class HexaPDF::Content::TransformationMatrix
A TransformationMatrix
is a matrix used in PDF graphics operations to specify the relationship between different coordinate systems.
All matrix operations modify the matrix in place. So if the original matrix should be preserved, duplicate it before the operation.
It is important to note that the matrix transforms from the new coordinate system to the untransformed coordinate system. This means that after the transformation all coordinates are specified in the new, transformed coordinate system and to get the untransformed coordinates the matrix needs to be applied.
Although all operations are done in 2D space the transformation matrix is a 3x3 matrix because homogeneous coordinates are used. This, however, also means that only six entries are actually used that are named like in the following graphic:
a b 0 c d 0 e f 1
Here is a simple transformation matrix to translate all coordinates by 5 units horizontally and 10 units vertically:
1 0 0 0 1 0 5 10 1
Details and some examples can be found in the PDF reference.
See: PDF1.7 s8.3
Attributes
The value at the position (1,1) in the matrix.
The value at the position (1,2) in the matrix.
The value at the position (2,1) in the matrix.
The value at the position (2,2) in the matrix.
The value at the position (3,1) in the matrix.
The value at the position (3,2) in the matrix.
Public Class Methods
Initializes the transformation matrix with the given values.
# File lib/hexapdf/content/transformation_matrix.rb, line 93 def initialize(a = 1, b = 0, c = 0, d = 1, e = 0, f = 0) @a = a @b = b @c = c @d = d @e = e @f = f end
Public Instance Methods
Returns true
if the other object is a transformation matrix with the same values.
# File lib/hexapdf/content/transformation_matrix.rb, line 161 def ==(other) (other.kind_of?(self.class) && @a == other.a && @b == other.b && @c == other.c && @d == other.d && @e == other.e && @f == other.f) end
Returns the untransformed coordinates of the given point.
# File lib/hexapdf/content/transformation_matrix.rb, line 103 def evaluate(x, y) [@a * x + @c * y + @e, @b * x + @d * y + @f] end
Transforms this matrix by premultiplying it with the given one (ie. given*this) and returns it.
# File lib/hexapdf/content/transformation_matrix.rb, line 146 def premultiply(a, b, c, d, e, f) a1 = a * @a + b * @c b1 = a * @b + b * @d c1 = c * @a + d * @c d1 = c * @b + d * @d @e = e * @a + f * @c + @e @f = e * @b + f * @d + @f @a = a1 @b = b1 @c = c1 @d = d1 self end
Rotates this matrix by an angle of q
degrees and returns it.
This equal to premultiply(cos(rad(q)), sin(rad(q)), -sin(rad(q)), cos(rad(q)), x, y).
# File lib/hexapdf/content/transformation_matrix.rb, line 130 def rotate(q) cq = Math.cos(deg_to_rad(q)) sq = Math.sin(deg_to_rad(q)) premultiply(cq, sq, -sq, cq, 0, 0) end
Scales this matrix by sx
units horizontally and y
units vertically and returns it.
This is equal to premultiply(sx, 0, 0, sy, 0, 0).
# File lib/hexapdf/content/transformation_matrix.rb, line 119 def scale(sx, sy) @a = sx * @a @b = sx * @b @c = sy * @c @d = sy * @d self end
Skews this matrix by an angle of a
degrees for the x axis and by an angle of b
degrees for the y axis and returns it.
This is equal to premultiply(1, tan(rad(a)), tan(rad(b)), 1, x, y).
# File lib/hexapdf/content/transformation_matrix.rb, line 140 def skew(a, b) premultiply(1, Math.tan(deg_to_rad(a)), Math.tan(deg_to_rad(b)), 1, 0, 0) end
Creates an array [a, b, c, d, e, f] from the transformation matrix.
# File lib/hexapdf/content/transformation_matrix.rb, line 167 def to_a [@a, @b, @c, @d, @e, @f] end
Translates this matrix by x
units horizontally and y
units vertically and returns it.
This is equal to premultiply(1, 0, 0, 1, x, y).
# File lib/hexapdf/content/transformation_matrix.rb, line 110 def translate(x, y) @e = x * @a + y * @c + @e @f = x * @b + y * @d + @f self end