jv.vecmath

Class PuLorentz

java.lang.Object

jv.vecmath.PuLorentz

public class PuLorentz
extends java.lang.Object

Utility methods for calculations in Lorentz model of hyperbolic space. Coordinate system in Lorentz R4 usually has signature (-1,1,1,...).

Author:

Konrad Polthier

Version:

27.12.99, 1.10 revised (kp) Converted to Java.
00.00.92, 1.00 created (kp) Original C code.

Constructor Summary

Constructors

Constructor and Description
PuLorentz()

Method Summary

Modifier and Type	Method and Description
static double	abs(PdVector p, PdVector sign) Compute absolute value of point in Minkowski space.
static double	dist(PdVector p, PdVector q, PdVector sign) Distance of two points in Lorentz model of hyperbolic space.
static double	distMinkowski(PdVector p, PdVector q, PdVector sign) Compute distance of two points in Minkowski space by taking Euclidean different and norm with respect to signature metric.
static double	distToOrigin(PdVector p, PdVector sign) Distance of a point and the origin in Lorentz model of hyperbolic space.
static double	dot(PdVector p, PdVector q, PdVector sign) Scalar product of two vectors in Lorentz model of hyperbolic space.
static void	getTangent(PdVector tangent, PdVector p, PdVector q, PdVector sign) Compute unit tangent vector at point p of geodesic from p to q in Lorentz model of hyperbolic space.
static void	getTangentAtOrigin(PdVector tangent, PdVector p, PdVector sign) Compute unit tangent vector at origin of geodesic to point p in Lorentz model of hyperbolic space.
static void	invertAtPoint(PdMatrix mat, PdVector p, PdVector sign) Compute transformation 4*4 matrix to invert at given point.
static void	normalize(PdVector p, PdVector sign) Normalize Minkowski length of point.
static void	reflectAtOrigin(PdMatrix mat, PdVector q, PdVector r, PdVector sign) Compute transformation 4*4 matrix to reflect at plane through origin spanned by two given points.
static void	reflectAtPlane(PdMatrix mat, PdVector p, PdVector q, PdVector r, PdVector sign) Compute transformation 4*4 matrix to reflect at arbitrary plane spanned by three given points.
static void	rotateAroundLine(PdMatrix mat, PdVector p, PdVector q, double angle, PdVector sign) Compute transformation 4*4 matrix to rotate around geodesic connecting two given points.
static void	rotateAtOrigin(PdMatrix mat, PdVector p, double angle, PdVector sign) Compute rotation 4*4 matrix to rotate tangent space at origin around line in Lorentz model of hyperbolic space.
static void	setLength(PdVector p, double length, PdVector sign) Set Minkowski length of point to given length.
static double	sqrAbs(PdVector p, PdVector sign) Compute square of absolute value of point in Minkowski space.
static double	sqrDistMinkowski(PdVector p, PdVector q, PdVector sign) Compute square distance of two points in Minkowski space by taking Euclidean different and square norm with respect to signature metric.
static void	translate(PdMatrix mat, PdVector p, PdVector q, PdVector sign) Compute translation 4*4 matrix to move a point p to a point q in Lorentz model of hyperbolic space.
static void	translate2Origin(PdMatrix mat, PdVector p, PdVector sign) Compute translation 4*4 matrix to move a point p to origin in Lorentz model of hyperbolic space.
static void	translate2Point(PdMatrix mat, PdVector p, PdVector sign) Compute translation 4*4 matrix to move a point p to origin in Lorentz model of hyperbolic space.

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

PuLorentz

public PuLorentz()

Method Detail

abs

public static double abs(PdVector p,
                         PdVector sign)

Compute absolute value of point in Minkowski space.

Parameters:

p - point in Minkowski space

sign - Signature of space form

Returns:

absolute value

sqrAbs

public static double sqrAbs(PdVector p,
                            PdVector sign)

Compute square of absolute value of point in Minkowski space.

Parameters:

p - point in Minkowski space

sign - Signature of space form

Returns:

square of absolute value

distMinkowski

public static double distMinkowski(PdVector p,
                                   PdVector q,
                                   PdVector sign)

Compute distance of two points in Minkowski space by taking Euclidean different and norm with respect to signature metric. dist = |p-q|_L

Parameters:

p - point in Minkowski space

q - point in Minkowski space

sign - Signature of space form

Returns:

Minkowski distance of both points

sqrDistMinkowski

public static double sqrDistMinkowski(PdVector p,
                                      PdVector q,
                                      PdVector sign)

Compute square distance of two points in Minkowski space by taking Euclidean different and square norm with respect to signature metric. dist = (|p-q|_L)^2

Parameters:

p - point in Minkowski space

q - point in Minkowski space

sign - Signature of space form

Returns:

Square Minkowski distance of both points

normalize

public static void normalize(PdVector p,
                             PdVector sign)

Normalize Minkowski length of point. |v|_L == 1.

Parameters:

p - point in Minkowski space

sign - Signature of space form

setLength

public static void setLength(PdVector p,
                             double length,
                             PdVector sign)

Set Minkowski length of point to given length. |v|_L == length

Parameters:

p - point in Minkowski space

sign - Signature of space form

dot

public static double dot(PdVector p,
                         PdVector q,
                         PdVector sign)

Scalar product of two vectors in Lorentz model of hyperbolic space.

Parameters:

p - point in Lorentz model in R4_L

q - point in Lorentz model in R4_L

sign - Signature of space form

dist

public static double dist(PdVector p,
                          PdVector q,
                          PdVector sign)

Distance of two points in Lorentz model of hyperbolic space.

Parameters:

p - point in Lorentz model in R4_L

q - point in Lorentz model in R4_L

sign - Signature of space form

distToOrigin

public static double distToOrigin(PdVector p,
                                  PdVector sign)

Distance of a point and the origin in Lorentz model of hyperbolic space.

Parameters:

p - point in Lorentz model in R4_L

sign - Signature of space form

getTangent

public static void getTangent(PdVector tangent,
                              PdVector p,
                              PdVector q,
                              PdVector sign)

Compute unit tangent vector at point p of geodesic from p to q in Lorentz model of hyperbolic space.

Parameters:

tangent - resulting unit length tangent vector at p of geodesic from p to q

p - point in Lorentz model in R4_L

q - point in Lorentz model in R4_L

sign - Signature of space form

getTangentAtOrigin

public static void getTangentAtOrigin(PdVector tangent,
                                      PdVector p,
                                      PdVector sign)

Compute unit tangent vector at origin of geodesic to point p in Lorentz model of hyperbolic space.

Parameters:

tangent - resulting unit length tangent vector at origin of geodesic to p

p - point in Lorentz model in R4_L

sign - Signature of space form

translate2Origin

public static void translate2Origin(PdMatrix mat,
                                    PdVector p,
                                    PdVector sign)

Compute translation 4*4 matrix to move a point p to origin in Lorentz model of hyperbolic space.

Parameters:

mat - resulting translation 4*4 matrix to move a point p to origin

p - point in Lorentz model in R4_L

sign - Signature of space form

translate2Point

public static void translate2Point(PdMatrix mat,
                                   PdVector p,
                                   PdVector sign)

Compute translation 4*4 matrix to move a point p to origin in Lorentz model of hyperbolic space.

Parameters:

mat - resulting translation 4*4 matrix to move origin to point p

p - point in Lorentz model in R4_L

sign - Signature of space form

translate

public static void translate(PdMatrix mat,
                             PdVector p,
                             PdVector q,
                             PdVector sign)

Compute translation 4*4 matrix to move a point p to a point q in Lorentz model of hyperbolic space.

Parameters:

mat - resulting translation 4*4 matrix to move a point p to point q

p - point in Lorentz model in R4_L

q - point in Lorentz model in R4_L

sign - Signature of space form

rotateAtOrigin

public static void rotateAtOrigin(PdMatrix mat,
                                  PdVector p,
                                  double angle,
                                  PdVector sign)

Compute rotation 4*4 matrix to rotate tangent space at origin around line in Lorentz model of hyperbolic space.

Parameters:

mat - resulting rotation 4*4 matrix to rotate around line through origin

p - point in Lorentz model in R4_L specifying geodesic around to rotate

angle - angle in degrees specifying amount to rotate

sign - Signature of space form

rotateAroundLine

public static void rotateAroundLine(PdMatrix mat,
                                    PdVector p,
                                    PdVector q,
                                    double angle,
                                    PdVector sign)

Compute transformation 4*4 matrix to rotate around geodesic connecting two given points.

Parameters:

mat - resulting rotation 4*4 matrix to rotate around line through origin

p - (p,q): two points in Lorentz model in R4_L specifying geodesic around to rotate

q - (p,q): two points in Lorentz model in R4_L specifying geodesic around to rotate

angle - angle in degrees specifying amount to rotate

sign - Signature of space form

reflectAtOrigin

public static void reflectAtOrigin(PdMatrix mat,
                                   PdVector q,
                                   PdVector r,
                                   PdVector sign)

Compute transformation 4*4 matrix to reflect at plane through origin spanned by two given points.

Parameters:

mat - resulting reflection 4*4 matrix to reflect at plane through origin

q - (q,r): two points in Lorentz model in R4_L specifying plane to reflect at

r - (q,r): two points in Lorentz model in R4_L specifying plane to reflect at

sign - Signature of space form

reflectAtPlane

public static void reflectAtPlane(PdMatrix mat,
                                  PdVector p,
                                  PdVector q,
                                  PdVector r,
                                  PdVector sign)

Compute transformation 4*4 matrix to reflect at arbitrary plane spanned by three given points.

Parameters:

mat - resulting reflection 4*4 matrix to reflect at plane

p - (p,q,r): three points in Lorentz model in R4_L specifying plane to reflect at

q - (p,q,r): three points in Lorentz model in R4_L specifying plane to reflect at

r - (p,q,r): three points in Lorentz model in R4_L specifying plane to reflect at

sign - Signature of space form

invertAtPoint

public static void invertAtPoint(PdMatrix mat,
                                 PdVector p,
                                 PdVector sign)

Compute transformation 4*4 matrix to invert at given point.

Parameters:

mat - resulting inversion 4*4 matrix to invert at given point

p - point in Lorentz model in R4_L specifying center of inversion

sign - Signature of space form