org.xmlcml.euclid

Class Transform3

java.lang.Object

org.xmlcml.euclid.RealMatrix

org.xmlcml.euclid.RealSquareMatrix

org.xmlcml.euclid.Transform3

All Implemented Interfaces:

EuclidConstants

public class Transform3
extends RealSquareMatrix

3-D transformation matrix class Transform3 represents a transformation matrix for 3-D objects. Its actual form may be implementation-dependent, but we have started with 4x4 matrices. The following transformations will be supported as the class is developed:

TRFORM3_NULL no transformation allowed
ROT_ORIG rotation about the origin
ROT_TRANS rotation and translation
ROT_TRANS_SCALE rotation, translation and single scale factor
ROT_TRANS_AXIAL_SCALE rotation, translation + 3 axial scale factors
ROT_TRANS_SCALE_PERSP rotation, translation, scale, perspective
TRFORM3_ANY any matrix at all - user beware!

The basic stuff is all there - the user will do best to look at examples.

Author:

(C) P. Murray-Rust, 1996

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	Transform3.Type type

Field Summary

Fields inherited from class org.xmlcml.euclid.RealMatrix

cols, flmat, rows

Fields inherited from interface org.xmlcml.euclid.EuclidConstants

C_AMP, C_APOS, C_ATSIGN, C_BACKSLASH, C_BACKSPACE, C_CARET, C_COLON, C_COMMA, C_DEL, C_DOLLAR, C_EQUALS, C_FORMFEED, C_HASH, C_LANGLE, C_LBRAK, C_LCURLY, C_LSQUARE, C_MINUS, C_NBSP, C_NEWLINE, C_NL, C_PERCENT, C_PERIOD, C_PIPE, C_PLUS, C_POUND, C_QUERY, C_QUOT, C_RANGLE, C_RBRAK, C_RCURLY, C_RETURN, C_RSQUARE, C_SEMICOLON, C_SHRIEK, C_SLASH, C_SPACE, C_STAR, C_TAB, C_TILDE, C_UNDER, EPS, F_S, NONWHITEPUNC, NONWHITEPUNC0, NONWHITEPUNC0REGEX, ONE_THIRD, PUNC, S_AMP, S_APOS, S_ATSIGN, S_BACKSLASH, S_CARET, S_COLON, S_COMMA, S_DOLLAR, S_EMPTY, S_EQUALS, S_FORMFEED, S_HASH, S_LANGLE, S_LBRAK, S_LCURLY, S_LSQUARE, S_MINUS, S_NEWLINE, S_NL, S_PERCENT, S_PERIOD, S_PIPE, S_PLUS, S_POUND, S_QUERY, S_QUOT, S_RANGLE, S_RBRAK, S_RCURLY, S_RETURN, S_RSQUARE, S_SEMICOLON, S_SHRIEK, S_SLASH, S_SPACE, S_STAR, S_TAB, S_TILDE, S_UNDER, S_WHITEREGEX, TWO_THIRDS, U_S, WHITESPACE

Constructor Summary

Constructors

Constructor and Description
Transform3() construct unit matrix T = I
Transform3(Angle xrot, Angle yrot, Angle zrot) from rotation about the three orthogonal axes.
Transform3(Axis.Axis3 axis, Angle rot) from rotation about an axis.
Transform3(double[] array) From array.
Transform3(Line3 l, Angle a) Rotation about a line.
Transform3(RealSquareMatrix m) from a matrix.
Transform3(RealSquareMatrix m, Vector3 v) from a matrix and vector.
Transform3(String opString) from a crystallographic operator.
Transform3(Transform3.Type t) This gives a default unit matrix of type t.
Transform3(Transform3 m) copy constructor.
Transform3(Transform3 t, Point3 p) from rotation about a point.
Transform3(Vector3 v) identity matrix with translation component.
Transform3(Vector3 v, Angle a) from rotation about a vector.
Transform3(Vector3 v1, Vector3 v2) rotation of one vector onto another.
Transform3(Vector3 v1, Vector3 v2, Vector3 v3) from 3 vector components.

Method Summary

Modifier and Type	Method and Description
static Transform3	applyScale(double scale) apply scale to each axis
static Transform3	applyScales(double scaleX, double scaleY, double scaleZ) apply scales to each axis
Transform3.Type	checkMatrix() get new matrix type.
static void	checkNotNull(Transform3 t) check not null
Transform3	clone(Transform3 m) clone.
Transform3	concatenate(Transform3 m2) concatenate.
int	getAxisAndAngle(Vector3 axis, Angle ang) interpret current matrix as rotation about general axis.
Point3	getCentreOfRotation() get centre of rotation.
String	getCrystallographicString() return operator in crystallographic form;
RealSquareMatrix	getRotationMatrix() get Unitary matrix.
RealArray	getScales() get scales.
Transform3.Type	getTransformationType() get transformation type.
Vector3	getTranslation() get translation component.
void	incrementTranslation(Vector3 dt) increment translation component.
boolean	isEqualTo(Transform3 m) equality of two transforms.
int	setTransformationType(Transform3.Type option) set transformation type.
void	setTranslation(Vector3 t) set translation component.

Methods inherited from class org.xmlcml.euclid.RealSquareMatrix

calculateEigenvalues, calculateEigenvectors, calculateInverse, copyLowerToUpper, copyUpperToLower, determinant, diagonal, diagonaliseAndReturnRank, fromLowerTriangle, fromUpperTriangle, getCrystallographicOrthogonalisation, getInverse, isEqualTo, isImproperRotation, isLowerTriangular, isOrthogonal, isOrthonormal, isSymmetric, isUnit, isUnitary, isUpperTriangular, lowerTriangle, multiply, orthogonalise, orthonormalize, outerProduct, plus, resetEigenDecomposition, shallowCopy, subtract, trace, transpose

Methods inherited from class org.xmlcml.euclid.RealMatrix

appendColumnData, appendColumnData, appendRowData, appendRowData, checkNonEmptyMatrix, clearMatrix, columnwiseDivide, createMatrixWithOriginShifted, deleteColumn, deleteColumns, deleteRow, deleteRows, elementAt, elementAt, elementsInRange, euclideanColumnLength, euclideanColumnLengths, euclideanRowLength, euclideanRowLengths, extractColumnData, extractColumns, extractRowData, extractRows, extractSubMatrixData, format, getCols, getFormat, getIntMatrix, getMatrix, getMatrixAsArray, getRows, getTranspose, indexOfLargestElement, indexOfLargestElementInColumn, indexOfLargestElementInRow, indexOfSmallestElement, indexOfSmallestElementInColumn, indexOfSmallestElementInRow, insertColumnData, insertColumnData, insertRowData, insertRowData, insertRows, isEqualTo, isSquare, isZero, largestElement, largestElementInColumn, largestElementInRow, makeSpaceForNewColumns, multiply, multiply, multiplyBy, multiplyEquals, negative, normaliseByColumns, normaliseByRows, plus, reorderColumnsBy, reorderRowsBy, replaceColumnData, replaceColumnData, replaceColumnData, replaceRowData, replaceRowData, replaceRowData, replaceSubMatrixData, scaleAndInterpolate, setAllElements, setElementAt, setFormat, shallowCopy, smallestElement, smallestElementInColumn, smallestElementInRow, subtract, toString, translateByColumn, writeXML

Methods inherited from class java.lang.Object

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

Constructor Detail

Transform3

public Transform3()

construct unit matrix T = I

Transform3

public Transform3(Transform3.Type t)

This gives a default unit matrix of type t.

Parameters:

t - type

Transform3

public Transform3(Vector3 v)

identity matrix with translation component. T = I|vector

Parameters:

v - translation vector

Transform3

public Transform3(Axis.Axis3 axis,
                  Angle rot)

from rotation about an axis. (use (Choice3.X), etc

Parameters:

axis - Choice.X, etc

rot - angle to rotate by

Transform3

public Transform3(Angle xrot,
                  Angle yrot,
                  Angle zrot)

from rotation about the three orthogonal axes. rotX then rotY then rotZ

Parameters:

xrot -

yrot -

zrot -

Transform3

public Transform3(Transform3 t,
                  Point3 p)

from rotation about a point.

Parameters:

t - rotation matrix

p - point to rotate about

Transform3

public Transform3(Vector3 v,
                  Angle a)

from rotation about a vector.

Parameters:

v - vector to rotate about

a - angle to rotate by

Transform3

public Transform3(Line3 l,
                  Angle a)

Rotation about a line. chooses any point on line as centre of rotation

Parameters:

l - line to rotate about

a - angle to rotate by

Transform3

public Transform3(Vector3 v1,
                  Vector3 v2)

rotation of one vector onto another. this documentation has not been checked

Parameters:

v1 - vector to rotate

v2 - vector to rotate v1 onto

Transform3

public Transform3(Vector3 v1,
                  Vector3 v2,
                  Vector3 v3)

from 3 vector components. NOT checked fills rows of T with v1, v2, v3

Parameters:

v1 - first row of T

v2 - second row of T

v3 - third row of T

Transform3

public Transform3(double[] array)
           throws EuclidRuntimeException

From array.

Parameters:

array - copied to m00, m01, m02, m03, m10 ...

Throws:

EuclidRuntimeException - array must have 16 elements

Transform3

public Transform3(Transform3 m)

copy constructor.

Parameters:

m - transform to copy

Transform3

public Transform3(RealSquareMatrix m)
           throws EuclidRuntimeException

from a matrix.

Parameters:

m - 3x3 or 4x4 matrix

Throws:

EuclidRuntimeException - m must be 3*3 or 4*4

Transform3

public Transform3(RealSquareMatrix m,
                  Vector3 v)
           throws EuclidRuntimeException

from a matrix and vector.

Parameters:

m - 3x3 rotation matrix

v - translation vector

Throws:

EuclidRuntimeException - m must be 3*3

Transform3

public Transform3(String opString)
           throws EuclidRuntimeException

from a crystallographic operator.

Parameters:

opString - for example 1/2-x,1/2+y,-z extended to 0.5+x, y-0.25, z // etc

Throws:

EuclidRuntimeException - corrupt/invalid string

Method Detail

applyScales

public static Transform3 applyScales(double scaleX,
                                     double scaleY,
                                     double scaleZ)

apply scales to each axis

Parameters:

scaleX -

scaleY -

scaleZ -

Returns:

transform

applyScale

public static Transform3 applyScale(double scale)

apply scale to each axis

Parameters:

scale -

Returns:

transform

clone

public Transform3 clone(Transform3 m)

clone.

Parameters:

m -

Returns:

transform

isEqualTo

public boolean isEqualTo(Transform3 m)

equality of two transforms. based on equality of RealSquareMatrix

Parameters:

m - transform to compare

Returns:

true if equal within Real.isEqual()

concatenate

public Transform3 concatenate(Transform3 m2)

concatenate. (I think this is right...) result = this * m2 i.e. if x' = m2 * x and x'' = this * x'' then x'' = result * x;

Parameters:

m2 - transform to be concatenated

Returns:

result of applying this to m2

setTransformationType

public int setTransformationType(Transform3.Type option)

set transformation type.

Parameters:

option - the type

Returns:

0 if ok else 1

getTransformationType

public Transform3.Type getTransformationType()

get transformation type.

Returns:

the type

checkMatrix

public Transform3.Type checkMatrix()

get new matrix type. not sure what this is!

Returns:

the type

getAxisAndAngle

public int getAxisAndAngle(Vector3 axis,
                           Angle ang)

interpret current matrix as rotation about general axis. user must supply an empty axis and an empty angle, which will be filled by the routine. will do better to create AxisAndAngle class

Parameters:

axis - (holds return values)

ang - angle (holds return value)

Returns:

flag

getTranslation

public Vector3 getTranslation()

get translation component.

Returns:

the translation

incrementTranslation

public void incrementTranslation(Vector3 dt)

increment translation component. add vector to current translation

Parameters:

dt - translation increment

setTranslation

public void setTranslation(Vector3 t)

set translation component.

Parameters:

t - translation vector

getCentreOfRotation

public Point3 getCentreOfRotation()

get centre of rotation. if R is rotation and t is translation compute p = ~(I - R) . t

Returns:

the centre

getScales

public RealArray getScales()

get scales.

Returns:

3-element RealArray)

getRotationMatrix

public RealSquareMatrix getRotationMatrix()

get Unitary matrix. eliminate scales and translation and normalize

Returns:

unitary 3X3 matrix

getCrystallographicString

public String getCrystallographicString()

return operator in crystallographic form;

Returns:

string of type "x,-y,1/2+z"

checkNotNull

public static void checkNotNull(Transform3 t)

check not null

Parameters:

t - transform3