DynaPDF Manual - Page 552

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Function Reference
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on the page it is used. Similarly, if a pattern is used within a template, the pattern
matrix maps pattern space to the template's default user space (that is, the template
coordinate space at the time the template is painted). A pattern may be used within
another pattern; the inner pattern’s matrix defines its relationship to the pattern space
of the outer pattern.
Working with Transformation Matrices
Coordinate transformations in PDF are achieved with so called Affine Transformations. Affine
transformations can represent any linear mapping from one coordinate system to another.
Affine transformations work with transformation matrices which consist of 6 real numbers. A
transformation matrix describes the coordinate origin, scaling factors of the x- and y-axis, as well as
the rotation angle of the coordinate system. A transformation matrix represents essentially a
coordinate space in which graphical objects can be drawn. Two coordinate spaces can easily be
concatenated by multiplying the corresponding transformation matrices.
Coordinates of objects which use their own coordinate space, such a text, templates, or patterns,
must be transformed to user space before the coordinates can be used. How this must be done is
described later.
Transformation matrices in DynaPDF are stored in the structure TCTM that is defined as follows:
struct TCTM
{
double a;
double b;
double c;
double d;
double x;
double y;
};
The identity matrix is [1, 0, 0, 1, 0, 0] (a, b, c, d, x, y).
The following overview lists the most important matrix manipulations:
Translations are specified as [1, 0, 0, 1, tx, ty] where tx and ty represent the distances to
translate the origin of the coordinate system in horizontal and vertical dimensions,
respectively.
Scaling is achieved by [sx, 0, 0, sy, 0, 0]. This scales the coordinates so that 1 unit in the
horizontal and vertical dimensions of the new coordinate system is the same size as sx and sy
units, respectively, in the previous coordinate system.
Rotations are achieved by [cos α, sin α, -sin α, cos α, 0, 0], which has the effect of rotating the
coordinate system axes by an angle α (measured in radians) counter clockwise.
Skew is specified by [1, tan α, tan β, 1, 0, 0], which skews the x-axis by an angle α, and the y-
axis by an angle β (measured in radians).
 

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