transform()

The "transform()" function can be used to generate spatial warps and rotations and such effects. It only operates on a single image and its only function is to displace pixels.

It can be given the operations in postfix notation or the module Affix::Infix2Postfix can be used to generate postfix code from infix code. Look in the test case t/t55trans.t for an example.

"transform()" needs expressions (or opcodes) that determine the source pixel for each target pixel. Source expressions are infix expressions using any of the +, -, *, / or ** binary operators, the - unary operator, ( and ) for grouping and the "sin()" and "cos()" functions. The target pixel is input as the variables x and y.

You specify the x and y expressions as "xexpr" and "yexpr" respectively. You can also specify opcodes directly, but that's magic deep enough that you can look at the source code.

Note: You can still use the transform() function, but the transform2() function is just as fast and is more likely to be enhanced and maintained.

  $new_img=$img->transform(xexpr=>'x',yexpr=>'y+10*sin((x+y)/10)')
  $new_img=$img->transform(xexpr=>'x+0.1*y+5*sin(y/10.0+1.57)',
                           yexpr=>'y+10*sin((x+y-0.785)/10)')

transform2()

Imager also supports a "transform2()" class method which allows you perform a more general set of operations, rather than just specifying a spatial transformation as with the transform() method, you can also perform color transformations, image synthesis and image combinations from multiple source images.

"transform2()" takes an reference to an options hash, and a list of images to operate one (this list may be empty):

  my %opts;
  my @imgs;
  ...
  my $img = Imager::transform2(\%opts, @imgs)
      or die "transform2 failed: $Imager::ERRSTR";

The options hash may define a transformation function, and optionally:

• width - the width of the image in pixels. If this isn't supplied the width of the first input image is used. If there are no input images an error occurs.
• height - the height of the image in pixels. If this isn't supplied the height of the first input image is used. If there are no input images an error occurs.
• constants - a reference to hash of constants to define for the expression engine. Some extra constants are defined by Imager
• channels - the number of channels in the output image. If this isn't supplied a 3 channel image will be created.

The transformation function is specified using either the "expr" or "rpnexpr" member of the options.

Infix expressions

You can supply infix expressions to transform 2 with the "expr" keyword.

  $opts{expr} = 'return getp1(w-x, h-y)'

The 'expression' supplied follows this general grammar:

   ( identifier '=' expr ';' )* 'return' expr

This allows you to simplify your expressions using variables.

A more complex example might be:

  $opts{expr} = 'pix = getp1(x,y); return if(value(pix)>0.8,pix*0.8,pix)'

Currently to use infix expressions you must have the Parse::RecDescent module installed (available from CPAN). There is also what might be a significant delay the first time you run the infix expression parser due to the compilation of the expression grammar.

Postfix expressions

You can supply postfix or reverse-polish notation expressions to transform2() through the "rpnexpr" keyword.

The parser for "rpnexpr" emulates a stack machine, so operators will expect to see their parameters on top of the stack. A stack machine isn't actually used during the image transformation itself.

You can store the value at the top of the stack in a variable called "foo" using "!foo" and retrieve that value again using @foo. The !foo notation will pop the value from the stack.

An example equivalent to the infix expression above:

 $opts{rpnexpr} = 'x y getp1 !pix @pix value 0.8 gt @pix 0.8 * @pix ifp'

At the end of the expression there should be a single pixel value left on the stack, which is used as the output pixel.

Operators

transform2() has a fairly rich range of operators.

Each entry below includes the usage with "rpnexpr", formatted as:

If the operand or result begins with "N" it is a numeric value, if it begins with "C" it is a color or pixel value.

+, *, -, /, %, **

multiplication, addition, subtraction, division, remainder and exponentiation. Multiplication, addition and subtraction can be used on color values too - though you need to be careful - adding 2 white values together and multiplying by 0.5 will give you gray, not white.

Division by zero (or a small number) just results in a large number. Modulo zero (or a small number) results in zero. % is implemented using fmod() so you can use this to take a value mod a floating point value.

"rpnexpr" usage:

sin(N), cos(N), atan2(y,x)

Some basic trig functions. They work in radians, so you can't just use the hue values.

"rpnexpr" usage:

distance(x1, y1, x2, y2)

Find the distance between two points. This is handy (along with atan2()) for producing circular effects.

"rpnexpr" usage:

sqrt(n)

Find the square root. I haven't had much use for this since adding the distance() function.

"rpnexpr" usage:

abs(n)

Find the absolute value.

"rpnexpr" usage:

getp1(x,y), getp2(x,y), getp3(x, y)

Get the pixel at position (x,y) from the first, second or third image respectively. I may add a getpn() function at some point, but this prevents static checking of the instructions against the number of images actually passed in.

"rpnexpr" usage:

value(c), hue(c), sat(c), hsv(h,s,v), hsva(h,s,v,alpha)

Separates a color value into it's value (brightness), hue (color) and saturation elements. Use hsv() to put them back together (after suitable manipulation), or hsva() to include a transparency value.

"rpnexpr" usage:

red(c), green(c), blue(c), rgb(r,g,b), rgba(r,g,b,a)

Separates a color value into it's red, green and blue colors. Use rgb(r,g,b) to put it back together, or rgba() to include a transparency value.

"rpnexpr" usage:

alpha(c)

Retrieve the alpha value from a color.

"rpnexpr" usage:

int(n)

Convert a value to an integer. Uses a C int cast, so it may break on large values.

"rpnexpr" usage:

if(cond,ntrue,nfalse), if(cond,ctrue,cfalse)

A simple (and inefficient) if function.

"rpnexpr" usage:

<=,<,==,>=,>,!=

Relational operators (typically used with if()). Since we're working with floating point values the equalities are 'near equalities' - an epsilon value is used.

&&, ||, not(n)

Basic logical operators.

"rpnexpr" usage:

log(n), exp(n)

Natural logarithm and exponential.

"rpnexpr" usage:

det(a, b, c, d)

Calculate the determinant of the 2 x 2 matrix;

  a b
  c d
    

"rpnexpr" usage:

Constants

transform2() defines the following constants:

"pi"

The classical constant.

"w"

"h"

The width and height of the output image.

"cx"

"cy"

The center of the output image.

"w"image number

"h"image number

The width and height of each of the input images, "w1" is the width of the first input image and so on.

"cx"image number

"cy"image number

The center of each of the input images, ("cx1", "cy1") is the center of the first input image and so on.

A few examples:

  rpnexpr=>'x 25 % 15 * y 35 % 10 * getp1 !pat x y getp1 !pix @pix sat 0.7 gt @pat @pix ifp'

  rpnexpr=>'x 25 % 15 * y 35 % 10 * getp1 !pat y 360 / !rat x y getp1 1 @rat - pmult @pat @rat pmult padd'

  rpnexpr=>'x y getp1 !pix @pix value 0.96 gt @pix sat 0.1 lt and 128 128 255 rgb @pix ifp'

  rpnexpr=>'x 35 % 10 * y 45 % 8 * getp1 !pat x y getp1 !pix @pix sat 0.2 lt @pix value 0.9 gt and @pix @pat @pix value 2 / 0.5 + pmult ifp'

  rpnexpr=>'x y 160 180 distance !d y 180 - x 160 - atan2 !a @d 10 / @a + 3.1416 2 * % !a2 @a2 180 * 3.1416 / 1 @a2 sin 1 + 2 / hsv'

  rpnexpr=>'x y 160 180 distance !d y 180 - x 160 - atan2 !a @d 10 / @a + 3.1416 2 * % !a2 @a 180 * 3.1416 / 1 @a2 sin 1 + 2 / hsv'

For details on expression parsing see Imager::Expr. For details on the virtual machine used to transform the images, see Imager::regmach.

  # generate a colorful spiral
  # requires that Parse::RecDescent be installed
  my $newimg = Imager::transform2({
                                   width => 160, height=>160,
                                   expr => <<EOS
  dist = distance(x, y, w/2, h/2);
  angle = atan2(y-h/2, x-w/2);
  angle2 = (dist / 10 + angle) % ( 2 * pi );
  return hsv(angle*180/pi, 1, (sin(angle2)+1)/2);
  EOS
                                  });
  # replace green portions of an image with another image
  my $newimg = Imager::transform2({
                                   rpnexpr => <<EOS
  x y getp2 !pat # used to replace green portions
  x y getp1 !pix # source with "green screen"
  @pix red 10 lt @pix blue 10 lt && # low blue and red
  @pix green 254 gt && # and high green
  @pat @pix ifp
  EOS
                                  }, $source, $background);

Matrix Transformations

matrix_transform()

Rather than having to write code in a little language, you can use a matrix to perform affine transformations, using the matrix_transform() method:

  my $newimg = $img->matrix_transform(matrix=>[ -1, 0, $img->getwidth-1,
                                            0,  1, 0,
                                            0,  0, 1 ]);
    

By default the output image will be the same size as the input image, but you can supply the "xsize" and "ysize" parameters to change the size.

Rather than building matrices by hand you can use the Imager::Matrix2d module to build the matrices. This class has methods to allow you to scale, shear, rotate, translate and reflect, and you can combine these with an overloaded multiplication operator.

WARNING: the matrix you provide in the matrix operator transforms the co-ordinates within the destination image to the co-ordinates within the source image. This can be confusing.

You can also supply a "back" argument which acts as a background color for the areas of the image with no samples available (outside the rectangle of the source image.) This can be either an Imager::Color or Imager::Color::Float object. This is not mixed transparent pixels in the middle of the source image, it is only used for pixels where there is no corresponding pixel in the source image.