jv.vecmath

Class PuReflect

java.lang.Object

jv.vecmath.PuReflect

public class PuReflect
extends java.lang.Object

Utility class with static methods to compute reflection and other symmetry matrices.

Most matrices are intended to work with homogenous coordinate representations, that means, the matrix of dimension (dim+1)*(dim+1) is later applied to points in ambient dim-space. See also the classes PdVector and PdMatrix which provide homogenous linear algebra multiplications.

Author:

Konrad Polthier

Version:

04.11.06, 1.50 revised (kp) Several methods for arbitrary dimension, new methods for rotation.
29.12.03, 1.40 revised (kp) New method getRotation().
26.06.03, 1.30 revised (kp) Reduce internal object allocations.
18.03.01, 1.20 revised (kp) Method scale added.
03.10.99, 1.10 revised (kp) Renamed from PdReflect to PuReflect.
11.07.99, 1.01 revised (kp) Included in JavaView, method mult43() moved to PdVector.
00.06.99, 1.00 created (kp) Converted from my c-code.

Constructor Summary

Constructors

Constructor and Description
PuReflect()

Method Summary

Modifier and Type	Method and Description
static java.lang.Double	getRotation(PdMatrix mat, PdVector axis) Get axis and angle of a 3x3 rotation matrix.
static boolean	makeRotation(PdMatrix mat, PdVector axis, double angle) Assign a (3*3)-rotation matrix to rotate around axis through origin with given angle.
static PdMatrix	planeReflect(PdVector base, PdVector normal) Generate a (dim+1)*(dim+1)-matrix to reflect in plane determined by a base point and a plane normal.
static PdMatrix	planeReflect(PdVector a, PdVector b, PdVector c) Generate a (4*4)-matrix to reflect in plane given by three vertices on the plane in R3.
static PdMatrix	pointReflect(PdVector p) Generate a (dim+1)*(dim+1)-matrix to invert space at a given center point.
static PdMatrix	rotate(PdMatrix mat, double angle, int indI, int indJ) Generate a homogeneous matrix to rotate in the (indI,indJ)-plane around a given angle in radians (i.e.
static PdMatrix	rotateLine(PdMatrix mat, PdVector base, PdVector axis) Fill a given (4*4)-matrix to rotate around axis base+t*dir by 180 degrees.
static PdMatrix	rotateLine(PdMatrix mat, PdVector base, PdVector axis, double angle) Fill a (4*4)-matrix to rotate around axis base+t*dir by given angle.
static PdMatrix	rotateLine(PdVector base, PdVector axis) Generate a (4*4)-matrix to rotate around axis base+t*dir by 180 degrees.
static PdMatrix	rotateLine(PdVector base, PdVector axis, double fi) Generate a (4*4)-matrix to rotate around axis base+t*dir by given angle.
static PdMatrix	rotateXY(double angle, int dim) Generate a homogeneous matrix to rotate in the XY-plane around a given angle in radians (i.e.
static PdMatrix	rotateXZ(double angle, int dim) Generate a homogeneous matrix to rotate in the XZ-plane around a given angle in radians (i.e.
static PdMatrix	rotateYZ(double angle, int dim) Generate a homogeneous matrix to rotate in the YZ-plane around a given angle in radians (i.e.
static PdMatrix	scale(double s, int dim) Generate a homogeneous matrix to non-uniform scale by a given vector p[i] = p[i]*s.
static PdMatrix	scale(PdVector v) Generate a homogeneous matrix to non-uniform scale by a given vector p[i] = p[i]*v[i].
static PdMatrix	translate(PdVector v) Generate a (dim+1)*(dim+1) matrix m to translate a point p by a given vector v: m*p=p+v.

Methods inherited from class java.lang.Object

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

Constructor Detail

PuReflect

public PuReflect()

Method Detail

makeRotation

public static boolean makeRotation(PdMatrix mat,
                                   PdVector axis,
                                   double angle)

Assign a (3*3)-rotation matrix to rotate around axis through origin with given angle. Parameter mat and axis must have dimension greater or equal to three. Only first three components are used.

Parameters:

mat - Matrix to hold the transformation matrix.

axis - direction of rotation axis, need not be normalized

angle - angle in radians about to rotate

Returns:

false missing axis or problems in its normalization

Version:

26.06.03, 1.10 revised (kp) Avoid internal object allocation.
07.09.99, 1.00 created (kp) Method moved from PdMatrix.

getRotation

public static java.lang.Double getRotation(PdMatrix mat,
                                           PdVector axis)

Get axis and angle of a 3x3 rotation matrix. I- and J-dimension of matrix must both be equal or greater than 3.

Parameters:

mat - Matrix to hold the transformation matrix.

axis - direction of rotation axis, need not be normalized

Returns:

angle in radians about to rotate or null if error

Version:

28.12.03, 1.00 created (kp)

rotateLine

public static PdMatrix rotateLine(PdMatrix mat,
                                  PdVector base,
                                  PdVector axis)

Fill a given (4*4)-matrix to rotate around axis base+t*dir by 180 degrees. Parameter base and axis must have dimension greater or equal to three. Only first three components are used.

There are no object allocations in this method.

Parameters:

mat - 4*4 matrix which will be filled.

base - Arbitrary point on rotation axis.

axis - Direction of rotation axis, need not be normalized

Returns:

given matrix

Since:

JavaView 2.83.000

Version:

26.06.03, 1.00 created (kp) From body of rotateLine(PdVector,PdVector).

rotateLine

public static PdMatrix rotateLine(PdVector base,
                                  PdVector axis)

Generate a (4*4)-matrix to rotate around axis base+t*dir by 180 degrees. Parameter base and axis must have dimension greater or equal to three. Only first three components are used.

Method allocates a new matrix and invokes rotateLine

Parameters:

base - Arbitrary point on rotation axis.

axis - Direction of rotation axis, need not be normalized

Returns:

new rotation matrix

Version:

26.06.03, 2.00 revised (kp) Body moved to rotateLine(PdMatrix,PdVector,PdVector).

rotateLine

public static PdMatrix rotateLine(PdMatrix mat,
                                  PdVector base,
                                  PdVector axis,
                                  double angle)

Fill a (4*4)-matrix to rotate around axis base+t*dir by given angle. Parameter base and axis must have dimension greater or equal to three. Only first three components are used.

There are no object allocations in this method.

Parameters:

mat - 4*4 matrix which will be filled.

base - Arbitrary point on rotation axis.

axis - Direction of rotation axis, need not be normalized

angle - Angle in radians about to rotate.

Returns:

given matrix

Since:

JavaView 2.83.000

Version:

26.06.03, 1.00 created (kp) From body of rotateLine(PdVector,PdVector,double).

rotateLine

public static PdMatrix rotateLine(PdVector base,
                                  PdVector axis,
                                  double fi)

Generate a (4*4)-matrix to rotate around axis base+t*dir by given angle. Parameter base and axis must have dimension greater or equal to three. Only first three components are used.

Parameters:

base - Arbitrary point on rotation axis.

axis - Direction of rotation axis, need not be normalized

fi - Angle in radians about to rotate.

Returns:

Rotation matrix

Version:

26.06.03, 2.00 revised (kp) Body moved to rotateLine(PdMatrix,PdVector,PdVector,double).

planeReflect

public static PdMatrix planeReflect(PdVector a,
                                    PdVector b,
                                    PdVector c)

Generate a (4*4)-matrix to reflect in plane given by three vertices on the plane in R3.

Parameters:

a - Point on the plane.

b - Point on the plane.

c - Point on the plane.

Returns:

Reflection matrix of dimension (4*4).

planeReflect

public static PdMatrix planeReflect(PdVector base,
                                    PdVector normal)

Generate a (dim+1)*(dim+1)-matrix to reflect in plane determined by a base point and a plane normal.

Parameters:

base - Arbitrary point on plane of dimension dim.

normal - Normal vector orthonormal to plane.

Returns:

Reflection matrix of dimension (dim+1)

Version:

26.06.03, 1.10 revised (kp) Reduce internal object allocation.

pointReflect

public static PdMatrix pointReflect(PdVector p)

Generate a (dim+1)*(dim+1)-matrix to invert space at a given center point. The mapping is: reflect(x) = -x+2p. If p=0 then x goes to -x. The matrix has dimension (dim+1) if dim is the dimension of the vector.

Parameters:

p - Arbitrary point of dimension dim as inversion center.

Returns:

Inversion matrix of dimension (dim+1)

Version:

12.09.07, 1.35 revised (kp) Bug in array index removed.
19.06.07, 1.30 revised (kp) Bug for 2d point removed.
04.11.06, 1.20 revised (kp) Arbitrary dimension.
28.12.03, 1.10 revised (kp) Assure 3d dimensionality of point.

translate

public static PdMatrix translate(PdVector v)

Generate a (dim+1)*(dim+1) matrix m to translate a point p by a given vector v: m*p=p+v. The matrix has dimension (dim+1) if dim is the dimension of the vector.

Parameters:

v - Translation vector.

Returns:

Translation matrix of dimension (dim+1)

Version:

29.03.06, 1.20 revised (ah) Arbitrary dimension.
28.12.03, 1.10 revised (kp) Assure 3d dimensionality of vector.

scale

public static PdMatrix scale(PdVector v)

Generate a homogeneous matrix to non-uniform scale by a given vector p[i] = p[i]*v[i]. The matrix has dimension (dim+1) if dim is the dimension of the vector.

Parameters:

v - Scaling vector of dimension dim.

Returns:

New scaling matrix of dimension (dim+1)

Version:

29.03.06, 1.20 revised (ah) Arbitrary dimension.
28.12.03, 1.10 revised (kp) Assure 3d dimensionality of vector.
18.03.01, 1.00 created (kp)

scale

public static PdMatrix scale(double s,
                             int dim)

Generate a homogeneous matrix to non-uniform scale by a given vector p[i] = p[i]*s. The generated matrix is a (dim+1) square matrix.

Parameters:

s - Scaling factor.

dim - Dimension of ambient space.

Returns:

New scaling matrix of dimension (dim+1)

Version:

29.03.06, 1.00 created (ah)

rotateXY

public static PdMatrix rotateXY(double angle,
                                int dim)

Generate a homogeneous matrix to rotate in the XY-plane around a given angle in radians (i.e. PI). The generated matrix is a (dim+1) square matrix.

Parameters:

angle - Angle in radians.

dim - Dimension of ambient space.

Returns:

New rotation matrix of dimension (dim+1)

Since:

JavaView 3.97.016

Version:

04.11.06, 1.00 created (kp)

rotateYZ

public static PdMatrix rotateYZ(double angle,
                                int dim)

Generate a homogeneous matrix to rotate in the YZ-plane around a given angle in radians (i.e. PI). The generated matrix is a (dim+1) square matrix.

Parameters:

angle - Angle in radians.

dim - Dimension of ambient space.

Returns:

New rotation matrix of dimension (dim+1)

Since:

JavaView 3.97.016

Version:

04.11.06, 1.00 created (kp)

rotateXZ

public static PdMatrix rotateXZ(double angle,
                                int dim)

Generate a homogeneous matrix to rotate in the XZ-plane around a given angle in radians (i.e. PI). The generated matrix is a (dim+1) square matrix.

Parameters:

angle - Angle in radians.

dim - Dimension of ambient space.

Returns:

New rotation matrix of dimension (dim+1)

Since:

JavaView 3.97.016

Version:

04.11.06, 1.00 created (kp)

rotate

public static PdMatrix rotate(PdMatrix mat,
                              double angle,
                              int indI,
                              int indJ)

Generate a homogeneous matrix to rotate in the (indI,indJ)-plane around a given angle in radians (i.e. PI). The generated matrix is a homogeneous (dim+1) square matrix.

Parameters:

angle - Angle in radians.

indI - Dimension of first coordinates axis which determines the plane of rotation.

indJ - Dimension of second coordinates axis which determines the plane of rotation.

Returns:

Given rotation matrix

Since:

JavaView 3.97.016

Version:

04.11.06, 1.00 created (kp)