Sgss_Graphics_Transform
Represents a two-dimensional affine transformation matrix

Description

Implements:

ArrayAccess (internal interface), Sgss_Graphics_Imagick_Get_Interface, Sgss_Graphics_Imagick_Draw_Interface

Author:

Matsuda Shota

Copyright:

(c) 2007-2008 Matsuda Shota

License:

http://creativecommons.org/licenses/GPL/2.0/

Located in:

/Graphics/Transform.php (line 69)

Class overview

Accessors

Variables

Methods

Variable detail

$_rx 

Shearing x element

Signature:

protected number $_rx

$_ry 

Shearing y element

Signature:

protected number $_ry

$_sx 

Scaling x element

Signature:

protected number $_sx

$_sy 

Scaling y element

Signature:

protected number $_sy

$_tx 

Translation x element

Signature:

protected number $_tx

$_ty 

Translation y element

Signature:

protected number $_ty

Method detail

__construct

The constructor

Parameters:

• number|array|Sgss_Graphics_Transform $sx

  Scaling x element or a transformation matrix

• number $rx

  Shearing x element

• number $tx

  Translation x element

• number $ry

  Shearing y element

• number $sy

  Scaling y element

• number $ty

  Translation y element

Signature:

public __construct ([number|array|Sgss_Graphics_Transform $sx = 1], [number $rx = 0], [number $tx = 0], [number $ry = 0], [number $sy = 1], [number $ty = 0])

composite

Composites this transformation matrix with another

The resulting transformation matrix A' is equivalent to the following:

     A' = A x T

where A denotes this transformation matrix and T denotes another.

Parameters:

• number|array|Sgss_Graphics_Transform $sx

  Scaling x element or a transformation matrix to be applied to this transformation matrix

• number $rx

  Shearing x element to be applied to this transformation matrix

• number $tx

  Translation x element to be applied to this transformation matrix

• number $ry

  Shearing y element to be applied to this transformation matrix

• number $sy

  Scaling y element to be applied to this transformation matrix

• number $ty

  Translation y element to be applied to this transformation matrix

Returns:

Sgss_Graphics_Transform -- This object for convenience

Signature:

public Sgss_Graphics_Transform composite (number|array|Sgss_Graphics_Transform $sx, [number $rx = 0], [number $tx = 0], [number $ry = 0], [number $sy = 1], [number $ty = 0])

composition

Returns the composited transformation matrix with another

This is the same as composition() except the returned value is a new object.

Parameters:

• number|array|Sgss_Graphics_Transform $sx

  Scaling x element or transformation matrix to be applied to this transformation matrix

• number $rx

  Shearing x element to be applied to this transformation matrix

• number $tx

  Translation x element to be applied to this transformation matrix

• number $ry

  Shearing y element to be applied to this transformation matrix

• number $sy

  Scaling y element to be applied to this transformation matrix

• number $ty

  Translation y element to be applied to this transformation matrix

Returns:

Sgss_Graphics_Transform -- Composited transformation

Signature:

public Sgss_Graphics_Transform composition (number|array|Sgss_Graphics_Transform $sx, [number $rx = 0], [number $tx = 0], [number $ry = 0], [number $sy = 1], [number $ty = 0])

createReflection 

Creates an returns the specified reflection transformation matrix

The resulting transformation matrix A is equivalent to the following:

         [ hori   0    x (1 - hori) ]
     A = [  0    vert  y (1 - vert) ]
         [  0     0          1      ]

where hori and vert denote -1 or 1 depending on whether the $vert and $hori are true or false.

Parameters:

• boolean $vert

  Wheter to reflect the resulting transformation matrix

• boolean $hori

  Wheter to reflect the resulting transformation matrix

• number $x

  Location of x axis along which the resulting transformation matrix to be refrected

• number $y

  Location of y axis along which the resulting transformation matrix to be refrected

Returns:

Sgss_Graphics_Transform -- Reflection transformation

Uses:

Sgss_Graphics_Transform::toReflection()

Signature:

public static Sgss_Graphics_Transform createReflection ([boolean $vert = false], [boolean $hori = false], [number $x = 0], [number $y = 0])

createRotation 

Creates an returns the specified rotation transformation matrix

The resulting transformation matrix A is equivalent to the following:

          [ cos(r)  -sin(r)  x - x cos(r) + y sin(r) ]
     A' = [ sin(r)   cos(r)  x - y cos(r) - x sin(r) ]
          [   0        0                1            ]

where sin(r) and cos(r) denote the sine and cosine values of the $theta parameter.

Parameters:

• number $theta

  Rotation angle of the resulting transformation matrix in degree

• number $x

  X coordinate of the rotation center

• number $y

  Y coordinate of the rotation center

Returns:

Sgss_Graphics_Transform -- Rotation transformation

Uses:

Sgss_Graphics_Transform::toRotation()

Signature:

public static Sgss_Graphics_Transform createRotation (number $theta, [number $x = 0], [number $y = 0])

createScale 

Creates an returns the specified scaling transformation matrix

The resulting transformation matrix A is equivalent to the following:

          [ sx  0   0 ]
     A' = [ 0   sy  0 ]
          [ 0   0   1 ]

Parameters:

• number $sx

  Scaling x element of the resulting transformation matrix

• number $sy

  Scaling y element of the resulting transformation matrix

Returns:

Sgss_Graphics_Transform -- Scaling transformation

Uses:

Sgss_Graphics_Transform::toScale()

Signature:

public static Sgss_Graphics_Transform createScale (number $sx, number $sy)

createShear 

Creates an returns the specified shearing transformation matrix

The resulting transformation matrix A is equivalent to the following:

         [ 1   rx  0 ]
     A = [ ry  1   0 ]
         [ 0   0   1 ]

Parameters:

• number $rx

  Shearing x element of the resulting transformation matrix

• number $ry

  Shearing y element of the resulting transformation matrix

Returns:

Sgss_Graphics_Transform -- Shearing transformation

Uses:

Sgss_Graphics_Transform::toShear()

Signature:

public static Sgss_Graphics_Transform createShear (number $rx, number $ry)

createTranslation 

Creates an returns the specified translation transformation matrix

The resulting transformation matrix A is equivalent to the following:

         [ 1   0   tx ]
     A = [ 0   1   ty ]
         [ 0   0   1  ]

Parameters:

• number $tx

  Translation x element of the resulting transformation matrix

• number $ty

  Translation y element of the resulting transformation matrix

Uses:

Sgss_Graphics_Transform::toTranslation() - Translation transformation

Signature:

public static Sgss_Graphics_Transform createTranslation (number $tx, number $ty)

determinant

Returns the determinant of this matrix

The determinant is caluculated by the following formula:

              | sx  rx  tx |
     det(A) = | ry  sy  ty | = sx sy - rx ry
              | 0   0   1  |

where A denotes this transformation matrix.

Returns:

number -- Determinant of this matrix

Used by:

Sgss_Graphics_Transform::inverse()

Signature:

public number determinant ()

drawImagick

Applies this transformation matrix to the specified ImagickDraw instance

Parameters:

• Imagick|ImagickDraw $imagick

  ImagickDraw instance

• number $x

  Offset x (ignored)

• number $y

  Offset y (ignored)

Returns:

boolean -- True when this operation succeeded

Specified by:

• Sgss_Graphics_Imagick_Draw_Interface::drawImagick()

  Draws to the specified ImagickDraw instance

Related subject:

Sgss_Graphics_Imagick_Draw_Interface::drawImagick()

Signature:

public boolean drawImagick (Imagick|ImagickDraw $imagick, [number $x = 0], [number $y = 0])

getImagick

Converts this transformation matrix to an array used with Imagick

Returned array takes the following form:

1.  array('sx' => $sx, 'ry' => $rx, 'tx' => $tx,
2.        'rx' => $ry, 'sy' => $sy, 'ty' => $ty)

Note that it seems not equivalent to the common naming of affine transformation matrix (rx and ry), but Imagick recognizes rx to be ry and vice versa. Probably because the y axis of the image is reversed to its apparance.

Returns:

array -- Array representing this transformation matrix to be used with Imagick

Specified by:

• Sgss_Graphics_Imagick_Get_Interface::getImagick()

  Returns the representation for the Imagick or ImagickDraw

Related subject:

Sgss_Graphics_Imagick_Get_Interface::getImagick()

Signature:

public array getImagick ()

getScaleX

Returns the scaling x element

Returns:

number -- Scaling x element

Signature:

public number getScaleX ()

getScaleY

Returns the scaling y element

Returns:

number -- Scaling y element

Signature:

public number getScaleY ()

getShearX

Returns the shearing x element

Returns:

number -- Shearing x element

Signature:

public number getShearX ()

getShearY

Returns the shearing y element

Returns:

number -- Shearing y element

Signature:

public number getShearY ()

getTransform

Returns another object representing this transformation matrix

Returns:

Sgss_Graphics_Transform -- Another object representing this transformation matrix

Signature:

public Sgss_Graphics_Transform getTransform ()

getTranslateX

Returns the translation x element

Returns:

number -- Translation x element

Signature:

public number getTranslateX ()

getTranslateY

Returns the translation y element

Returns:

number -- Translation y element

Signature:

public number getTranslateY ()

inverse

Returns the inversed transformation matrix

The resulting transformation matrix A' is equivalent to the following:

          [  sy / det(A)  -rx / det(A)   (rx ty - sy tx) / det(A) ]
     A' = [ -ry / det(A)   sx / det(A)   (ry tx - sx ty) / det(A) ]
          [       0            0                    1            ]

where A denotes this transformation matrix, and:

     det(A) = sx sy - rx ry != 0

The A and A' are in the following relation:

     A' x A = A x A' = I(3)

where I(3) denotes the 3x3 identity matrix.

Returns:

Sgss_Graphics_Transform -- Inversed transformation matrix

Throws:

• Sgss_Graphics_Transform_Exception

  When the determinant is 0

Uses:

Sgss_Graphics_Transform::determinant()

Signature:

public Sgss_Graphics_Transform inverse ()

offsetExists

Parameters:

• mixed $offset

Specified by:

• ArrayAccess::offsetExists

Related subject:

ArrayAccess::offsetExists()

Signature:

public boolean offsetExists (mixed $offset)

offsetGet

Parameters:

• mixed $offset

Specified by:

• ArrayAccess::offsetGet

Related subject:

ArrayAccess::offsetGet()

Signature:

public mixed offsetGet (mixed $offset)

offsetSet

Parameters:

• mixed $offset
• mixed $value

Specified by:

• ArrayAccess::offsetSet

Related subject:

ArrayAccess::offsetSet()

Signature:

public mixed offsetSet (mixed $offset, mixed $value)

offsetUnset

Parameters:

• mixed $offset

Specified by:

• ArrayAccess::offsetUnset

Related subject:

ArrayAccess::offsetUnset()

Signature:

public void offsetUnset (mixed $offset)

reflect

Reflects this transformation matrix

The resulting transformation matrix A' is equivalent to the following:

              [ hori   0    x (1 - hori) ]
     A' = A x [  0    vert  y (1 - vert) ]
              [  0     0          1      ]

where A denotes this transformation matrix, and hori and vert denote -1 or 1 depending on whether the $vert and $hori are true or false.

Parameters:

• boolean $vert

  Wheter to reflect this transformation matrix

• boolean $hori

  Wheter to reflect this transformation matrix

• number $x

  Location of x axis along which this transformation matrix to be refrected

• number $y

  Location of y axis along which this transformation matrix to be refrected

Returns:

Sgss_Graphics_Transform -- This object for convenience

Uses:

Sgss_Graphics_Transform::translate()

Signature:

public Sgss_Graphics_Transform reflect ([boolean $vert = false], [boolean $hori = false], [number $x = 0], [number $y = 0])

rotate

Rotates this transformation matrix

The resulting transformation matrix A' is equivalent to the following:

              [ cos(r)  -sin(r)  x - x cos(r) + y sin(r) ]
     A' = A x [ sin(r)   cos(r)  x - y cos(r) - x sin(r) ]
              [   0        0                1            ]

where A denotes this transformation matrix, and sin(r) and cos(r) denote the sine and cosine values of the $theta parameter.

Parameters:

• number $theta

  Rotation angle to be applied to this transformation matrix in degree

• number $x

  X coordinate of the rotation center

• number $y

  Y coordinate of the rotation center

Returns:

Sgss_Graphics_Transform -- This object for convenience

Uses:

Sgss_Graphics_Transform::translate()

Signature:

public Sgss_Graphics_Transform rotate (number $theta, [number $x = 0], [number $y = 0])

scale

Scales this transformation

The resulting transformation matrix A' is equivalent to the following:

              [ sx  0   0 ]
     A' = A x [ 0   sy  0 ]
              [ 0   0   1 ]

where A denotes this transformation matrix.

Parameters:

• number $sx

  Scaling x element to be applied to this transformation matrix

• number $sy

  Scaling y element to be applied to this transformation matrix

Returns:

Sgss_Graphics_Transform -- This object for convenience

Signature:

public Sgss_Graphics_Transform scale (number $sx, number $sy)

setScaleX

Sets the scaling x element to the specified value

Parameters:

• number $sx

  Scaling x element to set

Signature:

public void setScaleX (number $sx)

setScaleY

Sets the scaling y element to the specified value

Parameters:

• number $sy

  Scaling y element to set

Signature:

public void setScaleY (number $sy)

setShearX

Sets the shearing x element to the specified value

Parameters:

• number $rx

  Shearing x element to set

Signature:

public void setShearX (number $rx)

setShearY

Sets the shearing y element to the specified value

Parameters:

• number $ry

  Shearing y element to set

Signature:

public void setShearY (number $ry)

setTransform

Sets this transformation matrix to the specified value

Parameters:

• Sgss_Graphics_Transform $t

  Transformation matrix to set

Signature:

public void setTransform (Sgss_Graphics_Transform $t)

setTranslateX

Sets the translation x element to the specified value

Parameters:

• number $tx

  Translation x element to set

Signature:

public void setTranslateX (number $tx)

setTranslateY

Sets the translation y element to the specified value

Parameters:

• number $ty

  Translation y element to set

Signature:

public void setTranslateY (number $ty)

shear

Shears this transformation matrix

The resulting transformation matrix A' is equivalent to the following:

              [ 1   rx  0 ]
     A' = A x [ ry  1   0 ]
              [ 0   0   1 ]

where A denotes this transformation matrix.

Parameters:

• number $rx

  Shearing x element to be applied to this transformation matrix

• number $ry

  Shearing y element to be applied to this transformation matrix

Returns:

Sgss_Graphics_Transform -- This object for convenience

Signature:

public Sgss_Graphics_Transform shear (number $rx, number $ry)

toArray

Converts this transformation matrix to an array

Returned array takes the following form:

1.  array($sx, $rx, $tx,
2.        $ry, $sy, $ty)

Returns:

array -- Array representing this transformation matrix

Signature:

public array toArray ()

toReflection

Sets this transformation matrix to the specified reflection transformation

The resulting transformation matrix A is equivalent to the following:

         [ hori   0    x (1 - hori) ]
     A = [  0    vert  y (1 - vert) ]
         [  0     0          1      ]

where hori and vert denote -1 or 1 depending on whether the $vert and $hori are true or false.

Parameters:

• boolean $vert

  Wheter to reflect the resulting transformation matrix

• boolean $hori

  Wheter to reflect the resulting transformation matrix

• number $x

  Location of x axis along which the resulting transformation matrix to be refrected

• number $y

  Location of y axis along which the resulting transformation matrix to be refrected

Returns:

Sgss_Graphics_Transform -- This object for convenience

Used by:

Sgss_Graphics_Transform::createReflection()

Signature:

public Sgss_Graphics_Transform toReflection ([boolean $vert = false], [boolean $hori = false], [number $x = 0], [number $y = 0])

toRotation

Sets this transformation matrix to the specified rotation transformation

The resulting transformation matrix A is equivalent to the following:

          [ cos(r)  -sin(r)  x - x cos(r) + y sin(r) ]
     A' = [ sin(r)   cos(r)  x - y cos(r) - x sin(r) ]
          [   0        0                1            ]

where sin(r) and cos(r) denote the sine and cosine values of the $theta parameter.

Parameters:

• number $theta

  Rotation angle to set in degree

• number $x

  X coordinate of the rotation center

• number $y

  Y coordinate of the rotation center

Returns:

Sgss_Graphics_Transform -- This object for convenience

Used by:

Sgss_Graphics_Transform::createRotation()

Signature:

public Sgss_Graphics_Transform toRotation (number $theta, [number $x = 0], [number $y = 0])

toScale

Sets this transformation matrix to the specified scaling transformation

The resulting transformation matrix A is equivalent to the following:

          [ sx  0   0 ]
     A' = [ 0   sy  0 ]
          [ 0   0   1 ]

Parameters:

• number $sx

  Scaling x element to set

• number $sy

  Scaling y element to set

Returns:

Sgss_Graphics_Transform -- This object for convenience

Used by:

Sgss_Graphics_Transform::createScale()

Signature:

public Sgss_Graphics_Transform toScale (number $sx, number $sy)

toShear

Sets this transformation matrix to the specified shearing transformation

The resulting transformation matrix A is equivalent to the following:

         [ 1   rx  0 ]
     A = [ ry  1   0 ]
         [ 0   0   1 ]

Parameters:

• number $rx

  Shearing x element to set

• number $ry

  Shearing y element to set

Returns:

Sgss_Graphics_Transform -- This object for convenience

Used by:

Sgss_Graphics_Transform::createShear()

Signature:

public Sgss_Graphics_Transform toShear (number $rx, number $ry)

toTranslation

Sets this transformation matrix to the specified translation transformation

The resulting transformation matrix A is equivalent to the following:

         [ 1   0   tx ]
     A = [ 0   1   ty ]
         [ 0   0   1  ]

Parameters:

• number $tx

  Translation x element to set

• number $ty

  Translation y element to set

Returns:

Sgss_Graphics_Transform -- This object for convenience

Used by:

Sgss_Graphics_Transform::createTranslation() - Translation transformation

Signature:

public Sgss_Graphics_Transform toTranslation (number $tx, number $ty)

transform

Transform the specified vector with this transformation matrix

The resulting vector (x', y') is equivalent to the following:

     [ x']   [ x ]
     [ y'] = [ y ] x A
     [ 1 ]   [ 1 ]

where A denotes this transformation matrix.

Parameters:

• number $x

  X coodinate of the vector to be transformed

• number $y

  Y coodinate of the vector to be transformed

Returns:

array -- Tranformed vector array

Signature:

public array transform (number $x, number $y)

translate

Translates this transformation matrix

The resulting transformation matrix A' is equivalent to the following:

              [ 1   0   tx ]
     A' = A x [ 0   1   ty ]
              [ 0   0   1  ]

where A denotes this transformation matrix.

Parameters:

• number $tx

  Translation x element to be applied to this transformation matrix

• number $ty

  Translation y element to be applied to this transformation matrix

Returns:

Sgss_Graphics_Transform -- This object for convenience

Used by:

Sgss_Graphics_Transform::reflect(), Sgss_Graphics_Transform::rotate()

Signature:

public Sgss_Graphics_Transform translate (number $tx, number $ty)

__get

Parameters:

• mixed $name

Signature:

public mixed __get (mixed $name)

__set

Parameters:

• mixed $name
• mixed $value

Signature:

public mixed __set (mixed $name, mixed $value)

__toString

Signature:

public string __toString ()