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] computermuseumfh-kielde
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