Introduction This is a variant of a similar past problem: draw something interesting, using a sequence of joined straight line segments, without ever lifting your pen. Or in this case, with one continuous thread. As far as I can tell, the first realization of this particular idea was in 2016, when artist Petros Vrellis [1]…
Wave Function Collapse is a procedural generation algorithm which produces images by arranging a collection of tiles according to rules about which tiles may be adjacent to each other tile, and relatively how frequently each tile should appear. The algorithm maintains, for each pixel of the output image, a probability distribution of the tiles which may be placed there. It repeatedly chooses a pixel to “collapse” - choosing a tile to use for that pixel based on its distribution. WFC gets its name from quantum physics. The goal of this post is to build an intuition for how and why the WFC algorithm works.
While implementing a quick toy example of Crane and Sawhney's really great Monte Carlo Geometry Processing paper, the question arose about whether a quick function I grabbed from The Internet to equally distribute points on a sphere was correct or not. Since it's absolutely the crux of the method, this is an important question! This notebook performs a rather unscientific check for equal distribution of points on the surface of a sphere. It uses the first algorithm from MathWorld: Sphere Point Picking. Foll
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
N. Zhukova, and A. Korotkov. (2022)cite arxiv:2206.10992Comment: 29 pages, 9 figures. This work will be published in Journal of Difference Equations and Applications.