Class JxnVectorTransformation

java.lang.Object

JxnVectorTransformation

public class JxnVectorTransformation
extends Object

Implements an affine transformation and mapping methods for vectors and curves (experimental status).

See Also:

Wikipedia

Constructor Summary

Constructors

Modifier	Constructor	Description
	JxnVectorTransformation()	Creates a three-dimensional identity transformation.
protected	JxnVectorTransformation(double[][] tm)	Creates a transformation object from a given matrix tm.
	JxnVectorTransformation(int dim)	Creates an identity transformation of dimension dim.
	JxnVectorTransformation(JxnVectorAlgebra ex, JxnVectorAlgebra ey, JxnVectorAlgebra ez)	Creates a transformation object from given coordinate (basis) vectors.
	JxnVectorTransformation(JxnVectorTransformation t)	Creates a copy of t.

Method Summary

Modifier and Type	Method	Description
JxnVectorTransformation	concat(JxnVectorTransformation t2)	Returns the resulting transformation for this transformation (not changed) followed by a 2nd transformation t2 .
static JxnVectorTransformation	div(JxnVectorTransformation tNum, JxnVectorTransformation tDen)	Returns tNum * tDen-1.
static double	getRMSDiff(JxnVectorTransformation tA, JxnVectorTransformation tB)	Checks the difference of two transformations.
double[][]	getT()	Returns the transformation matrix.
static JxnVectorTransformation	inv(JxnVectorTransformation t)	Returns the inverse of t.
JxnVectorTransformation	inverse()	Returns the inverse of this (without changing it).
double[]	map(double[] v)	Called internally.
double	map(int i, double x, double y, double z)	Called internally.
JxnRealArrayAlgebra	map(int i, JxnRealArrayAlgebra rx, JxnRealArrayAlgebra ry, JxnRealArrayAlgebra rz)	Returns the i-th coordinate of the mapping of the curve given by rx, ry and rz.
JxnRealArrayAlgebra[]	map(JxnRealArrayAlgebra[] rxyz)	Returns the mapping of the curve given by an array rxyz = { rx, ry, rz }.
JxnVectorAlgebra	map(JxnVectorAlgebra v)	Returns the mapping of v.
JxnVectorTransformation	move(double dx, double dy, double dz)	Returns the resulting transformation for this transformation (not changed) followed by a translation defined by dx, dy and dz .
JxnVectorTransformation	move(double f, JxnVectorAlgebra v)	Returns the resulting transformation for this transformation (not changed) followed by a translation defined by v scaled by f .
JxnVectorTransformation	move(JxnVectorAlgebra v)	Returns the resulting transformation for this transformation (not changed) followed by a translation defined by v.
JxnVectorTransformation	moveIt(double dx, double dy, double dz)	Modifies this transformation by appending a translation defined by dx, dy and dz .
JxnVectorTransformation	moveIt(double f, JxnVectorAlgebra v)	Modifies this transformation by appending a translation defined by v scaled by f .
JxnVectorTransformation	moveIt(JxnVectorAlgebra v)	Modifies this transformation by appending a translation defined by v.
JxnRealArrayAlgebra[]	mul(JxnRealArrayAlgebra[] rxyz)	Returns the mapping of rxyz = { rx, ry, rz }.
JxnVectorAlgebra	mul(JxnVectorAlgebra v)	Returns the mapping of v.
static JxnVectorTransformation	mul(JxnVectorTransformation tLeft, JxnVectorTransformation tRght)	Returns the combination of tLeft and tRght.
JxnVectorTransformation	rotate(double phiX, double phiY, double phiZ)	Returns the resulting transformation for this transformation (not changed) followed by rotations defined by phiX, phiY and phiZ (in this sequence).
JxnVectorTransformation	rotate(JxnVectorAlgebra v0, JxnVectorAlgebra v1, double alpha)	Returns the resulting transformation for this transformation (not changed) followed by a rotation around the axis v(t) = v0 + v1 * t; t = -oo, +oo with angle alpha
JxnVectorTransformation	rotateD(double phiX, double phiY, double phiZ)	Returns the resulting transformation for this transformation (not changed) followed by rotations defined by phiX, phiY and phiZ (parameters in degrees).
JxnVectorTransformation	rotateD(JxnVectorAlgebra v0, JxnVectorAlgebra v1, double alpha)	Returns the resulting transformation for this transformation (not changed) followed by a rotation around the axis v(t) = v0 + v1 * t; t = -oo, +oo with angle alpha in degrees.
JxnVectorTransformation	rotateIt(double phiX, double phiY, double phiZ)	Modifies this transformation by appending rotations defined by phiX, phiY and phiZ (in this sequence).
JxnVectorTransformation	rotateIt(JxnVectorAlgebra v0, JxnVectorAlgebra v1, double alpha)	Modifies this transformation by appending a rotation around the axis v(t) = v0 + v1 * t; t = -oo, +oo with angle alpha
JxnVectorTransformation	rotateItD(double phiX, double phiY, double phiZ)	Modifies this transformation by appending rotations defined by phiX, phiY and phiZ (parameters in degrees).
JxnVectorTransformation	rotateItD(JxnVectorAlgebra v0, JxnVectorAlgebra v1, double alpha)	Modifies this transformation by appending a rotation around the axis v(t) = v0 + v1 * t; t = -oo, +oo with angle alpha in degrees.
JxnVectorTransformation	rotD(double phiX, double phiY, double phiZ)	Deprecated. Use rotateD(double, double, double).
JxnVectorTransformation	scale(double f)	Returns the resulting transformation for this transformation (not changed) followed by a scaling of all components by f .
JxnVectorTransformation	scale(double fx, double fy, double fz)	Returns the resulting transformation for this transformation (not changed) followed by a scaling defined by fx, fy and fz .
JxnVectorTransformation	scale(JxnVectorAlgebra v0, double f)	Returns the resulting transformation for this transformation (not changed) followed by a scaling defined by the fixed point v0 and the scale factor f .
JxnVectorTransformation	scaleIt(double f)	Modifies this transformation by appending a scaling of all components by f .
JxnVectorTransformation	scaleIt(double fx, double fy, double fz)	Modifies this transformation by appending a scaling defined by fx, fy and fz .
JxnVectorTransformation	scaleIt(JxnVectorAlgebra v0, double f)	Modifies this transformation by appending a scaling defined by the fixed point v0 and the scale factor f .
String	toString()

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Constructor Detail

JxnVectorTransformation

public JxnVectorTransformation()

Creates a three-dimensional identity transformation.

JxnVectorTransformation

public JxnVectorTransformation(int dim)

Creates an identity transformation of dimension dim.

JxnVectorTransformation

protected JxnVectorTransformation(double[][] tm)

Creates a transformation object from a given matrix tm.
The transformation y = A x + b is represented by the augmented n x n+1 matrix tm = ( A | b ).

See Also:

Wikipedia

JxnVectorTransformation

public JxnVectorTransformation(JxnVectorTransformation t)

Creates a copy of t.

JxnVectorTransformation

public JxnVectorTransformation(JxnVectorAlgebra ex,
                               JxnVectorAlgebra ey,
                               JxnVectorAlgebra ez)

Creates a transformation object from given coordinate (basis) vectors.
The vectors ex, ey and ez must be linear independent but need not necessarily be orthogonal or normalized.
If ex, ey and ez are ...
... target coordinate vectors given in source coordinates the transformation object maps target coordinates into source coordinates.
... source coordinate vectors given in target coordinates the transformation object maps source coordinates into target coordinates.
Use the inverse() method to get the reverse mapping.

Method Detail

move

public JxnVectorTransformation move(JxnVectorAlgebra v)

Returns the resulting transformation for this transformation (not changed) followed by a translation defined by v.

moveIt

public JxnVectorTransformation moveIt(JxnVectorAlgebra v)

Modifies this transformation by appending a translation defined by v.

Returns:

this

move

public JxnVectorTransformation move(double f,
                                    JxnVectorAlgebra v)

Returns the resulting transformation for this transformation (not changed) followed by a translation defined by v scaled by f .

moveIt

public JxnVectorTransformation moveIt(double f,
                                      JxnVectorAlgebra v)

Modifies this transformation by appending a translation defined by v scaled by f .

Returns:

this

move

public JxnVectorTransformation move(double dx,
                                    double dy,
                                    double dz)

Returns the resulting transformation for this transformation (not changed) followed by a translation defined by dx, dy and dz .

moveIt

public JxnVectorTransformation moveIt(double dx,
                                      double dy,
                                      double dz)

Modifies this transformation by appending a translation defined by dx, dy and dz .

Returns:

this

scale

public JxnVectorTransformation scale(double fx,
                                     double fy,
                                     double fz)

Returns the resulting transformation for this transformation (not changed) followed by a scaling defined by fx, fy and fz .

scaleIt

public JxnVectorTransformation scaleIt(double fx,
                                       double fy,
                                       double fz)

Modifies this transformation by appending a scaling defined by fx, fy and fz .

Returns:

this

scale

public JxnVectorTransformation scale(double f)

Returns the resulting transformation for this transformation (not changed) followed by a scaling of all components by f .

scaleIt

public JxnVectorTransformation scaleIt(double f)

Modifies this transformation by appending a scaling of all components by f .

Returns:

this

scale

public JxnVectorTransformation scale(JxnVectorAlgebra v0,
                                     double f)

Returns the resulting transformation for this transformation (not changed) followed by a scaling defined by the fixed point v0 and the scale factor f . Note: a point reflection is achieved by scale( v0, -1 ).

scaleIt

public JxnVectorTransformation scaleIt(JxnVectorAlgebra v0,
                                       double f)

Modifies this transformation by appending a scaling defined by the fixed point v0 and the scale factor f .

Returns:

this

rotate

public JxnVectorTransformation rotate(double phiX,
                                      double phiY,
                                      double phiZ)

Returns the resulting transformation for this transformation (not changed) followed by rotations defined by phiX, phiY and phiZ (in this sequence).

rotateD

public JxnVectorTransformation rotateD(double phiX,
                                       double phiY,
                                       double phiZ)

Returns the resulting transformation for this transformation (not changed) followed by rotations defined by phiX, phiY and phiZ (parameters in degrees).

rotD

public JxnVectorTransformation rotD(double phiX,
                                    double phiY,
                                    double phiZ)

Deprecated.

Use rotateD(double, double, double).

rotateIt

public JxnVectorTransformation rotateIt(double phiX,
                                        double phiY,
                                        double phiZ)

Modifies this transformation by appending rotations defined by phiX, phiY and phiZ (in this sequence).

Returns:

this

rotateItD

public JxnVectorTransformation rotateItD(double phiX,
                                         double phiY,
                                         double phiZ)

Modifies this transformation by appending rotations defined by phiX, phiY and phiZ (parameters in degrees).

Returns:

this

rotate

public JxnVectorTransformation rotate(JxnVectorAlgebra v0,
                                      JxnVectorAlgebra v1,
                                      double alpha)

Returns the resulting transformation for this transformation (not changed) followed by a rotation around the axis v(t) = v0 + v1 * t; t = -oo, +oo with angle alpha

rotateD

public JxnVectorTransformation rotateD(JxnVectorAlgebra v0,
                                       JxnVectorAlgebra v1,
                                       double alpha)

Returns the resulting transformation for this transformation (not changed) followed by a rotation around the axis v(t) = v0 + v1 * t; t = -oo, +oo with angle alpha in degrees.

rotateIt

public JxnVectorTransformation rotateIt(JxnVectorAlgebra v0,
                                        JxnVectorAlgebra v1,
                                        double alpha)

Modifies this transformation by appending a rotation around the axis v(t) = v0 + v1 * t; t = -oo, +oo with angle alpha

rotateItD

public JxnVectorTransformation rotateItD(JxnVectorAlgebra v0,
                                         JxnVectorAlgebra v1,
                                         double alpha)

Modifies this transformation by appending a rotation around the axis v(t) = v0 + v1 * t; t = -oo, +oo with angle alpha in degrees.

inv

public static JxnVectorTransformation inv(JxnVectorTransformation t)

Returns the inverse of t.

inverse

public JxnVectorTransformation inverse()

Returns the inverse of this (without changing it).

mul

public static JxnVectorTransformation mul(JxnVectorTransformation tLeft,
                                          JxnVectorTransformation tRght)

Returns the combination of tLeft and tRght.

mapping sequence = transformation sequence:
- v' = T3 * T2 * T1 * v right to left: multiply the transformation matrices Ti
- v' = T1.t2(...).t3(...).map(v) left to right: method chaining of the transformation methods ti
- v' = T3.map( T2.map( T1.map( v ) ) ) = T3 * ( T2 * ( T1 * v ) )
- v' = T3 * ( T2 * ( T1 * v ) ) = ( ( T3 * T2 ) * T1 ) * v = T3 * T2 * T1 * v

concat

public JxnVectorTransformation concat(JxnVectorTransformation t2)

Returns the resulting transformation for this transformation (not changed) followed by a 2nd transformation t2 .

Returns:

mul( t2, this )

div

public static JxnVectorTransformation div(JxnVectorTransformation tNum,
                                          JxnVectorTransformation tDen)

Returns tNum * tDen^-1.

mul

public JxnVectorAlgebra mul(JxnVectorAlgebra v)

Returns the mapping of v.

Returns:

map(v)

mul

public JxnRealArrayAlgebra[] mul(JxnRealArrayAlgebra[] rxyz)

Returns the mapping of rxyz = { rx, ry, rz }.

Returns:

map(rxyz)

map

public JxnVectorAlgebra map(JxnVectorAlgebra v)

Returns the mapping of v.
Calls map(double []).

map

public double[] map(double[] v)

Called internally.

map

public JxnRealArrayAlgebra[] map(JxnRealArrayAlgebra[] rxyz)

Returns the mapping of the curve given by an array rxyz = { rx, ry, rz }.
Calls map(int, JxnRealArrayAlgebra, JxnRealArrayAlgebra, JxnRealArrayAlgebra).

map

public JxnRealArrayAlgebra map(int i,
                               JxnRealArrayAlgebra rx,
                               JxnRealArrayAlgebra ry,
                               JxnRealArrayAlgebra rz)

Returns the i-th coordinate of the mapping of the curve given by rx, ry and rz.
Call for each coordinate to get the mapping of the curve:

   map_rx = map( 0, rx, ry, rz )
   map_ry = map( 1, rx, ry, rz )
   map_rz = map( 2, rx, ry, rz )
 

map

public double map(int i,
                  double x,
                  double y,
                  double z)

Called internally.

toString

public String toString()

Overrides:

toString in class Object

getT

public double[][] getT()

Returns the transformation matrix.

getRMSDiff

public static double getRMSDiff(JxnVectorTransformation tA,
                                JxnVectorTransformation tB)

Checks the difference of two transformations.