This book explains the algorithms behind those collisions using basic shapes like circles, rectangles, and lines so you can implement them into your own projects.
A pair of mathematicians has built on an obscure, 30-year-old mathematical theory to show that soap-filmlike minimal surfaces appear abundantly in a wide range
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. Chéritat. (2014)cite arxiv:1410.4417Comment: 16 pages, 7 figures. This version has the following changes: Added computer generated images of the key positions S1 and S2. Corrected several minor mistakes. Corrected the proof of the main proposition (I had forgotten to ensure that the top and bottom curves remain embedded during the homotopy) and slightly changed the statement of Lemma 3 to adapt.
C. Gunn. (2014)cite arxiv:1411.6502Comment: 25 pages, 4 figures in Advances in Applied Clifford Algebras, pages 1--24, 2016, online at link.springer.com.