While simple approximations to the bbox are trivial (such as computing the bounding box of their control points), in this article we deduce the exact bounding box analytically.
I made another thing! This is a torus, made from 24 crescent-shaped pieces of paper with slots cut into them so they interlock with each other. I followed these instructions on cutoutfoldup.com. There is also a template with some ideas for nice variations here. The idea of this model is to highlight Villarceau circles. Everyone…
GPUs are designed to do many things well, but drawing transparent 3D objects is not one of them. Opacity doesn't commute so that the order in which you draw surfaces makes a big difference. Of course simple additive blending does commute, but it's not really what we think of as "transparent objects". The simplest way to draw transparent objects is from back to front via the painter's algorithm. In this approach we sort geometry and draw only from back to front. This requires sorting triangles, which, in add
John D. Cook, Greg Egan, Dan Piponi and I had a fun mathematical adventure on Twitter. It started when John Cook wrote a program to compute the probability distribution of distances $latex |xy - yx|$ where $latex x$ and $latex y$ were two randomly chosen unit quaternions: • John D. Cook, How far is xy…
A minimal surface is the surface of minimal area between any given boundaries. In nature such shapes result from an equilibrium of homogeneous tension, e.g. in a soap film. Minimal surfaces have a constant mean curvature of zero, i.e. the sum of the principal curvatures at each point is zero. Particularly fascinating are minimal surfaces…