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 meshfree 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.