Shear
Some applications provide features that shear objects drawn in the client
area. If your application features shear capabilities, use the
SetWorldTransform function to set appropriate values in the world-space to page-space
transformation. This function receives a pointer to an
XFORM structure containing the appropriate values. The
eM12 and
eM21 members of
XFORM specify the horizontal and vertical proportionality constants, respectively.
There are two components of the
shear transformation. The first alters the vertical lines in an object; the second
alters the horizontal lines. The following illustration shows a 20- by 20-unit
rectangle sheared horizontally when copied from world space to page space.
A horizontal shear can be represented by the following algorithm:
x' = x + (Sx * y)
where
x is the original x-coordinate,
Sx is the proportionality constant, and
x' is the result of the shear transformation.
A vertical shear can be represented by the following algorithm:
y' = y + (Sy * x)
where
y is the original y-coordinate,
Sy is the proportionality constant, and
y' is the result of the shear transformation.
The horizontal-shear and vertical-shear transformations can be combined into a
single operation using a 2-by-2 matrix.
|x' y'| == |x y| * | 1 Sx|
| Sy 1|
The 2-by-2 matrix that produced the shear contains the following values.
|1 1|
|0 1|
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