C# Class R3.Geometry.H3Models.Ball

Public Methods

Method	Description
ApplyMobius ( Mobius m, Vector3D v ) : Vector3D	Helper to apply a Mobius to the ball model. Vector is taken to UHS, mobius applied, then taken back.
ClosestToOrigin ( Circle3D c ) : Vector3D	Given a geodesic circle, find the point closest to the origin.
ClosestToOrigin ( Sphere s ) : Vector3D	Given a geodesic sphere, find the point closest to the origin.
DupinCyclideSphere ( Vector3D vNonEuclidean, double radiusEuclideanOrigin, Geometry g, Vector3D &centerEuclidean, double &radiusEuclidean ) : void	Helper that works in all geometries. center: http://www.wolframalpha.com/input/?i=%28+%28+%28+r+%2B+p+%29+%2F+%28+1+-+rp+%29+%29+%2B+%28+%28+-r+%2B+p+%29+%2F+%28+1+%2B+rp+%29+%29++%29+%2F+2 radius: http://www.wolframalpha.com/input/?i=%28+%28+%28+r+%2B+p+%29+%2F+%28+1+-+rp+%29+%29+-+%28+%28+-r+%2B+p+%29+%2F+%28+1+%2B+rp+%29+%29++%29+%2F+2
DupinCyclideSphere ( Vector3D v, double radiusEuclideanOrigin, Vector3D &centerEuclidean, double &radiusEuclidean ) : void	Calculates the euclidean center/radius of a standard sphere transformed to the nonEuclidean point v. The standard sphere is the sphere at the origin having euclidean radius 'radiusEuclideanOrigin'.
Geodesic ( Vector3D v1, Vector3D v2, Vector3D &center, double &radius, Vector3D &normal, double &angleTot ) : void
GeodesicIdealEndpoints ( Vector3D v1, Vector3D v2, Vector3D &b1, Vector3D &b2 ) : void	Given two points (in the ball model), find the endpoints of the associated geodesic that lie on the boundary.
GeodesicPoints ( Vector3D v1, Vector3D v2, double quality = 1.0 ) : Vector3D[]	Calculate points along a geodesic segment from v1 to v2. quality can vary from 0 to 1.
GeodesicPoints ( Vector3D v1, Vector3D v2, int div ) : Vector3D[]	Calculate points along a geodesic segment from v1 to v2.
HDist ( Vector3D u, Vector3D v ) : double	Returns the hyperbolic distance between two points.
IdealCircle ( Sphere s ) : Circle3D	Given a geodesic sphere, returns it's intersection with the boundary plane.
IdealPoints ( Sphere s, Vector3D &s1, Vector3D &s2, Vector3D &s3 ) : void	Given a geodesic sphere, calculates 3 ideal points of the sphere. NOTE: s1 and s2 will be antipodal on the ideal circle.
LODThin ( Vector3D e1, Vector3D e2, int &div ) : void
LOD_Finite ( Vector3D e1, Vector3D e2, int &div1, int &div2, H3 settings ) : void	LOD
LOD_Ideal ( Vector3D e1, Vector3D e2, int &div1, int &div2, H3 settings ) : void
Midpoint ( H3 edge ) : Vector3D	Calculate the hyperbolic midpoint of an edge. Only works for non-ideal edges at the moment.
OrthogonalCircle ( Circle3D c, Vector3D v1, Vector3D v2 ) : Circle3D	Given 2 points on the boundary of a circle, calculate the orthogonal circle.
OrthogonalCircle ( Vector3D v1, Vector3D v2 ) : Circle3D
OrthogonalCircle ( Vector3D v1, Vector3D v2, Vector3D &center, double &radius ) : void	Given 2 points on the surface of the ball, calculate the center and radius of the orthogonal circle.
OrthogonalCircleInterior ( Vector3D v1, Vector3D v2, Circle3D &circle ) : void	Given 2 points in the interior of the ball, calculate the center and radius of the orthogonal circle. One point may optionally be on the boundary, but one shoudl be in the interior. If both points are on the boundary, we'll fall back on our other method.
OrthogonalSphere ( Vector3D b1, Vector3D b2, Vector3D b3 ) : Sphere	Find the sphere defined by 3 points on the unit sphere, and orthogonal to the unit sphere. Returns null if points are not on the unit sphere.
OrthogonalSphereInterior ( Vector3D v ) : Sphere	Find an orthogonal sphere defined by a single interior point. This point is the unique point on the sphere that is furthest from the ball boundary. (equivalently, closest to the origin)
OrthogonalSphereInterior ( Vector3D c1, Vector3D c2, Vector3D c3 ) : Sphere	Find the sphere defined by 3 points in the interior of the unit sphere, and orthogonal to the unit sphere.
SizeFunc ( Vector3D v, double angularThickness ) : double	A size function for the ball model. Returns a radius.

Private Methods

Method	Description
ApplyMinRadiusForPrinting ( double &radius ) : void
ApplyMinRadiusForWiki ( double &radius ) : void
HalfTo ( Vector3D v ) : Vector3D

Method Details

ApplyMobius() public static method

Helper to apply a Mobius to the ball model. Vector is taken to UHS, mobius applied, then taken back.

public static ApplyMobius ( Mobius m, Vector3D v ) : Vector3D
m	R3.Math.Mobius
v	Vector3D
return	Vector3D

ClosestToOrigin() public static method

Given a geodesic circle, find the point closest to the origin.

public static ClosestToOrigin ( Circle3D c ) : Vector3D
c	Circle3D
return	Vector3D

ClosestToOrigin() public static method

Given a geodesic sphere, find the point closest to the origin.

public static ClosestToOrigin ( Sphere s ) : Vector3D
s	Sphere
return	Vector3D

DupinCyclideSphere() public static method

Helper that works in all geometries. center: http://www.wolframalpha.com/input/?i=%28+%28+%28+r+%2B+p+%29+%2F+%28+1+-+r*p+%29+%29+%2B+%28+%28+-r+%2B+p+%29+%2F+%28+1+%2B+r*p+%29+%29++%29+%2F+2 radius: http://www.wolframalpha.com/input/?i=%28+%28+%28+r+%2B+p+%29+%2F+%28+1+-+r*p+%29+%29+-+%28+%28+-r+%2B+p+%29+%2F+%28+1+%2B+r*p+%29+%29++%29+%2F+2

public static DupinCyclideSphere ( Vector3D vNonEuclidean, double radiusEuclideanOrigin, Geometry g, Vector3D &centerEuclidean, double &radiusEuclidean ) : void
vNonEuclidean	Vector3D
radiusEuclideanOrigin	double
g	Geometry
centerEuclidean	Vector3D
radiusEuclidean	double
return	void

DupinCyclideSphere() public static method

Calculates the euclidean center/radius of a standard sphere transformed to the nonEuclidean point v. The standard sphere is the sphere at the origin having euclidean radius 'radiusEuclideanOrigin'.

public static DupinCyclideSphere ( Vector3D v, double radiusEuclideanOrigin, Vector3D &centerEuclidean, double &radiusEuclidean ) : void
v	Vector3D
radiusEuclideanOrigin	double
centerEuclidean	Vector3D
radiusEuclidean	double
return	void

Geodesic() public static method

public static Geodesic ( Vector3D v1, Vector3D v2, Vector3D &center, double &radius, Vector3D &normal, double &angleTot ) : void
v1	Vector3D
v2	Vector3D
center	Vector3D
radius	double
normal	Vector3D
angleTot	double
return	void

GeodesicIdealEndpoints() public static method

Given two points (in the ball model), find the endpoints of the associated geodesic that lie on the boundary.

public static GeodesicIdealEndpoints ( Vector3D v1, Vector3D v2, Vector3D &b1, Vector3D &b2 ) : void
v1	Vector3D
v2	Vector3D
b1	Vector3D
b2	Vector3D
return	void

GeodesicPoints() public static method

Calculate points along a geodesic segment from v1 to v2. quality can vary from 0 to 1.

public static GeodesicPoints ( Vector3D v1, Vector3D v2, double quality = 1.0 ) : Vector3D[]
v1	Vector3D
v2	Vector3D
quality	double
return	Vector3D[]

GeodesicPoints() public static method

Calculate points along a geodesic segment from v1 to v2.

public static GeodesicPoints ( Vector3D v1, Vector3D v2, int div ) : Vector3D[]
v1	Vector3D
v2	Vector3D
div	int
return	Vector3D[]

HDist() public static method

Returns the hyperbolic distance between two points.

public static HDist ( Vector3D u, Vector3D v ) : double
u	Vector3D
v	Vector3D
return	double

IdealCircle() public static method

Given a geodesic sphere, returns it's intersection with the boundary plane.

public static IdealCircle ( Sphere s ) : Circle3D
s	Sphere
return	Circle3D

IdealPoints() public static method

Given a geodesic sphere, calculates 3 ideal points of the sphere. NOTE: s1 and s2 will be antipodal on the ideal circle.

public static IdealPoints ( Sphere s, Vector3D &s1, Vector3D &s2, Vector3D &s3 ) : void
s	Sphere
s1	Vector3D
s2	Vector3D
s3	Vector3D
return	void

LODThin() public static method

public static LODThin ( Vector3D e1, Vector3D e2, int &div ) : void
e1	Vector3D
e2	Vector3D
div	int
return	void

LOD_Finite() public static method

LOD

public static LOD_Finite ( Vector3D e1, Vector3D e2, int &div1, int &div2, H3 settings ) : void
e1	Vector3D
e2	Vector3D
div1	int
div2	int
settings	H3
return	void

LOD_Ideal() public static method

public static LOD_Ideal ( Vector3D e1, Vector3D e2, int &div1, int &div2, H3 settings ) : void
e1	Vector3D
e2	Vector3D
div1	int
div2	int
settings	H3
return	void

Midpoint() public static method

Calculate the hyperbolic midpoint of an edge. Only works for non-ideal edges at the moment.

public static Midpoint ( H3 edge ) : Vector3D
edge	H3
return	Vector3D

OrthogonalCircle() public static method

Given 2 points on the boundary of a circle, calculate the orthogonal circle.

public static OrthogonalCircle ( Circle3D c, Vector3D v1, Vector3D v2 ) : Circle3D
c	Circle3D
v1	Vector3D
v2	Vector3D
return	Circle3D

OrthogonalCircle() public static method

public static OrthogonalCircle ( Vector3D v1, Vector3D v2 ) : Circle3D
v1	Vector3D
v2	Vector3D
return	Circle3D

OrthogonalCircle() public static method

Given 2 points on the surface of the ball, calculate the center and radius of the orthogonal circle.

public static OrthogonalCircle ( Vector3D v1, Vector3D v2, Vector3D &center, double &radius ) : void
v1	Vector3D
v2	Vector3D
center	Vector3D
radius	double
return	void

OrthogonalCircleInterior() public static method

Given 2 points in the interior of the ball, calculate the center and radius of the orthogonal circle. One point may optionally be on the boundary, but one shoudl be in the interior. If both points are on the boundary, we'll fall back on our other method.

public static OrthogonalCircleInterior ( Vector3D v1, Vector3D v2, Circle3D &circle ) : void
v1	Vector3D
v2	Vector3D
circle	Circle3D
return	void

OrthogonalSphere() public static method

Find the sphere defined by 3 points on the unit sphere, and orthogonal to the unit sphere. Returns null if points are not on the unit sphere.

public static OrthogonalSphere ( Vector3D b1, Vector3D b2, Vector3D b3 ) : Sphere
b1	Vector3D
b2	Vector3D
b3	Vector3D
return	Sphere

OrthogonalSphereInterior() public static method

Find an orthogonal sphere defined by a single interior point. This point is the unique point on the sphere that is furthest from the ball boundary. (equivalently, closest to the origin)

public static OrthogonalSphereInterior ( Vector3D v ) : Sphere
v	Vector3D
return	Sphere

OrthogonalSphereInterior() public static method

Find the sphere defined by 3 points in the interior of the unit sphere, and orthogonal to the unit sphere.

public static OrthogonalSphereInterior ( Vector3D c1, Vector3D c2, Vector3D c3 ) : Sphere
c1	Vector3D
c2	Vector3D
c3	Vector3D
return	Sphere

SizeFunc() public static method

A size function for the ball model. Returns a radius.

public static SizeFunc ( Vector3D v, double angularThickness ) : double
v	Vector3D
angularThickness	double
return	double