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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 * yTransforms can be applied to pairs, guides, paths, pens, 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)
; they can also be raised to any
integer power with the ^
operator.
The built-in transforms are:
identity();
shift(pair z);
z
;
xscale(real x);
x
in the x direction;
yscale(real y);
y
in the y direction;
scale(real s);
s
in both x and y directions;
slant(real s);
(x,y)
–> (x+s*y,y)
;
rotate(real angle, pair z=(0,0));
angle
in degrees about z
;
reflect(pair a, pair b);
a--b
.
The implicit initializer for transforms is identity()
.