Fast generation of 2-D node distributions for mesh-free PDE discretizations

Many applications require that nodes be scattered locally quasi-uniformly within 2-D regions or on curved surfaces in 3-D space, while obeying some prescribed spatially varying density function. This study focuses on creating variable density node layouts that are suitable for mesh-free discretizations of PDEs. Another application is ‘dithering’ to simulate half-tone images. The method is an ‘advancing-front type’ scheme, inspired by the physical process of dropping of variable sized grains into a bucket.