Methods for Generating Random Points Inside a Triangle
By
ibobev
Crusty in the right places. Worth the chew.
Summary
This article explains two methods for generating random points inside a triangle: barycentric coordinates (which produces non-uniform distribution) and an accept-reject method (which produces uniform distribution). The barycentric method involves generating three random numbers, normalizing them to sum to 1, and using them as weights for the triangle vertices. The accept-reject method involves drawing a bounding rectangle around the triangle, generating random points within it, and discarding those that fall outside the triangle.
Key quotes
· 3 pulledGenerate random numbers α, β, and γ from the interval [0, 1]. Normalize the points to have sum 1 by dividing each by their sum.
Return αA + βB + γC. This generates points inside the triangle, but not uniformly.
Draw a rectangle around the triangle, generate points in the square, and throw them away if they land outside the triangle.
You might also wanna read
Deriving the Sparse Cholesky Elimination Tree for Matrix Factorization
This article provides a technical derivation of the elimination tree for the right-looking sparse Cholesky algorithm (A = LL^T) for sparse m
Reducing Trigonometric Functions in Computer Graphics Algorithms
The article argues for reducing trigonometric functions in computer graphics algorithms, advocating for more efficient mathematical approach
iquilezles.org·2mo ago
Understanding the Geometric Foundations of Tangent Space and Normal Mapping in Computer Graphics
This article provides a deep dive into the geometric foundations of tangent space and normal mapping in computer graphics. It explains how t
shlom.dev·6mo ago
GPU-Accelerated Distance Calculation for Cubic Bézier Curves
This technical article explores the mathematical and computational challenges of calculating distance fields to cubic Bézier curves on GPUs.
blog.pkh.me·7mo agoUnderstanding OpenGL Matrices: A Visual Approach for Programmers
This article provides a beginner-friendly explanation of OpenGL matrices for graphics programming, focusing on making matrix concepts access
Understanding Wilson's Algorithm for Uniform Spanning Trees
The article explains Wilson's Algorithm, a method for generating uniform spanning trees using loop-erased random walks. It describes how the