Graphics and Geometry twitter, if we define a plane3d as a normal & offset, why do we not define lines in 2d the same? It seems that it might provide clarity when moving between spaces.
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Normally, I see math libs (and I've done this in the past) describe geometric objects where Line, for example, is templated on type and size. Line<float, 2>, Line<float, 3>, etc. Triangle<float, 2>, Triangle<float, 3>.
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If instead we defined it using terms like Plane, Simplex, Facet, Ridge, Peak, it scales much more elegantly, I think. And algorithms can be written against types that scale to all dimensions (unless the compiler stops you).pic.twitter.com/1D63bqRjKn
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For instance, say we write a function that finds the intersection between two planes. That same idea (plane v plane) doesn't really make sense in 2D, but line vs line does. The way a seg2f is the "segment" of a 2d plane (line2f), a tri3f is the "segment" of a plane3f.
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I think it makes writing these algorithms easier to write for all spaces (templated). Say you wrote an algo to clip a tri2f against a line2f. When you need to do that in 3D, it's clearer that it's you need the analog of seg2f clipped by line2f.
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Of course I haven't proven this out yet. The thought just occurred to me and I have yet to try it out. Has anybody else described objects this way in their own code? Has it proven fruitful?
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I think there might be issues when you try to deal with cross products, but if you instead think of wedge products, maybe this still all works out?
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