Math

Worley Noise Worley Noise1 (also known as Voronoi noise or Cellular noise) was introduced by Steven Worley2 in 1996 as a type of procedural noise function. Its appearance resembles biological cells, which is why the author originally called it “Cellular Texture.” The algorithm for generating Worley Noise works as follows: the image is divided into a grid of cells, and each cell contains a single feature point. The value of any given pixel is the minimum distance from that pixel to the feature points in the surrounding cells. ...

Introduction to SDF Signed Distance Field (SDF) Signed Distance Field (SDF)1 is a mathematical function or data structure used to represent shapes. In 2D or 3D space, it assigns each point a signed distance value, which represents the distance to the nearest surface (or boundary), with the sign distinguishing between inside and outside: Positive value: The point is outside the shape, and the value indicates the nearest distance to the surface. Negative value: The point is inside the shape, and the absolute value indicates the nearest distance to the surface. Zero: The point lies exactly on the surface of the shape. Formally, for a point $x$ in space, an SDF can be defined as: ...

Introduction to Perlin Noise Perlin Noise was developed by Ken Perlin in 1983 for the film Tron as a smooth pseudo-random noise algorithm1. It can generate random patterns with natural-looking texture and is widely used in computer graphics to simulate natural phenomena such as clouds, terrain, fire, wood grain, and water flow2. Unlike plain white noise, Perlin Noise has spatial correlation: values at neighboring sample points vary smoothly without abrupt jumps. This smoothness makes the generated textures resemble the continuous variations found in nature. ...

This article focuses solely on the following topics: Transition from trigonometric series expansion to the Euler form of the Fourier transform What the Discrete Fourier Transform is What the 2D Fourier Transform is Explanation of the 2D Discrete Fourier Transform from the 2D Fourier Transform How to perform a 2D Fourier transform on an image Periodicity issues in the 2D Fourier transform Understanding the centering of the 2D frequency spectrum from the periodicity of the 2D Fourier transform Fourier Series A Fourier series is a mathematical tool that represents a periodic function as an infinite sum of sines and cosines. ...