PuProj ("JavaView Reference Manual")

java.lang.Object
- jv.vecmath.PuProj

```
public class PuProj
extends java.lang.Object
```
Projection between different models of Euclidean, spherical and hyperbolic space. All vertex projection methods implicitly use the dimension of the argument point which is being projected. The dimension of the resulting projected point depends on the dimension of the target model space.
Coordinate system in Lorentz Rn+1 has signature (1,..,1,-1).

Constructor Summary

Constructors
Constructor and Description

PuProj()

Constructors
Constructor and Description
`PuProj()`

Method Summary

Methods
Modifier and Type	Method and Description
`static void`	`diffKlein2Lorentz(PdMatrix diffMat, PdVector p)` Compute differential of projection map of H3 from Klein ball into Lorentz model at given point in Klein ball.
`static void`	`diffPoincare2Lorentz(PdMatrix diffMat, PdVector p)` Compute differential of projection map of H3 from Poincare ball into Lorentz model at given point in Poincare ball.
`static void`	`diffStereoInvR3_to_S3(PdMatrix diffMat, PdVector p)` Compute differential of inverse stereographic projection R3 to S3.
`static void`	`diffStereoS3_to_R3(PdMatrix diffMat, PdVector p)` Compute differential of stereographic projection S3 to R3 with projection center (1,0,0,0).
`static void`	`klein2Lorentz(PdVector pl, PdVector p)` Projection from Klein ball in Rn into Lorentz model in Rn+1 of n-dim hyperbolic space.
`static void`	`klein2Poincare(PdVector p, PdVector pk)` Projection from Klein ball to Poincare ball of n-dim hyperbolic space.
`static void`	`klein2Uhm(PdVector pu, PdVector p)` Projection of H3 from Klein ball to UHM of n-dim hyperbolic space.
`static void`	`lorentz2Klein(PdVector p, PdVector pl)` Projection from Lorentz model in Rn+1 into Klein ball in Rn of n-dim hyperbolic space.
`static void`	`lorentz2Poincare(PdVector p, PdVector pl)` Projection from Lorentz model in Rn+1 into Poincare ball in Rn of n-dim hyperbolic space.
`static void`	`lorentz2Uhm(PdVector p, PdVector pl)` Projection from Lorentz model in Rn+1 into UHM in Rn of n-dim hyperbolic space.
`static void`	`poincare2Klein(PdVector pk, PdVector p)` Projection from Poincare ball to Klein ball of n-dim hyperbolic space.
`static void`	`poincare2Lorentz(PdVector pl, PdVector p)` Projection from Poincare ball in Rn into Lorentz model in Rn+1 of n-dim hyperbolic space.
`static void`	`poincare2Uhm(PdVector pu, PdVector p)` Projection of H3 from Poincare ball to UHM of n-dim hyperbolic space.
`static void`	`stereographic(PdVector p, PdVector pl)` Stereographic projection of a sphere Sn into Rn with projection center (0,..,0,1).
`static void`	`stereoInvR3_to_S3(PdVector pl, PdVector p)` Projection from Rn p=(a,b,c) to Sn pl=(x,y,z,t).
`static void`	`stereoS3_to_R3(PdVector p, PdVector pl)` Deprecated. use stereographic(PdVector, PdVector)
`static void`	`uhm2Klein(PdVector p, PdVector pu)` Projection from UHM to Klein ball of n-dim hyperbolic space.
`static void`	`uhm2Lorentz(PdVector pl, PdVector p)` Projection from UHM in Rn into Lorentz model in Rn+1 of n-dim hyperbolic space.
`static void`	`uhm2Poincare(PdVector p, PdVector pu)` Projection from UHM to Poincare ball of n-dim hyperbolic space.

Methods inherited from class java.lang.Object
equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Constructor Detail
  - PuProj
```
public PuProj()
```
- Method Detail
  - lorentz2Klein
```
public static void lorentz2Klein(PdVector p,
                 PdVector pl)
```
    Projection from Lorentz model in Rn+1 into Klein ball in Rn of n-dim hyperbolic space. For Lorentz R4, a point (x,y,z,t) is mapped to (a, b, c) = (x, y, z)/t. Coordinate system in Lorentz R4 has signature (1,1,1,-1). The parameters may be identical vectors.
    
    Parameters:
    p - resulting vector in Klein ball
    pl - argument vector in Lorentz model
  - klein2Lorentz
```
public static void klein2Lorentz(PdVector pl,
                 PdVector p)
```
    Projection from Klein ball in Rn into Lorentz model in Rn+1 of n-dim hyperbolic space. For H3, (t, x, y, z) = (t, t * a, t * b, t * c) with t = 1/sqrt(1 - |p|^2) Coordinate system in Lorentz R4 has signature (1,1,1,-1). The parameters may be identical vectors.
    
    Parameters:
    p - argument vector in Klein ball
    pl - resulting vector in Lorentz model
  - diffKlein2Lorentz
```
public static void diffKlein2Lorentz(PdMatrix diffMat,
                     PdVector p)
```
    Compute differential of projection map of H3 from Klein ball into Lorentz model at given point in Klein ball. Coordinate system in Lorentz R4 has signature (1,1,1,-1).
    
    Parameters:
    diffMat - resulting differential matrix of size 4*3
    p - argument vector of size 3 in Klein ball
  - lorentz2Poincare
```
public static void lorentz2Poincare(PdVector p,
                    PdVector pl)
```
    Projection from Lorentz model in Rn+1 into Poincare ball in Rn of n-dim hyperbolic space. For H3, (a, b, c) = (x, y, z)/(1 + t) Coordinate system in Lorentz R4 has signature (1,1,1,-1). The parameters may be identical vectors.
    
    Parameters:
    p - resulting vector in Poincare ball
    pl - argument vector in Lorentz model
  - poincare2Lorentz
```
public static void poincare2Lorentz(PdVector pl,
                    PdVector p)
```
    Projection from Poincare ball in Rn into Lorentz model in Rn+1 of n-dim hyperbolic space. For H3, (t, x, y, z) = (t, (1 + t) * a, (1 + t) * b, (1 + t) * c) with t = (1 + |p|^2)/(1 - |p|^2), 1 + t = 2/(1 - |p|^2). Coordinate system in Lorentz R4 has signature (1,1,1,-1). The parameters may be identical vectors.
    
    Parameters:
    pl - resulting vector in Lorentz model
    p - argument vector in Poincare ball
  - diffPoincare2Lorentz
```
public static void diffPoincare2Lorentz(PdMatrix diffMat,
                        PdVector p)
```
    Compute differential of projection map of H3 from Poincare ball into Lorentz model at given point in Poincare ball. Coordinate system in Lorentz R4 has signature (1,1,1,-1).
    
    Parameters:
    diffMat - resulting differential matrix of size 4*3
    p - argument vector of size 3 in Klein ball
  - lorentz2Uhm
```
public static void lorentz2Uhm(PdVector p,
               PdVector pl)
```
    Projection from Lorentz model in Rn+1 into UHM in Rn of n-dim hyperbolic space. For H3, (a, b, c) = (x, y, 1)/(t - z) Coordinate system in Lorentz Rn+1 has signature (1,..,1,-1). The parameters may be identical vectors.
    
    Parameters:
    p - resulting vector in Upper Halfspace model
    pl - argument vector in Lorentz model
  - uhm2Lorentz
```
public static void uhm2Lorentz(PdVector pl,
               PdVector p)
```
    Projection from UHM in Rn into Lorentz model in Rn+1 of n-dim hyperbolic space. For H3, (x, y, z, t) = (2 x, 2 y, t - 1, 1 + t)/(2 * z) with t = |p|^2. Coordinate system in Lorentz Rn+1 has signature (1,..,1,-1). The parameters may be identical vectors.
    
    Parameters:
    pl - resulting vector in Lorentz model
    p - argument vector in Upper Halfspace model
  - poincare2Klein
```
public static void poincare2Klein(PdVector pk,
                  PdVector p)
```
    Projection from Poincare ball to Klein ball of n-dim hyperbolic space. For H3, (a, b, c) = 2/(1-|p|^2) * (x, y, z) The parameters may be identical vectors.
    
    Parameters:
    pk - resulting vector in Klein ball
    p - argument vector in Poincare ball
  - klein2Poincare
```
public static void klein2Poincare(PdVector p,
                  PdVector pk)
```
    Projection from Klein ball to Poincare ball of n-dim hyperbolic space. For H3, (a, b, c) = (x, y, z) / (1+sqrt(1-|p|^2)) The parameters may be identical vectors.
    
    Parameters:
    p - resulting vector in Poincare ball
    pk - argument vector in Klein ball
  - poincare2Uhm
```
public static void poincare2Uhm(PdVector pu,
                PdVector p)
```
    Projection of H3 from Poincare ball to UHM of n-dim hyperbolic space. For H3, (a, b, c) = (2 x, 2 y, 1 - |p|^2)/(x^2 + y^2 + (z - 1)^2). The parameters may be identical vectors.
    
    Parameters:
    pu - resulting vector in Upper Halfspace model
    p - argument vector in Poincare ball
  - uhm2Poincare
```
public static void uhm2Poincare(PdVector p,
                PdVector pu)
```
    Projection from UHM to Poincare ball of n-dim hyperbolic space. For H3, (a, b, c) = (2 x, 2 y, |p|^2 - 1)/(x^2 + y^2 + (z + 1)^2). The parameters may be identical vectors.
    
    Parameters:
    p - resulting vector of size 3 in Poincare ball
    pu - argument vector of size 3 in Upper Halfspace model
  - klein2Uhm
```
public static void klein2Uhm(PdVector pu,
             PdVector p)
```
    Projection of H3 from Klein ball to UHM of n-dim hyperbolic space. For H3, (a, b, c) = (x, y, 1 - |p|^2/(1 + sqrt(1 - |p|^2)))/(1 - z). The parameters may be identical vectors.
    
    Parameters:
    pu - resulting vector in Upper Halfspace model
    p - argument vector in Klein ball
  - uhm2Klein
```
public static void uhm2Klein(PdVector p,
             PdVector pu)
```
    Projection from UHM to Klein ball of n-dim hyperbolic space. For H3, (a, b, c) = (2 x, 2 y, |p|^2 - 1)/(1 + |p|^2). The parameters may be identical vectors.
    
    Parameters:
    p - resulting vector in Klein ball
    pu - argument vector in Upper Halfspace model
  - stereoS3_to_R3
```
public static void stereoS3_to_R3(PdVector p,
                  PdVector pl)
```
    Deprecated. use stereographic(PdVector, PdVector)
    
    Stereographic projection of S3 into R3 with projection center (0,0,0,1).
  - stereographic
```
public static void stereographic(PdVector p,
                 PdVector pl)
```
    Stereographic projection of a sphere Sn into Rn with projection center (0,..,0,1). (a_1, .., a_n) = (x_1, ..., x_n)/(1 - x_n+1). The parameters may be identical vectors of any dimension.
    
    Parameters:
    p - resulting vector of size n in euclidean space
    pl - argument vector of size n+1 in Sn
  - diffStereoS3_to_R3
```
public static void diffStereoS3_to_R3(PdMatrix diffMat,
                      PdVector p)
```
    Compute differential of stereographic projection S3 to R3 with projection center (1,0,0,0).
    
    Parameters:
    diffMat - resulting 3*4 differential matrix of size 4*3
    p - argument vector of size 3 in Klein ball
  - stereoInvR3_to_S3
```
public static void stereoInvR3_to_S3(PdVector pl,
                     PdVector p)
```
    Projection from Rn p=(a,b,c) to Sn pl=(x,y,z,t). (x, y, z, t) = ((1 + t) * a, (1 + t) * b, (1 + t) * c, t) with t = (1 - |p|^2)/(1 + |p|^2), 1 + t = 2/(1 + |p|^2). The parameters may be identical vectors.
    
    Parameters:
    pl - resulting vector in Sn
    p - argument vector in Euclidean space Rn
  - diffStereoInvR3_to_S3
```
public static void diffStereoInvR3_to_S3(PdMatrix diffMat,
                         PdVector p)
```
    Compute differential of inverse stereographic projection R3 to S3.
    
    Parameters:
    diffMat - resulting 4*3 differential matrix of size 4*3
    p - argument vector of size 3 in euclidean R3

Class PuProj

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

PuProj

Method Detail

lorentz2Klein

klein2Lorentz

diffKlein2Lorentz

lorentz2Poincare

poincare2Lorentz

diffPoincare2Lorentz

lorentz2Uhm

uhm2Lorentz

poincare2Klein

klein2Poincare

poincare2Uhm

uhm2Poincare

klein2Uhm

uhm2Klein

stereoS3_to_R3

stereographic

diffStereoS3_to_R3

stereoInvR3_to_S3

diffStereoInvR3_to_S3