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The same concept is used for pen styles in 2D drawing programs: the center
of the pen is moved along a path, and all points reachable with the pen
shape from the current location on this path are painted with the drawing
color, i.e. all painted points are obtained by location_vector+shape_vector
for all possible location_vectors and shape_vectors.
A practical application of the Minkowski sum would be as a *great* morphing
device. For example
minkowski_sum {
object { StartObject scale 1-clock }
object { FinalObject scale clock }
}
would give a smooth transition from StartObject to FinalObject. The
transition could be controlled by more complex blending functions. Given
blending functions, usually with Blend(0)=0 and Blend(1)=1 or even
Blend(0)=<0,0,0> and Blend(1)=<1,1,1>, I'm dreaming of
minkowski { StartObject*(1-Blend1(clock)) + FinalObject*Blend2(clock) }
Another interesting effect would be
minkowski { BaseObject + object { PaddingObject rotate Rotation(clock) } }
At least for meshes this should be possible, especially for convex shapes.
Sputnik
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e-mail: fr### [at] computermuseum fh-kiel de
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