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Maybe a mathematician can correct me. But could you not also model 3D vertices of uniform density into a 1D space and then uniformly sample the 1D space. Of c
by cjhanks 8y ago
Maybe a mathematician can correct me. But could you not also model 3D vertices of uniform density into a 1D space and then uniformly sample the 1D space. Of course this may have issues with highly dense objects or very large ones.
- lixtra 8y agoI don’t get what you mean by 1D spaces but you could triangulate into tetrahedra and sample those[1] (taking their volume into account). You will write a lot of code and still have the triangulation approximation error. For high dimensional spheres you can possibly subdivide the space in hyper cubes and do the in/out approach inside each cube that contains a part of the sphere to get a better hit miss ratio. [1] http://vcg.isti.cnr.it/jgt/tetra.htm http://vcg.isti.cnr.it/jgt/tetra.htm
- cjhanks 8y agoYes, I was thinking you could triangulate the sphere at discreet shells. I have done 2D symmetric polygons where you needed to uniquely index into a 1D array of vertex values. Ie, based on the magnitude you can estimate which shell. By knowing the shell, you know the number of vertices for the shell, by knowing both you can map it to a specific vertex, as you can define a priori the absolute traversal order. I have no idea if the 2D case extends to higher dimensions.