C# 클래스 R3.Geometry.H3Models.Ball

공개 메소드들

메소드	설명
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.

비공개 메소드들

메소드	설명
ApplyMinRadiusForPrinting ( double &radius ) : void
ApplyMinRadiusForWiki ( double &radius ) : void
HalfTo ( Vector3D v ) : Vector3D

메소드 상세

ApplyMobius() 공개 정적인 메소드

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
리턴	Vector3D

ClosestToOrigin() 공개 정적인 메소드

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

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

ClosestToOrigin() 공개 정적인 메소드

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

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

DupinCyclideSphere() 공개 정적인 메소드

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
리턴	void

DupinCyclideSphere() 공개 정적인 메소드

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
리턴	void

Geodesic() 공개 정적인 메소드

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
리턴	void

GeodesicIdealEndpoints() 공개 정적인 메소드

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
리턴	void

GeodesicPoints() 공개 정적인 메소드

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
리턴	Vector3D[]

GeodesicPoints() 공개 정적인 메소드

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
리턴	Vector3D[]

HDist() 공개 정적인 메소드

Returns the hyperbolic distance between two points.

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

IdealCircle() 공개 정적인 메소드

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

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

IdealPoints() 공개 정적인 메소드

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
리턴	void

LODThin() 공개 정적인 메소드

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

LOD_Finite() 공개 정적인 메소드

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
리턴	void

LOD_Ideal() 공개 정적인 메소드

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
리턴	void

Midpoint() 공개 정적인 메소드

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

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

OrthogonalCircle() 공개 정적인 메소드

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
리턴	Circle3D

OrthogonalCircle() 공개 정적인 메소드

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

OrthogonalCircle() 공개 정적인 메소드

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
리턴	void

OrthogonalCircleInterior() 공개 정적인 메소드

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
리턴	void

OrthogonalSphere() 공개 정적인 메소드

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
리턴	Sphere

OrthogonalSphereInterior() 공개 정적인 메소드

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
리턴	Sphere

OrthogonalSphereInterior() 공개 정적인 메소드

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
리턴	Sphere

SizeFunc() 공개 정적인 메소드

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

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