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Asymptote makes extensive use of affine transforms. A pair
(x,y) is transformed by the transform
t=(t.x,t.y,t.xx,t.xy,t.yx,t.yy) to (x',y'), where
x' = t.x + t.xx * x + t.xy * y y' = t.y + t.yx * x + t.yy * y
This is equivalent to the PostScript transformation
[t.xx t.yx t.xy t.yy t.x t.y].
Transforms can be applied to pairs, guides, paths, pens, strings,
transforms, frames, and pictures by multiplication (via the binary operator
*) on the left (see circle for an example).
Transforms can be composed with one another and inverted with the
function transform inverse(transform t); they can also be raised to any
integer power with the ^ operator.
The built-in transforms are:
transform identity();the identity transform;
transform shift(pair z);translates by the pair z;
transform shift(real x, real y);translates by the pair (x,y);
transform xscale(real x);scales by x in the x direction;
transform yscale(real y);scales by y in the y direction;
transform scale(real s);scale by s in both x and y directions;
transform scale(real x, real y);scale by x in the x direction and by y in the
y direction;
transform slant(real s);maps (x,y) –> (x+s*y,y);
transform rotate(real angle, pair z=(0,0));rotates by angle in degrees about z;
transform reflect(pair a, pair b);reflects about the line a--b.
The implicit initializer for transforms is identity().
The routines shift(transform t) and shiftless(transform t)
return the transforms (t.x,t.y,0,0,0,0) and
(0,0,t.xx,t.xy,t.yx,t.yy) respectively.
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