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A simple counterexample to imagine is a curve that represents a circle (or a circular arc). The parallel curve to this is a scaling of the circle, with a bigger
by Jasper_ 4y ago
A simple counterexample to imagine is a curve that represents a circle (or a circular arc). The parallel curve to this is a scaling of the circle, with a bigger/smaller radii, not a translation.
- jabbany 4y agoThough the circle case is a little bit misleading, since it's only the same as scaling in that one case. In general, finding the parallel curve can't be approximated by affine transforms like scaling or translation, which is why it's so annoying. Also this is surprisingly relevant in a lot of weird places. First I encountered this was trying to create a closed polygon "outline" based on a vector graphics font -- the idea was to approximate the concept of "stroke width" on a platform that could not understand strokes and instead only worked with filled polygons.