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
Turning procedural and structural knowledge into programs has established methodologies, but what about turning knowledge into probabilistic models? I explore a few examples of what such a process could look like.
This course covers the design and analysis of randomized algorithms and, more generally, applications of randomness in computing. You will learn fundamental tools from probability and see many applications of randomness in computing.
- Robust and stochastic optimization
- Convex analysis
- Linear programming
- Monte Carlo simulation
- Model-based estimation
- Matrix algebra review
- Probability and statistics basics
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. Ulusoy, A. Geiger, and M. Black. Proceedings of the 2015 International Conference on 3D Vision, page 10--18. Washington, DC, USA, IEEE Computer Society, (2015)