C# Class R3.Geometry.SimplexCalcs

显示文件 Open project: roice3/Honeycombs Class Usage Examples

Public Methods

Method	Description
CalcEScale ( ) : void
DualEdgeBall ( Sphere facets ) : H3.Cell.Edge
FCOrientMobius ( int p, int q ) : Mobius
GoursatTetrahedron ( double A, double B, double C, double A_, double B_, double C_ ) : Vector3D[]	This calculates the 4 vertices of a general (but finite) Goursat Tetrahedron. Result is in the ball model. The method comes from the dissertation "Hyperbolic polyhedra: volume and scissors congruence", by Yana Zilberberg Mohanty, section 2.4, steps 1-5. A,B,C are the three dihedral angles surrounding a vertex. A_,B_,C_ are the three oppoite dihedral angles.
GramSchmidt ( Matrix4D input, Matrix4D innerProductValues ) : Matrix4D
HoneycombEdgeBall ( Sphere facets, Vector3D vertex ) : H3.Cell.Edge
HoneycombEdgeBall ( int p, int q, int r ) : H3.Cell.Edge
HyperboloidToBall ( VectorND hyperboloidPoint ) : Vector3D
Mirrors ( Vector3D verts ) : R3.Geometry.Sphere[]	Given the 4 verts of a tetrahedron (must lie within ball), Calculate the faces of the tetrahedron. Input and Output in ball model.
Mirrors ( int p, int q, int r, Vector3D &cellCenter, bool moveToBall = true, double scaling = -1 ) : R3.Geometry.Sphere[]
Mirrors ( int p, int q, int r, bool moveToBall = true, double scaling = -1 ) : R3.Geometry.Sphere[]
MirrorsEuclidean ( ) : R3.Geometry.Sphere[]
MirrorsSpherical ( int p, int q, int r ) : R3.Geometry.Sphere[]	Mirrors for Spherical geometry, in the ball model.
PrepForFacetCentering ( int p, int q, Sphere spheres, Vector3D &cellCenter ) : void	Inputs must be in UHS!
ReverseRows ( Matrix4D m ) : Matrix4D
SimplexEdgesBall ( int p, int q, int r ) : H3.Cell.Edge[]	Returns the 6 simplex edges in the Ball model.
SimplexEdgesUHS ( int p, int q, int r ) : H3.Cell.Edge[]	Returns the 6 simplex edges in the UHS model.
ToPovRay ( Sphere mirrors ) : void
VertexPointBall ( int p, int q, int r ) : Vector3D	Calculates the point of our simplex that is at a vertex.
VertexSpherical ( int p, int q, int r ) : Vector3D
VertsBall ( int p, int q, int r ) : Vector3D[]	Return the 4 simplex vertices in the ball model.
VertsEuclidean ( ) : Vector3D[]

Private Methods

Method	Description
BaseTileSegments ( int p, int q ) : Segment[]
CellCenterBall ( int p, int q, int r ) : Vector3D	Calculates the point of our simplex that is at the middle of an edge.
FaceCenterBall ( int p, int q, int r ) : Vector3D	Calculates the point of our simplex that is at the middle of an edge.
Finite ( int t ) : bool
FiniteOrInfinite ( int t ) : bool
HoneycombEdgeUHS ( int p, int q, int r ) : Circle3D
Infinite ( int t ) : bool
InteriorMirrors ( int p, int q ) : R3.Geometry.Sphere[]	Calculates the 3 mirrors connected to the cell center. This works in all geometries and returns results in the UHS model (or the appropriate analogue).
MidEdgePointBall ( int p, int q, int r ) : Vector3D	Calculates the point of our simplex that is at the middle of an edge.
MinkowskiInnerProduct ( VectorND v1, VectorND v2 ) : double
MinkowskiNormalize ( VectorND v ) : VectorND
RotateSphere ( Sphere s, double rotation ) : void	Helper to rotate a sphere about the z axis.
TilePoints ( int p, int q, Vector3D &p1, Vector3D &p2, Vector3D &p3, Segment &seg ) : void	Helper to construct some points we need for calculating simplex facets for a {p,q,r} honeycomb.

Method Details

CalcEScale() public static method

public static CalcEScale ( ) : void
return	void

DualEdgeBall() public static method

public static DualEdgeBall ( Sphere facets ) : H3.Cell.Edge
facets	Sphere
return	H3.Cell.Edge

FCOrientMobius() public static method

public static FCOrientMobius ( int p, int q ) : Mobius
p	int
q	int
return	R3.Math.Mobius

GoursatTetrahedron() public static method

This calculates the 4 vertices of a general (but finite) Goursat Tetrahedron. Result is in the ball model. The method comes from the dissertation "Hyperbolic polyhedra: volume and scissors congruence", by Yana Zilberberg Mohanty, section 2.4, steps 1-5. A,B,C are the three dihedral angles surrounding a vertex. A_,B_,C_ are the three oppoite dihedral angles.

public static GoursatTetrahedron ( double A, double B, double C, double A_, double B_, double C_ ) : Vector3D[]
A	double
B	double
C	double
A_	double
B_	double
C_	double
return	Vector3D[]

GramSchmidt() public static method

public static GramSchmidt ( Matrix4D input, Matrix4D innerProductValues ) : Matrix4D
input	R3.Math.Matrix4D
innerProductValues	R3.Math.Matrix4D
return	R3.Math.Matrix4D

HoneycombEdgeBall() public static method

public static HoneycombEdgeBall ( Sphere facets, Vector3D vertex ) : H3.Cell.Edge
facets	Sphere
vertex	Vector3D
return	H3.Cell.Edge

HoneycombEdgeBall() public static method

public static HoneycombEdgeBall ( int p, int q, int r ) : H3.Cell.Edge
p	int
q	int
r	int
return	H3.Cell.Edge

HyperboloidToBall() public static method

public static HyperboloidToBall ( VectorND hyperboloidPoint ) : Vector3D
hyperboloidPoint	VectorND
return	Vector3D

Mirrors() public static method

Given the 4 verts of a tetrahedron (must lie within ball), Calculate the faces of the tetrahedron. Input and Output in ball model.

public static Mirrors ( Vector3D verts ) : R3.Geometry.Sphere[]
verts	Vector3D
return	R3.Geometry.Sphere[]

Mirrors() public static method

public static Mirrors ( int p, int q, int r, Vector3D &cellCenter, bool moveToBall = true, double scaling = -1 ) : R3.Geometry.Sphere[]
p	int
q	int
r	int
cellCenter	Vector3D
moveToBall	bool
scaling	double
return	R3.Geometry.Sphere[]

Mirrors() public static method

public static Mirrors ( int p, int q, int r, bool moveToBall = true, double scaling = -1 ) : R3.Geometry.Sphere[]
p	int
q	int
r	int
moveToBall	bool
scaling	double
return	R3.Geometry.Sphere[]

MirrorsEuclidean() public static method

public static MirrorsEuclidean ( ) : R3.Geometry.Sphere[]
return	R3.Geometry.Sphere[]

MirrorsSpherical() public static method

Mirrors for Spherical geometry, in the ball model.

public static MirrorsSpherical ( int p, int q, int r ) : R3.Geometry.Sphere[]
p	int
q	int
r	int
return	R3.Geometry.Sphere[]

PrepForFacetCentering() public static method

Inputs must be in UHS!

public static PrepForFacetCentering ( int p, int q, Sphere spheres, Vector3D &cellCenter ) : void
p	int
q	int
spheres	Sphere
cellCenter	Vector3D
return	void

ReverseRows() public static method

public static ReverseRows ( Matrix4D m ) : Matrix4D
m	R3.Math.Matrix4D
return	R3.Math.Matrix4D

SimplexEdgesBall() public static method

Returns the 6 simplex edges in the Ball model.

public static SimplexEdgesBall ( int p, int q, int r ) : H3.Cell.Edge[]
p	int
q	int
r	int
return	H3.Cell.Edge[]

SimplexEdgesUHS() public static method

Returns the 6 simplex edges in the UHS model.

public static SimplexEdgesUHS ( int p, int q, int r ) : H3.Cell.Edge[]
p	int
q	int
r	int
return	H3.Cell.Edge[]

ToPovRay() public static method

public static ToPovRay ( Sphere mirrors ) : void
mirrors	Sphere
return	void

VertexPointBall() public static method

Calculates the point of our simplex that is at a vertex.

public static VertexPointBall ( int p, int q, int r ) : Vector3D
p	int
q	int
r	int
return	Vector3D

VertexSpherical() public static method

public static VertexSpherical ( int p, int q, int r ) : Vector3D
p	int
q	int
r	int
return	Vector3D

VertsBall() public static method

Return the 4 simplex vertices in the ball model.

public static VertsBall ( int p, int q, int r ) : Vector3D[]
p	int
q	int
r	int
return	Vector3D[]

VertsEuclidean() public static method

public static VertsEuclidean ( ) : Vector3D[]
return	Vector3D[]