensor< T, N >

  Calculate inertia tensor (matrix) of a body as a sum of inertia tensors for tetrahedrons.
• template <class Figure>
interior_contains(const Figure & figure, const typename Figure::value_type & vertex) -> bool
• template <class T, int N>
intersect(const Plane< T, N > & plane, const Triangle< T, N > & triangle, const Vertex< Plane_position, 3 > & positions, Polygon< T, N > & front, Polygon< T, N > & back) -> void
• template <class T, int N>
intersect(const Ray< T, N > & ray, const Triangle< T, N > & triangle, T eps) -> bool

  Check if ray intersects triangle.
• template <class T, int N>
intersection(const Ray< T, N > & ray, const Plane< T, N > & plane) -> Vertex< T, N >

  Returns intersection point of ray and plane. Edge cases are ignored.
• template <int dim, class T, int N>
intersection_point(const Line_segment< T, N > & segment, T level) -> Vertex< T, N >
• template <class T, int N>
intersection_point(const Plane< T, N > & plane, const Line_segment< T, N > & segment) -> Vertex< T, N >
• template <class T, int N>
inverse(const Rotation_matrix< T, N > & rot) -> Basis< T, N >
• template <class T, int N>
inverse(const Basis< T, N > & basis) -> Basis< T, N >
• template <class T>
length(const Quaternion< T > & q) -> T
• template <class T>
line_normal(const Vertex< T, 2 > & v0, const Vertex< T, 2 > & v1) -> Vertex< T, 2 >

  Rotates line segment by 90 degrees counterclockwise and normalises resulting vector.
• template <class T>
make_coordinate_system(const Quaternion< T > & q, const Quaternion< T > & q_conj, const Vertex< T, 3 > & origin) -> Quaternion_coordinate_system< T >
• template <class T>
make_coordinate_system(const Quaternion< T > & q, const Vertex< T, 3 > & origin) -> Quaternion_coordinate_system< T >
• template <class T, int N>
make_coordinate_system(const Rotation_matrix< T, N > & rot, const Vertex< T, N > & origin) -> Coordinate_system< T, N >
• template <class T, int N>
make_coordinate_system(const Basis< T, N > & basis, const Basis< T, N > & ibasis, const Vertex< T, N > & origin) -> Coordinate_system< T, N >
• template <class T, int N>
make_coordinate_system(const Basis< T, N > & basis, const Vertex< T, N > & origin) -> Coordinate_system< T, N >
• template <class T, int N>
make_rotation(const Basis< T, N > & basis) -> Rotation_matrix< T, N >
• template <class T, int N>
make_rotation(const Basis< T, N > & basis, const Basis< T, N > & ibasis) -> Rotation_matrix< T, N >
• template <class T>
make_rotation_xyz(const Vertex< T, 3 > & angles) -> Rotation_matrix< T, 3 >
• template <class T>
make_rotation_zyx(const Vertex< T, 3 > & angles) -> Rotation_matrix< T, 3 >

  Rotation_matrix matrix for Euler angles in $ZYX$ order.
• template <class T, int N>
mass_moments(const Polyline< T, N > & polyline) -> Mass_moments< T, N >

  Calculate area, centroid and inertia tensor.
• template <class T, int N>
near(const Line_segment< T, N > & lhs, const Line_segment< T, N > & rhs, T eps) -> bool
• template <class T, int N>
operator!=(const Line_segment< T, N > & lhs, const Line_segment< T, N > & rhs) -> bool
• template <int N>
operator!=(const Face< N > & lhs, const Face< N > & rhs) -> bool
• template <class T>
operator*(const Vertex< T, 3 > & a, const Quaternion< T > & b) -> Quaternion< T >
• template <class T>
operator*(const Quaternion< T > & a, const Vertex< T, 3 > & b) -> Quaternion< T >
• template <class T>
operator*(T a, const Quaternion< T > & b) -> Quaternion< T >
• template <class T>
operator*(const Quaternion< T > & a, T b) -> Quaternion< T >
• template <class T>
operator*(const Quaternion< T > & a, const Quaternion< T > & b) -> Quaternion< T >

  Hamilton product.
• template <class T, int N, class X>
operator*(const Basis< T, N > & lhs, const X & rhs) -> auto
• template <class T>
operator*=(Quaternion< T > & a, const Quaternion< T > & b) -> Quaternion< T >
• template <class T>
operator+(Quaternion< T > & a, const Quaternion< T > & b) -> Quaternion< T >
• template <class T, int N>
operator+(const Polyhedron< T, N > & lhs, const Polyhedron< T, N > & rhs) -> Polyhedron< T, N >
• template <class T>
operator+=(Quaternion< T > & a, const Quaternion< T > & b) -> Quaternion< T >
• template <class T>
operator/(const Quaternion< T > & a, T b) -> Quaternion< T >
• template <class T, int N>
operator<(const Line_segment< T, N > & lhs, const Line_segment< T, N > & rhs) -> bool
• template <int N>
operator<(const Face< N > & lhs, const Face< N > & rhs) -> bool
• template <class T, int N>
operator<<(bstream & out, const Rotation_matrix< T, N > & rhs) -> bstream &
• template <class T>
operator<<(std::ostream & out, const Quaternion< T > & q) -> std::ostream &
• template <class T, int N>
operator<<(vtb::core::bstream & out, const Polyhedron< T, N > & rhs) -> vtb::core::bstream &
• operator<<(std::ostream & out, Plane_position rhs) -> std::ostream &
• template <class T, int N>
operator<<(std::ostream & out, const Plane< T, N > & rhs) -> std::ostream &
• template <class Figure>
operator<<(std::ostream & out, const Figure & figure) -> std::enable_if< is_figure< Figure >::value, std::ostream & >::type
• template <int N>
operator<<(vtb::core::bstream & out, const Face< N > & rhs) -> vtb::core::bstream &
• template <int N>
operator<<(std::ostream & out, const Face< N > & rhs) -> std::ostream &
• template <class T, int N>
operator<<(bstream & out, const Coordinate_system< T, N > & rhs) -> bstream &
• template <class T, int N>
operator==(const Line_segment< T, N > & lhs, const Line_segment< T, N > & rhs) -> bool
• template <int N>
operator==(const Face< N > & lhs, const Face< N > & rhs) -> bool
• template <class T, int N>
operator>>(bstream & in, Rotation_matrix< T, N > & rhs) -> bstream &
• template <class T, int N>
operator>>(vtb::core::bstream & in, Polyhedron< T, N > & rhs) -> vtb::core::bstream &
• template <int N>
operator>>(vtb::core::bstream & in, Face< N > & rhs) -> vtb::core::bstream &
• template <int N>
operator>>(std::istream & in, Face< N > & rhs) -> std::istream &
• template <class T, int N>
operator>>(bstream & in, Coordinate_system< T, N > & rhs) -> bstream &
• operator|(Plane_position a, Plane_position b) -> constexpr Plane_position
• template <class T>
orientation(const Vertex< T, 2 > & origin, const Vertex< T, 2 > & a, const Vertex< T, 2 > & b) -> Vertex< T, 1 >
• template <class Figure>
perimeter(const Figure & figure) -> Figure::value_type
• template <class T>
real(const Quaternion< T > & q) -> T
• template <class T>
rotate(const Vertex< T, 3 > & v, const Quaternion< T > & q) -> Vertex< T, 3 >
• template <int dimension, int degrees, class T, int N>
rotate(const Vertex< T, N > & v) -> Vertex< T, N >
• template <class T>
rotation_matrix(const Quaternion< T > & q) -> Rotation_matrix< T, 3 >

  Rotation matrix for a quaternion.
• template <class T, int N>
rotation_matrix_xyz(const Vertex< T, N > & angle) -> Basis< T, N >
• template <class T, int N>
rotation_matrix_zyx(const Vertex< T, N > & angle) -> Basis< T, N >

  Return rotation matrix specified by Euler angles.
• template <class T, int N>
signed_volume(const Tetrahedron< T, N > & t) -> T
• template <class T, int N>
signed_volume(const Polyhedron< T, N > & geometry) -> T
• template <class T>
solid_angle(const Tetrahedron< T, 3 > & t) -> T
• template <class T>
sphere(T radius, int resolution_u, int resolution_v) -> Polyhedron< T >

  Generate sphere using NURBS.
• template <class T>
surface_normal(const Triangle< T, 3 > & t) -> Vertex< T, 3 >
• template <class T>
surface_normal(const Vertex< T, 3 > & v0, const Vertex< T, 3 > & v1, const Vertex< T, 3 > & v2) -> Vertex< T, 3 >
• template <class T, int N>
swap(Polyhedron< T, N > & lhs, Polyhedron< T, N > & rhs) -> void
• template <class T>
tetrahedron_signed_volume(const Triangle< T, 2 > & tr) -> T
• template <class T>
tetrahedron_signed_volume(const Triangle< T, 3 > & tr) -> T

  Signed volume of a tetrahedron with the origin $(0,0,0)$.
• template <class T, int N>
to(const Rotation_matrix< T, N > & rot, const Vertex< T, N > & v) -> Vertex< T, N >
• template <class T>
to(const Quaternion_coordinate_system< T > & cs, const Vertex< T, 3 > & v) -> Vertex< T, 3 >
• template <class T, int N>
to(const Coordinate_system< T, N > & cs, const Vertex< T, N > & v) -> Vertex< T, N >
• template <class T, int N>
to(const Basis< T, N > & b, const Vertex< T, N > & v) -> Vertex< T, N >
• template <class T>
to_euler_angles(const Quaternion< T > & q) -> Vertex< T, 3 >

  Convert quaternion to Euler angles.
• to_string(Plane_position rhs) -> const char *
• template <class T>
to_vector(const Quaternion< T > & q) -> Quaternion< T >
• template <class T, int N>
transpose(Basis< T, N > & basis) -> void
• template <class T>
unit(const Quaternion< T > & q) -> Quaternion< T >
• template <class T, int N>
unit(const Vertex< T, N > & v) -> Vertex< T, N >
• template <class T>
vector_from(const Quaternion_coordinate_system< T > & cs, const Vertex< T, 3 > & v) -> Vertex< T, 3 >
• template <class T, int N>
vector_from(const Coordinate_system< T, N > & cs, const Vertex< T, N > & v) -> Vertex< T, N >
• template <class T, int N>
vector_to(const Rotation_matrix< T, N > & r, const Vertex< T, N > & v) -> Vertex< T, N >
• template <class T>
vector_to(const Quaternion_coordinate_system< T > & cs, const Vertex< T, 3 > & v) -> Vertex< T, 3 >
• template <class T, int N>
vector_to(const Coordinate_system< T, N > & cs, const Vertex< T, N > & v) -> Vertex< T, N >
• template <class T, int N>
volume(const Tetrahedron< T, N > & t) -> T
• template <class T, int N>
volume(const Polyhedron< T, N > & geometry) -> T
• template <class T, int N>
winding_number(const Polyhedron< T, N > & geometry, const Vertex< T, N > & origin) -> T
• template <class Container, class T>
winding_number(const Container & vertices, const Vertex< T, 2 > & origin) -> int