meshes.h File Reference

#include <triangle.h>

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Functions
template<class T >
void	centreMesh (std::vector< Trixel< T > > &mesh)
	Centre a triangulation at (0,0,0).

Variables
template<class T >
const T	phi = (1.0+2.23606797749979)*0.5
	Golden ratio.
template<class T >
const std::vector< vec3< T > >	DODECAHEDRON_VERTICES
	A centred Dodecahedron's vertices.
template<class T >
const std::vector< Trixel< T > >	DODECAHEDRON
	A centred Dodecahedron's triangulation.
template<class T >
const T	ICOSAHEDRON_X = 0.525731112119133606
	Golden ratio scaled for a unit icosahedron.
template<class T >
const T	ICOSAHEDRON_Z = 0.850650808352039932
	1 scaled for a unit icosahedron.
template<class T >
const std::vector< vec3< T > >	ICOSAHEDRON_VERTICES
	A centred Icosahedron's vertices.
template<class T >
const std::vector< Trixel< T > >	ICOSAHEDRON
	A centred Icosahedrons's triangulation.
template<class T >
const std::vector< vec3< T > >	OCTAHEDRON_VERTICES
	A centred Octahedron's vertices.
template<class T >
const std::vector< Trixel< T > >	OCTAHEDRON
	A centred Octahedron's triangulation.
template<class T >
const T	INV_SQRT3 = 1.0/1.7320508075688772
template<class T >
const std::vector< vec3< T > >	TETRAHEDRON_VERTICES
	A centred Tetrahedron's vertices.
template<class T >
const std::vector< Trixel< T > >	TETRAHEDRON
	A centred Tetrahedron's triangulation.
template<class T >
const T	INV_SQRT2 = 1.0/1.4142135623730951
template<class T >
const std::vector< vec3< T > >	CUBE_VERTICES
	A centred Cube's vertices.
template<class T >
const std::vector< Trixel< T > >	CUBE
	A centred Cube's triangulation.
template<class T >
const T	SQRT3 = 1.7320508075688772
template<class T >
const T	SQRT6 = 2.449489742783178
template<class T >
const T	C = 0.5021179759100816
template<class T >
const std::vector< vec3< T > >	TRIAUGMENTED_TRIANGULAR_PRISM_VERTICES
	A centred Triagmented triangular prism's vertices.
template<class T >
const std::vector< Trixel< T > >	TRIAUGMENTED_TRIANGULAR_PRISM
	A centred Triagmented triangular prism's triangulation.

Function Documentation

centreMesh()

template<class T >

void centreMesh

(

std::vector< Trixel< T > > &

mesh

)

Centre a triangulation at (0,0,0).

Template Parameters

T	numeric type.

Parameters

mesh	the triangulation to centre.

Variable Documentation

C

template<class T >

const T C = 0.5021179759100816

CUBE

template<class T >

const std::vector<Trixel<T> > CUBE

Initial value:

=
{
        {"F0", CUBE_VERTICES<T>[0], CUBE_VERTICES<T>[1], CUBE_VERTICES<T>[2]},
        {"F1", CUBE_VERTICES<T>[2], CUBE_VERTICES<T>[3], CUBE_VERTICES<T>[0]},
        {"R0", CUBE_VERTICES<T>[1], CUBE_VERTICES<T>[5], CUBE_VERTICES<T>[6]},
        {"R1", CUBE_VERTICES<T>[6], CUBE_VERTICES<T>[2], CUBE_VERTICES<T>[1]},
        {"B0", CUBE_VERTICES<T>[7], CUBE_VERTICES<T>[6], CUBE_VERTICES<T>[5]},
        {"B1", CUBE_VERTICES<T>[5], CUBE_VERTICES<T>[4], CUBE_VERTICES<T>[7]},
        {"L0", CUBE_VERTICES<T>[4], CUBE_VERTICES<T>[0], CUBE_VERTICES<T>[3]},
        {"L1", CUBE_VERTICES<T>[3], CUBE_VERTICES<T>[7], CUBE_VERTICES<T>[4]},
        {"L0", CUBE_VERTICES<T>[4], CUBE_VERTICES<T>[5], CUBE_VERTICES<T>[1]},
        {"L1", CUBE_VERTICES<T>[1], CUBE_VERTICES<T>[0], CUBE_VERTICES<T>[4]},
        {"T0", CUBE_VERTICES<T>[3], CUBE_VERTICES<T>[2], CUBE_VERTICES<T>[6]},
        {"T1", CUBE_VERTICES<T>[6], CUBE_VERTICES<T>[7], CUBE_VERTICES<T>[3]}
}

A centred Cube's triangulation.

Template Parameters

T	numeric type.

CUBE_VERTICES

template<class T >

const std::vector<vec3<T> > CUBE_VERTICES

Initial value:

=
{
  INV_SQRT2<T>*vec3<T>(-1.0, -1.0, 1.0),
  INV_SQRT2<T>*vec3<T>(1.0, -1.0, 1.0),
  INV_SQRT2<T>*vec3<T>(1.0, 1.0, 1.0),
  INV_SQRT2<T>*vec3<T>(-1.0, 1.0, 1.0),
  INV_SQRT2<T>*vec3<T>(-1.0, -1.0, -1.0),
  INV_SQRT2<T>*vec3<T>(1.0, -1.0, -1.0),
  INV_SQRT2<T>*vec3<T>(1.0, 1.0, -1.0),
  INV_SQRT2<T>*vec3<T>(-1.0, 1.0, -1.0)
}

A centred Cube's vertices.

Template Parameters

T	numeric type.

DODECAHEDRON

template<class T >

const std::vector<Trixel<T> > DODECAHEDRON

A centred Dodecahedron's triangulation.

Template Parameters

T	numeric type.

DODECAHEDRON_VERTICES

template<class T >

const std::vector<vec3<T> > DODECAHEDRON_VERTICES

Initial value:

=
{
    vec3<T>(1.0, 1.0, 1.0)/phi<T>,
    vec3<T>(1.0, 1.0, -1.0)/phi<T>,
    vec3<T>(1.0, -1.0, 1.0)/phi<T>,
    vec3<T>(-1.0, 1.0, 1.0)/phi<T>,
    vec3<T>(-1.0, -1.0, -1.0)/phi<T>,
    vec3<T>(-1.0, -1.0, 1.0)/phi<T>,
    vec3<T>(-1.0, 1.0, -1.0)/phi<T>,
    vec3<T>(1.0, -1.0, -1.0)/phi<T>,
    vec3<T>(0.0, phi<T>, 1.0/phi<T>)/phi<T>,
    vec3<T>(0.0, phi<T>, -1.0/phi<T>)/phi<T>,
    vec3<T>(0.0, -phi<T>, 1.0/phi<T>)/phi<T>,
    vec3<T>(0.0, -phi<T>, -1.0/phi<T>)/phi<T>,
    vec3<T>(1.0/phi<T>, 0.0, phi<T>)/phi<T>,
    vec3<T>(1.0/phi<T>, 0.0, -phi<T>)/phi<T>,
    vec3<T>(-1.0/phi<T>, 0.0, phi<T>)/phi<T>,
    vec3<T>(-1.0/phi<T>, 0.0, -phi<T>)/phi<T>,
    vec3<T>(phi<T>, 1.0/phi<T>, 0.0)/phi<T>,
    vec3<T>(phi<T>, -1.0/phi<T>, 0.0)/phi<T>,
    vec3<T>(-phi<T>, 1.0/phi<T>, 0.0)/phi<T>,
    vec3<T>(-phi<T>, -1.0/phi<T>, 0.0)/phi<T>
}

A centred Dodecahedron's vertices.

Template Parameters

T	numeric type.

ICOSAHEDRON

template<class T >

const std::vector<Trixel<T> > ICOSAHEDRON

Initial value:

=
{
  {"0", ICOSAHEDRON_VERTICES<T>[1],ICOSAHEDRON_VERTICES<T>[4],ICOSAHEDRON_VERTICES<T>[0]},
  {"1", ICOSAHEDRON_VERTICES<T>[4],ICOSAHEDRON_VERTICES<T>[9],ICOSAHEDRON_VERTICES<T>[0]},
  {"2", ICOSAHEDRON_VERTICES<T>[4],ICOSAHEDRON_VERTICES<T>[5],ICOSAHEDRON_VERTICES<T>[9]},
  {"3", ICOSAHEDRON_VERTICES<T>[8],ICOSAHEDRON_VERTICES<T>[5],ICOSAHEDRON_VERTICES<T>[4]},
  {"4", ICOSAHEDRON_VERTICES<T>[1],ICOSAHEDRON_VERTICES<T>[8],ICOSAHEDRON_VERTICES<T>[4]},
  {"5", ICOSAHEDRON_VERTICES<T>[1],ICOSAHEDRON_VERTICES<T>[10],ICOSAHEDRON_VERTICES<T>[8]},
  {"6", ICOSAHEDRON_VERTICES<T>[10],ICOSAHEDRON_VERTICES<T>[3],ICOSAHEDRON_VERTICES<T>[8]},
  {"7", ICOSAHEDRON_VERTICES<T>[8],ICOSAHEDRON_VERTICES<T>[3],ICOSAHEDRON_VERTICES<T>[5]},
  {"8", ICOSAHEDRON_VERTICES<T>[3],ICOSAHEDRON_VERTICES<T>[2],ICOSAHEDRON_VERTICES<T>[5]},
  {"9", ICOSAHEDRON_VERTICES<T>[3],ICOSAHEDRON_VERTICES<T>[7],ICOSAHEDRON_VERTICES<T>[2]},
  {"10", ICOSAHEDRON_VERTICES<T>[3],ICOSAHEDRON_VERTICES<T>[10],ICOSAHEDRON_VERTICES<T>[7]},
  {"11", ICOSAHEDRON_VERTICES<T>[10],ICOSAHEDRON_VERTICES<T>[6],ICOSAHEDRON_VERTICES<T>[7]},
  {"12", ICOSAHEDRON_VERTICES<T>[6],ICOSAHEDRON_VERTICES<T>[11],ICOSAHEDRON_VERTICES<T>[7]},
  {"13", ICOSAHEDRON_VERTICES<T>[6],ICOSAHEDRON_VERTICES<T>[0],ICOSAHEDRON_VERTICES<T>[11]},
  {"14", ICOSAHEDRON_VERTICES<T>[6],ICOSAHEDRON_VERTICES<T>[1],ICOSAHEDRON_VERTICES<T>[0]},
  {"15", ICOSAHEDRON_VERTICES<T>[10],ICOSAHEDRON_VERTICES<T>[1],ICOSAHEDRON_VERTICES<T>[6]},
  {"16", ICOSAHEDRON_VERTICES<T>[11],ICOSAHEDRON_VERTICES<T>[0],ICOSAHEDRON_VERTICES<T>[9]},
  {"17", ICOSAHEDRON_VERTICES<T>[2],ICOSAHEDRON_VERTICES<T>[11],ICOSAHEDRON_VERTICES<T>[9]},
  {"18", ICOSAHEDRON_VERTICES<T>[5],ICOSAHEDRON_VERTICES<T>[2],ICOSAHEDRON_VERTICES<T>[9]},
  {"19", ICOSAHEDRON_VERTICES<T>[11],ICOSAHEDRON_VERTICES<T>[2],ICOSAHEDRON_VERTICES<T>[7]}
}

A centred Icosahedrons's triangulation.

Template Parameters

T	numeric type.

ICOSAHEDRON_VERTICES

template<class T >

const std::vector<vec3<T> > ICOSAHEDRON_VERTICES

Initial value:

=
{
  {-ICOSAHEDRON_X<T>,0.0,ICOSAHEDRON_Z<T>}, {ICOSAHEDRON_X<T>,0.0,ICOSAHEDRON_Z<T>}, {-ICOSAHEDRON_X<T>,0.0,-ICOSAHEDRON_Z<T>}, {ICOSAHEDRON_X<T>,0.0,-ICOSAHEDRON_Z<T>},
  {0.0,ICOSAHEDRON_Z<T>,ICOSAHEDRON_X<T>}, {0.0,ICOSAHEDRON_Z<T>,-ICOSAHEDRON_X<T>}, {0.0,-ICOSAHEDRON_Z<T>,ICOSAHEDRON_X<T>}, {0.0,-ICOSAHEDRON_Z<T>,-ICOSAHEDRON_X<T>},
  {ICOSAHEDRON_Z<T>,ICOSAHEDRON_X<T>,0.0}, {-ICOSAHEDRON_Z<T>,ICOSAHEDRON_X<T>, 0.0}, {ICOSAHEDRON_Z<T>,-ICOSAHEDRON_X<T>,0.0}, {-ICOSAHEDRON_Z<T>,-ICOSAHEDRON_X<T>, 0.0}
}

A centred Icosahedron's vertices.

Template Parameters

T	numeric type.

ICOSAHEDRON_X

template<class T >

const T ICOSAHEDRON_X = 0.525731112119133606

Golden ratio scaled for a unit icosahedron.

Template Parameters

T	numeric type.

ICOSAHEDRON_Z

template<class T >

const T ICOSAHEDRON_Z = 0.850650808352039932

1 scaled for a unit icosahedron.

Template Parameters

T	numeric type.

INV_SQRT2

template<class T >

const T INV_SQRT2 = 1.0/1.4142135623730951

INV_SQRT3

template<class T >

const T INV_SQRT3 = 1.0/1.7320508075688772

OCTAHEDRON

template<class T >

const std::vector<Trixel<T> > OCTAHEDRON

Initial value:

=
{
  {"S0",OCTAHEDRON_VERTICES<T>[1],OCTAHEDRON_VERTICES<T>[5],OCTAHEDRON_VERTICES<T>[2],3},
  {"N0",OCTAHEDRON_VERTICES<T>[1],OCTAHEDRON_VERTICES<T>[0],OCTAHEDRON_VERTICES<T>[4],3},
  {"S1",OCTAHEDRON_VERTICES<T>[2],OCTAHEDRON_VERTICES<T>[5],OCTAHEDRON_VERTICES<T>[3],3},
  {"N1",OCTAHEDRON_VERTICES<T>[4],OCTAHEDRON_VERTICES<T>[0],OCTAHEDRON_VERTICES<T>[3],3},
  {"S2",OCTAHEDRON_VERTICES<T>[3],OCTAHEDRON_VERTICES<T>[5],OCTAHEDRON_VERTICES<T>[4],3},
  {"N2",OCTAHEDRON_VERTICES<T>[3],OCTAHEDRON_VERTICES<T>[0],OCTAHEDRON_VERTICES<T>[2],3},
  {"S3",OCTAHEDRON_VERTICES<T>[4],OCTAHEDRON_VERTICES<T>[5],OCTAHEDRON_VERTICES<T>[1],3},
  {"N3",OCTAHEDRON_VERTICES<T>[2],OCTAHEDRON_VERTICES<T>[0],OCTAHEDRON_VERTICES<T>[1],3}
}

A centred Octahedron's triangulation.

Template Parameters

T	numeric type.

OCTAHEDRON_VERTICES

template<class T >

const std::vector<vec3<T> > OCTAHEDRON_VERTICES

Initial value:

=
{
  {0.0,0.0,1.0},
  {1.0,0.0,0.0},
  {0.0,1.0,0.0},
  {-1.0,0.0,0.0},
  {0.0,-1.0,0.0},
  {0.0,0.0,-1.0}
}

A centred Octahedron's vertices.

Template Parameters

T	numeric type.

phi

template<class T >

const T phi = (1.0+2.23606797749979)*0.5

Golden ratio.

Template Parameters

T	numeric type.

SQRT3

template<class T >

const T SQRT3 = 1.7320508075688772

SQRT6

template<class T >

const T SQRT6 = 2.449489742783178

TETRAHEDRON

template<class T >

const std::vector<Trixel<T> > TETRAHEDRON

Initial value:

=
{
  {"0",TETRAHEDRON_VERTICES<T>[1],TETRAHEDRON_VERTICES<T>[0],TETRAHEDRON_VERTICES<T>[2]},
  {"1",TETRAHEDRON_VERTICES<T>[3],TETRAHEDRON_VERTICES<T>[0],TETRAHEDRON_VERTICES<T>[1]},
  {"2",TETRAHEDRON_VERTICES<T>[2],TETRAHEDRON_VERTICES<T>[3],TETRAHEDRON_VERTICES<T>[1]},
  {"3",TETRAHEDRON_VERTICES<T>[0],TETRAHEDRON_VERTICES<T>[3],TETRAHEDRON_VERTICES<T>[2]},
}

A centred Tetrahedron's triangulation.

Template Parameters

T	numeric type.

TETRAHEDRON_VERTICES

template<class T >

const std::vector<vec3<T> > TETRAHEDRON_VERTICES

Initial value:

=
{
  vec3<T>(1.0, 1.0, 1.0)*INV_SQRT3<T>,
  vec3<T>(-1.0,1.0, -1.0)*INV_SQRT3<T>,
  vec3<T>(1.0, -1.0, -1.0)*INV_SQRT3<T>,
  vec3<T>(-1.0, -1.0, 1.0)*INV_SQRT3<T>
}

A centred Tetrahedron's vertices.

Template Parameters

T	numeric type.

TRIAUGMENTED_TRIANGULAR_PRISM

template<class T >

const std::vector<Trixel<T> > TRIAUGMENTED_TRIANGULAR_PRISM

Initial value:

=
{
  {"0",TRIAUGMENTED_TRIANGULAR_PRISM_VERTICES<T>[3],TRIAUGMENTED_TRIANGULAR_PRISM_VERTICES<T>[6],TRIAUGMENTED_TRIANGULAR_PRISM_VERTICES<T>[2]},
  {"1",TRIAUGMENTED_TRIANGULAR_PRISM_VERTICES<T>[5],TRIAUGMENTED_TRIANGULAR_PRISM_VERTICES<T>[6],TRIAUGMENTED_TRIANGULAR_PRISM_VERTICES<T>[3]},
  {"2",TRIAUGMENTED_TRIANGULAR_PRISM_VERTICES<T>[4],TRIAUGMENTED_TRIANGULAR_PRISM_VERTICES<T>[6],TRIAUGMENTED_TRIANGULAR_PRISM_VERTICES<T>[5]},
  {"3",TRIAUGMENTED_TRIANGULAR_PRISM_VERTICES<T>[2],TRIAUGMENTED_TRIANGULAR_PRISM_VERTICES<T>[6],TRIAUGMENTED_TRIANGULAR_PRISM_VERTICES<T>[4]},
  {"4",TRIAUGMENTED_TRIANGULAR_PRISM_VERTICES<T>[7],TRIAUGMENTED_TRIANGULAR_PRISM_VERTICES<T>[2],TRIAUGMENTED_TRIANGULAR_PRISM_VERTICES<T>[4]},
  {"5",TRIAUGMENTED_TRIANGULAR_PRISM_VERTICES<T>[0],TRIAUGMENTED_TRIANGULAR_PRISM_VERTICES<T>[3],TRIAUGMENTED_TRIANGULAR_PRISM_VERTICES<T>[2]},
  {"6",TRIAUGMENTED_TRIANGULAR_PRISM_VERTICES<T>[1],TRIAUGMENTED_TRIANGULAR_PRISM_VERTICES<T>[4],TRIAUGMENTED_TRIANGULAR_PRISM_VERTICES<T>[5]},
  {"7",TRIAUGMENTED_TRIANGULAR_PRISM_VERTICES<T>[5],TRIAUGMENTED_TRIANGULAR_PRISM_VERTICES<T>[3],TRIAUGMENTED_TRIANGULAR_PRISM_VERTICES<T>[8]},
  {"8",TRIAUGMENTED_TRIANGULAR_PRISM_VERTICES<T>[8],TRIAUGMENTED_TRIANGULAR_PRISM_VERTICES<T>[0],TRIAUGMENTED_TRIANGULAR_PRISM_VERTICES<T>[1]},
  {"9",TRIAUGMENTED_TRIANGULAR_PRISM_VERTICES<T>[1],TRIAUGMENTED_TRIANGULAR_PRISM_VERTICES<T>[0],TRIAUGMENTED_TRIANGULAR_PRISM_VERTICES<T>[7]},
  {"10",TRIAUGMENTED_TRIANGULAR_PRISM_VERTICES<T>[0],TRIAUGMENTED_TRIANGULAR_PRISM_VERTICES<T>[2],TRIAUGMENTED_TRIANGULAR_PRISM_VERTICES<T>[7]},
  {"11",TRIAUGMENTED_TRIANGULAR_PRISM_VERTICES<T>[8],TRIAUGMENTED_TRIANGULAR_PRISM_VERTICES<T>[3],TRIAUGMENTED_TRIANGULAR_PRISM_VERTICES<T>[0]},
  {"12",TRIAUGMENTED_TRIANGULAR_PRISM_VERTICES<T>[1],TRIAUGMENTED_TRIANGULAR_PRISM_VERTICES<T>[7],TRIAUGMENTED_TRIANGULAR_PRISM_VERTICES<T>[4]},
  {"13",TRIAUGMENTED_TRIANGULAR_PRISM_VERTICES<T>[5],TRIAUGMENTED_TRIANGULAR_PRISM_VERTICES<T>[8],TRIAUGMENTED_TRIANGULAR_PRISM_VERTICES<T>[1]}
}

A centred Triagmented triangular prism's triangulation.

Template Parameters

T	numeric type.

TRIAUGMENTED_TRIANGULAR_PRISM_VERTICES

template<class T >

const std::vector<vec3<T> > TRIAUGMENTED_TRIANGULAR_PRISM_VERTICES

Initial value:

=
{
  C<T>*vec3<T>(0.0, -2.0/SQRT3<T>, 1.0),
  C<T>*vec3<T>(0.0, -2.0/SQRT3<T>, -1.0),
  C<T>*vec3<T>(1.0, 1.0/SQRT3<T>, 1.0),
  C<T>*vec3<T>(-1.0, 1.0/SQRT3<T>, 1.0),
  C<T>*vec3<T>(1.0, 1.0/SQRT3<T>, -1.0),
  C<T>*vec3<T>(-1.0, 1.0/SQRT3<T>, -1.0),
  C<T>*vec3<T>(0.0, (1.0+SQRT6<T>)/SQRT3<T>, 0.0),
  C<T>*vec3<T>((1.0+SQRT6<T>)/2.0, -(1.0+SQRT6<T>)/(2.0*SQRT3<T>), 0.0),
  C<T>*vec3<T>(-(1.0+SQRT6<T>)/2.0, -(1.0+SQRT6<T>)/(2.0*SQRT3<T>), 0.0)
}

A centred Triagmented triangular prism's vertices.

Template Parameters

T	numeric type.