com.esri.core.geometry
Class Transformation2D

java.lang.Object
  com.esri.core.geometry.Transformation2D

public class Transformation2D
extends Object

The affine transformation class for 2D.
Vector is a row:
|m11 m12 0|
| x y 1| * |m21 m22 0| = |m11 * x + m21 * y + m31 m12 * x + m22 * y + m32 1|
|m31 m32 1|
Then elements of the Transformation2D are as follows:
|xx yx 0|
| x y 1| * |xy yy 0| = |xx * x + xy * y + xd yx * x + yy * y + yd 1|
|xd yd 1|
Matrices are used for transformations of the vectors as rows (case 2). That means the math expressions on the Geometry matrix operations should be writen like this:
v' = v * M1 * M2 * M3 = ( (v * M1) * M2 ) * M3, where v is a vector, Mn are the matrices.
This is equivalent to the following line of code:
ResultVector = (M1.mul(M2).mul(M3)).transform(Vector)

Field Summary

double	xd X translation component of the transformation.
double	xx Matrix coefficient XX of the transformation.
double	xy Matrix coefficient XY of the transformation.
double	yd Y translation component of the transformation.
double	yx Matrix coefficient YX of the transformation.
double	yy Matrix coefficient YY of the transformation.

Constructor Summary

Transformation2D()
Creates a 2D affine transformation with identity transformation.

Transformation2D(double scale)
Creates a 2D affine transformation with a specified scale.

Method Summary

Transformation2D	copy() Returns a copy of the Transformation2D object.
boolean	equals(Object other) Returns True when all members of this transformation are equal to the corresponding members of the other.
void	extractScaleTransform(Transformation2D scale, Transformation2D rotateNshearNshift) Extracts scaling part of the transformation.
void	flipX(double x0, double x1) Flips the transformation around the X axis.
void	flipY(double y0, double y1) Flips the transformation around the Y axis.
void	getCoefficients(double[] coefs) Writes the matrix coefficients in the order XX, XY, XD, YX, YY, YD into the given array.
int	hashCode() Returns the hash code for the 2D transformation.
void	inverse() Inverses the matrix.
void	inverse(Transformation2D inverse) Produces inverse matrix for this matrix and puts result into the inverse parameter.
boolean	isDegenerate(double tol) Returns TRUE if this matrix is degenerated (does not have an inverse) within the given tolerance.
boolean	isIdentity() Returns TRUE if this matrix is the identity matrix.
boolean	isIdentity(double tol) Returns TRUE if this matrix is an identity matrix within the given tolerance.
boolean	isOrthonormal(double tol) Returns TRUE if this is an orthonormal transformation with the given tolerance.
boolean	isReflective() Returns TRUE for reflective transformations.
boolean	isScaleAndShift(double tol) Returns TRUE, if this transformation does not have rotation and shear within the given tolerance.
boolean	isShift() Returns TRUE if this transformation is a shift transformation.
boolean	isShift(double tol) Returns TRUE if this transformation is a shift transformation within the given tolerance.
boolean	isUniform(double eps) Returns TRUE if this transformation is a uniform transformation.
void	mulLeft(Transformation2D left) Multiplies this matrix on the left with the "left" matrix.
void	multiply(Transformation2D right) Multiplies this matrix on the right with the "right" matrix.
static void	multiply(Transformation2D a, Transformation2D b, Transformation2D result) Performs multiplication of matrices a and b and places the result into this matrix.
void	rotate(double angle_in_Radians) Rotates the transformation.
void	rotate(double cos, double sin) Rotates the transformation.
void	rotate(double cos, double sin, com.esri.core.geometry.Point2D rotationCenter) Rotates the transformation aroung a center point.
void	scale(double x, double y) Scales the transformation.
void	setFlipX(double x0, double x1) Sets the transformation to be a flip around the X axis.
void	setFlipY(double y0, double y1) Sets the transformation to be a flip around the Y axis.
void	setIdentity() Sets this matrix to be the identity matrix.
void	setRotate(double angle_in_Radians) Sets this transformation to be a rotation around point (0, 0).
void	setRotate(double cosA, double sinA) Sets rotation for this transformation.
void	setScale(double _scale) Set transformation to be a uniform scale.
void	setScale(double x, double y) Set this transformation to be a scale.
void	setShear(double proportionX, double proportionY) Set transformation to a shear.
void	setShift(double x, double y) Set this transformation to be a shift.
void	setZero() Initializes a zero transformation.
void	shear(double proportionX, double proportionY) Shears the transformation.
void	shift(double x, double y) Shifts the transformation.
double	transform(double tolerance) Transforms a tolerance value.
void	transform(double[] pointsXYInterleaved, int start, int count) Transforms an array of points stored in an array of doubles as interleaved XY coordinates.
void	transform(Point[] pointsIn, int count, Point[] pointsOut) Transforms an array of points.

Methods inherited from class java.lang.Object

getClass, notify, notifyAll, toString, wait, wait, wait

Field Detail

xx

public double xx

Matrix coefficient XX of the transformation.

xy

public double xy

Matrix coefficient XY of the transformation.

xd

public double xd

X translation component of the transformation.

yx

public double yx

Matrix coefficient YX of the transformation.

yy

public double yy

Matrix coefficient YY of the transformation.

yd

public double yd

Y translation component of the transformation.

Constructor Detail

Transformation2D

public Transformation2D()

Creates a 2D affine transformation with identity transformation.

Transformation2D

public Transformation2D(double scale)

Creates a 2D affine transformation with a specified scale.

Parameters:

scale - The scale to use for the transformation.

Method Detail

setZero

public void setZero()

Initializes a zero transformation. Transforms any coordinate to (0, 0).

equals

public boolean equals(Object other)

Returns True when all members of this transformation are equal to the corresponding members of the other.

Overrides:

equals in class Object

hashCode

public int hashCode()

Returns the hash code for the 2D transformation.

Overrides:

hashCode in class Object

transform

public void transform(Point[] pointsIn,
                      int count,
                      Point[] pointsOut)

Transforms an array of points.

Parameters:

pointsIn - The points to be transformed.

count - The number of points to transform.

pointsOut - The transformed points are returned using this array. It should have the same or greater size as the input array.

transform

public void transform(double[] pointsXYInterleaved,
                      int start,
                      int count)

Transforms an array of points stored in an array of doubles as interleaved XY coordinates.

Parameters:

pointsXYInterleaved - The array of points with interleaved X, Y values to be transformed.

start - The start point index to transform from (the actual element index is 2 * start).

count - The number of points to transform (the actual element count is 2 * count).

multiply

public void multiply(Transformation2D right)

Multiplies this matrix on the right with the "right" matrix. Stores the result into this matrix and returns a reference to it.
Equivalent to this *= right.

Parameters:

right - The matrix to be multiplied with.

mulLeft

public void mulLeft(Transformation2D left)

Multiplies this matrix on the left with the "left" matrix. Stores the result into this matrix and returns a reference to it.
Equivalent to this = left * this.

Parameters:

left - The matrix to be multiplied with.

multiply

public static void multiply(Transformation2D a,
                            Transformation2D b,
                            Transformation2D result)

Performs multiplication of matrices a and b and places the result into this matrix. The a, b, and result could point to same objects.
Equivalent to result = a * b.

Parameters:

a - The 2D transformation to be multiplied.

b - The 2D transformation to be multiplied.

result - The 2D transformation created by multiplication of matrices.

copy

public Transformation2D copy()

Returns a copy of the Transformation2D object.

Returns:

A copy of this object.

getCoefficients

public void getCoefficients(double[] coefs)

Writes the matrix coefficients in the order XX, XY, XD, YX, YY, YD into the given array.

Parameters:

coefs - The array into which the coefficients are returned. Should be of size 6 elements.

transform

public double transform(double tolerance)

Transforms a tolerance value.

Parameters:

tolerance - The tolerance value.

setIdentity

public void setIdentity()

Sets this matrix to be the identity matrix.

isIdentity

public boolean isIdentity()

Returns TRUE if this matrix is the identity matrix.

isIdentity

public boolean isIdentity(double tol)

Returns TRUE if this matrix is an identity matrix within the given tolerance.

Parameters:

tol - The tolerance value.

isReflective

public boolean isReflective()

Returns TRUE for reflective transformations. It inverts the sign of vector cross product.

isUniform

public boolean isUniform(double eps)

Returns TRUE if this transformation is a uniform transformation. The uniform transformation is a transformation, which transforms a square to a square.

isShift

public boolean isShift()

Returns TRUE if this transformation is a shift transformation. The shift transformation performs shift only.

isShift

public boolean isShift(double tol)

Returns TRUE if this transformation is a shift transformation within the given tolerance.

Parameters:

tol - The tolerance value.

isOrthonormal

public boolean isOrthonormal(double tol)

Returns TRUE if this is an orthonormal transformation with the given tolerance. The orthonormal: Rotation or rotoinversion and shift (preserves lengths of vectors and angles between vectors).

Parameters:

tol - The tolerance value.

isDegenerate

public boolean isDegenerate(double tol)

Returns TRUE if this matrix is degenerated (does not have an inverse) within the given tolerance.

Parameters:

tol - The tolerance value.

isScaleAndShift

public boolean isScaleAndShift(double tol)

Returns TRUE, if this transformation does not have rotation and shear within the given tolerance.

Parameters:

tol - The tolerance value.

setShift

public void setShift(double x,
                     double y)

Set this transformation to be a shift.

Parameters:

x - The X coordinate to shift to.

y - The Y coordinate to shift to.

setScale

public void setScale(double x,
                     double y)

Set this transformation to be a scale.

Parameters:

x - The X coordinate to scale to.

y - The Y coordinate to scale to.

setScale

public void setScale(double _scale)

Set transformation to be a uniform scale.

Parameters:

_scale - The scale of the transformation.

setFlipX

public void setFlipX(double x0,
                     double x1)

Sets the transformation to be a flip around the X axis. Flips the X coordinates so that the x0 becomes x1 and vice verse.

Parameters:

x0 - The X coordinate to flip.

x1 - The X coordinate to flip to.

setFlipY

public void setFlipY(double y0,
                     double y1)

Sets the transformation to be a flip around the Y axis. Flips the Y coordinates so that the y0 becomes y1 and vice verse.

Parameters:

y0 - The Y coordinate to flip.

y1 - The Y coordinate to flip to.

setShear

public void setShear(double proportionX,
                     double proportionY)

Set transformation to a shear.

Parameters:

proportionX - The proportion of shearing in x direction.

proportionY - The proportion of shearing in y direction.

setRotate

public void setRotate(double angle_in_Radians)

Sets this transformation to be a rotation around point (0, 0). When the axis Y is directed up and X is directed to the right, the positive angle corresponds to the anti-clockwise rotation. When the axis Y is directed down and X is directed to the right, the positive angle corresponds to the clockwise rotation.

Parameters:

angle_in_Radians - The rotation angle in radian.

setRotate

public void setRotate(double cosA,
                      double sinA)

Sets rotation for this transformation. When the axis Y is directed up and X is directed to the right, the positive angle corresponds to the anti-clockwise rotation. When the axis Y is directed down and X is directed to the right, the positive angle corresponds to the clockwise rotation.

Parameters:

cosA - The rotation angle.

sinA - The rotation angle.

shift

public void shift(double x,
                  double y)

Shifts the transformation.

Parameters:

x - The shift factor in X direction.

y - The shift factor in Y direction.

scale

public void scale(double x,
                  double y)

Scales the transformation.

Parameters:

x - The scale factor in X direction.

y - The scale factor in Y direction.

flipX

public void flipX(double x0,
                  double x1)

Flips the transformation around the X axis.

Parameters:

x0 - The X coordinate to flip.

x1 - The X coordinate to flip to.

flipY

public void flipY(double y0,
                  double y1)

Flips the transformation around the Y axis.

Parameters:

y0 - The Y coordinate to flip.

y1 - The Y coordinate to flip to.

shear

public void shear(double proportionX,
                  double proportionY)

Shears the transformation.

Parameters:

proportionX - The proportion of shearing in x direction.

proportionY - The proportion of shearing in y direction.

rotate

public void rotate(double angle_in_Radians)

Rotates the transformation.

Parameters:

angle_in_Radians - The rotation angle in radian.

rotate

public void rotate(double cos,
                   double sin)

Rotates the transformation.

Parameters:

cos - The cos angle of the rotation.

sin - The sin angle of the rotation.

rotate

public void rotate(double cos,
                   double sin,
                   com.esri.core.geometry.Point2D rotationCenter)

Rotates the transformation aroung a center point.

Parameters:

cos - The cos angle of the rotation.

sin - sin angle of the rotation.

rotationCenter - The center point of the rotation.

inverse

public void inverse(Transformation2D inverse)

Produces inverse matrix for this matrix and puts result into the inverse parameter.

Parameters:

inverse - The result inverse matrix.

inverse

public void inverse()

Inverses the matrix.

extractScaleTransform

public void extractScaleTransform(Transformation2D scale,
                                  Transformation2D rotateNshearNshift)

Extracts scaling part of the transformation. this == scale * rotateNshearNshift.

Parameters:

scale - The destination matrix where the scale part is copied.

rotateNshearNshift - The destination matrix where the part excluding rotation is copied.