com.tinyline.tiny2d
Class TinyMatrix

java.lang.Object
  com.tinyline.tiny2d.TinyMatrix

public final class TinyMatrix

extends java.lang.Object

The TinyMatrix class represents a 2D affine transformation matrix. By modifying a TinyMatrix, objects can be scaled, rotated, translated, or transformed. TinyMatrix is represented by a transformation matrix written as:

  [  a    b   0 ]
  [  c    d   0 ]
  [  tx   ty  1 ]
 

Here tx and ty are single fixed point numbers and a,b,c,d are double fixed point numbers.

The transformations could be specified as combinations of those listed below:

• Translation is equivalent to the TinyMatrix [1 0 0 1 tx ty], where tx and ty are the distances to translate coordinates in X and Y.
• Scaling is equivalent to the TinyMatrix [sx 0 0 sy 0 0]. One unit in the X and Y directions in the new coordinate system equals sx and sy units in the previous coordinate system.
• Rotation about the origin is equivalent to the TinyMatrix [cos(a) sin(a) -sin(a) cos(a) 0 0], which has the effect of rotating the coordinate system axes by angle a.
• A skew transformation along the x-axis is equivalent to the TinyMatrix [1 0 tan(a) 1 0 0], which has the effect of skewing X coordinates by angle a.
• A skew transformation along the y-axis is equivalent to the TinyMatrix [1 tan(a) 0 1 0 0], which has the effect of skewing Y coordinates by angle a.

If several transformations are applied, the order is important. In general, trnasformations should be done in the following order: translate, rotate, scale.

Coordinate trnasformations could be expressed as:

                            [  a    b   0 ]
    [x' y' 1 ] = [x  y  1]  [  c    d   0 ]
                            [  tx   ty  1 ]

 

By carring out the multiplication:

    x' = ax + cy + tx;

    y' = bx + dy + ty;
 

If a series of transformations is carried out, the transformatios can be multiplied together to produce a single equivalent transformation.

Version:

1.11

Author:

Andrew Girow

Field Summary

int	a The X coordinate scaling element of the 3x3 matrix.
int	angle A convenience attribute for TRANSFORM_ROTATE, TRANSFORM_SKEWX and TRANSFORM_SKEWY.
int	b The X coordinate shearing element of the 3x3 matrix.
int	c The Y coordinate shearing element of the 3x3 matrix.
int	d The Y coordinate scaling element of the 3x3 matrix.
int	rotateOriginX The rotate is about the point with rotateOriginX X coordinate.
int	rotateOriginY The rotate is about the point with rotateOriginY Y coordinate.
static byte	TRANSFORM_MATRIX A 'matrix(...)' transformation type
static byte	TRANSFORM_ROTATE A 'rotate(...)' transformation type
static byte	TRANSFORM_SCALE A 'scale(...)' transformation type
static byte	TRANSFORM_SKEWX A 'skewX(...)' transformation type
static byte	TRANSFORM_SKEWY A 'skewY(...)' transformation type
static byte	TRANSFORM_TRANSLATE A 'translate(...)' transformation type
static byte	TRANSFORM_UNKNOWN A transformation type is not one of predefined types.
int	tx The X coordinate of the translation element of the 3x3 matrix.
int	ty The Y coordinate of the translation element of the 3x3 matrix.
byte	type The transformation type of the value as specified by one of the constants specified.

Constructor Summary

TinyMatrix()
Constructs a new TinyMatrix representing the Identity transformation

TinyMatrix(TinyMatrix src)
Constructs a new TinyMatrix that is a copy of the specified TinyMatrix object.

Method Summary

void	concatenate(TinyMatrix matrix1) Concatenates an TinyMatrix matrix1 to this TinyMatrix .
void	copy(TinyMatrix src) Copyies TinyMatrix src to this TinyMatrix .
TinyMatrix	inverse() Returns an TinyMatrix object representing the inverse transformation.
void	preConcatenate(TinyMatrix matrix) Concatenates an TinyMatrix matrix to this TinyMatrix .
void	reset() Sets this TinyMatrix object to the Identity transformation
void	rotate(int theta, int cx, int cy) Sets this transform to a rotation transformation that rotates coordinates around an anchor point.
void	scale(int sx, int sy) Sets this transform matrix to a scaling transformation.
void	skew(int alpha, int betta) Sets this transform to a skew transformation.
void	transform(TinyPoint point) Transforms the specified point
void	transformToDev(TinyPoint point, TinyPoint point1) Transforms the specified point to DEVICE SPACE and stores the result in point1.
TinyRect	transformToDev(TinyRect rect) Transforms the specified TinyRect rect to DEVICE SPACE.
void	translate(int tx, int ty) Sets this transform matrix to a translating transformation.

Methods inherited from class java.lang.Object

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

Field Detail

TRANSFORM_UNKNOWN

public static final byte TRANSFORM_UNKNOWN

A transformation type is not one of predefined types.

See Also:

Constant Field Values

TRANSFORM_MATRIX

public static final byte TRANSFORM_MATRIX

A 'matrix(...)' transformation type

See Also:

Constant Field Values

TRANSFORM_TRANSLATE

public static final byte TRANSFORM_TRANSLATE

A 'translate(...)' transformation type

See Also:

Constant Field Values

TRANSFORM_SCALE

public static final byte TRANSFORM_SCALE

A 'scale(...)' transformation type

See Also:

Constant Field Values

TRANSFORM_ROTATE

public static final byte TRANSFORM_ROTATE

A 'rotate(...)' transformation type

See Also:

Constant Field Values

TRANSFORM_SKEWX

public static final byte TRANSFORM_SKEWX

A 'skewX(...)' transformation type

See Also:

Constant Field Values

TRANSFORM_SKEWY

public static final byte TRANSFORM_SKEWY

A 'skewY(...)' transformation type

See Also:

Constant Field Values

type

public byte type

The transformation type of the value as specified by one of the constants specified.

angle

public int angle

A convenience attribute for TRANSFORM_ROTATE, TRANSFORM_SKEWX and TRANSFORM_SKEWY. It holds the angle that was specified

rotateOriginX

public int rotateOriginX

The rotate is about the point with rotateOriginX X coordinate.

rotateOriginY

public int rotateOriginY

The rotate is about the point with rotateOriginY Y coordinate.

a

public int a

The X coordinate scaling element of the 3x3 matrix.

b

public int b

The X coordinate shearing element of the 3x3 matrix.

c

public int c

The Y coordinate shearing element of the 3x3 matrix.

d

public int d

The Y coordinate scaling element of the 3x3 matrix.

tx

public int tx

The X coordinate of the translation element of the 3x3 matrix.

ty

public int ty

The Y coordinate of the translation element of the 3x3 matrix.

Constructor Detail

TinyMatrix

public TinyMatrix()

Constructs a new TinyMatrix representing the Identity transformation

TinyMatrix

public TinyMatrix(TinyMatrix src)

Constructs a new TinyMatrix that is a copy of the specified TinyMatrix object.

Parameters:

src - the TinyMatrix object to copy

Method Detail

reset

public final void reset()

Sets this TinyMatrix object to the Identity transformation

concatenate

public final void concatenate(TinyMatrix matrix1)

Concatenates an TinyMatrix matrix1 to this TinyMatrix . In matrix notation, this method does the following:

[this] = [this] x [matrix]

Parameters:

matrix1 - the TinyMatrix object.

copy

public final void copy(TinyMatrix src)

Copyies TinyMatrix src to this TinyMatrix . In matrix notation, this method does the following:

[this] = [src]

Parameters:

src - the TinyMatrix object.

preConcatenate

public final void preConcatenate(TinyMatrix matrix)

Concatenates an TinyMatrix matrix to this TinyMatrix . In matrix notation, this method does the following:

[this] = [matrix] x [this]

Parameters:

matrix - The TinyMatrix object.

inverse

public final TinyMatrix inverse()

Returns an TinyMatrix object representing the inverse transformation.

Returns:

a new TinyMatrix object representing the inverse transformation.

translate

public final void translate(int tx,
                            int ty)

Sets this transform matrix to a translating transformation. The matrix representing this transform is:

    [  1  0  0  1  tx  ty ]
 

Parameters:

tx - the distance along the x-axis in FIXED POINT precision

ty - the distance along the y-axis in FIXED POINT precision

scale

public final void scale(int sx,
                        int sy)

Sets this transform matrix to a scaling transformation. The matrix representing this transform is:

    [  sx  0  0  sy  0  0 ]
 

Parameters:

sx - the factor along the x-axis in DOUBLE FIXED POINT precision

sy - the factor along the y-axis in DOUBLE FIXED POINT precision

rotate

public final void rotate(int theta,
                         int cx,
                         int cy)

Sets this transform to a rotation transformation that rotates coordinates around an anchor point. The matrix representing this transform is:

    [ cos(theta)  sin(theta)  -sin(theta)  cos(theta)  x-x*cos+y*sin  y-x*sin-y*cos ]
 

Rotating the coordinate system axes by degrees counterclockwise.

Parameters:

theta - the angle of rotation in degrees

skew

public void skew(int alpha,
                 int betta)

Sets this transform to a skew transformation. The matrix representing this transform is:

    [ 1  tan(alpha) tan(betta) 1  0  0  1 ]
 

Parameters:

alpha - (in degrees) skews the x-axis by an angle alpha

betta - (in degrees) skews the y-axis by an angle betta

transform

public final void transform(TinyPoint point)

Transforms the specified point

Parameters:

point - the specified point to be transformed

transformToDev

public final void transformToDev(TinyPoint point,
                                 TinyPoint point1)

Transforms the specified point to DEVICE SPACE and stores the result in point1.

Parameters:

point - the specified point to be transformed

point1 - the specified point that stores the result.

transformToDev

public final TinyRect transformToDev(TinyRect rect)

Transforms the specified TinyRect rect to DEVICE SPACE.

Parameters:

rect - the specified TinyRect rect to be transformed

Returns:

the transformed TinyRect rectangle