Mathematical Structures For Computer Graphics

Tiling theory is an elegant branch of mathematics that has applications in several areas of computer science. The most immediate application area is graphics, where tiling theory has been used in the contexts of texture generation, sampling theory, remeshing, and of course the generation of decorative patterns. The combination of a solid theoretical base (complete with tantalizing open problems), practical algorithmic techniques, and exciting applications make tiling theory a worthwhile area of study for practitioners and students in computer science.

Visualization is one of the most active and exciting areas of Mathematics and Computing Science, and indeed one which is only beginning to mature. Current visualization algorithms break down for very large data sets. While present approaches use multi-resolution ideas, future data sizes will not be handled that way. New algorithms based on sophisticated mathematical modeling techniques must be devised which will permit the extraction of high-level topological structures that can be visualized.

Implicit objects have gained increasing importance in geometric modeling, visualisation, animation, and computer graphics, because their geometric properties provide a good alternative to traditional parametric objects. This book presents the mathematics, computational methods and data structures, as well as the algorithms needed to render implicit curves and surfaces, and shows how implicit objects can easily describe smooth, intricate, and articulatable shapes, and hence why they are being increasingly used in graphical applications.

A Beginner's Guide to Essential Mathematics, Data Structures and Algorithms used in Game Programming applied in Unity

L systems are language-theoretic models for developmental biology.

This textbook effectively builds a bridge from basic number theory to recent advances in applied number theory. It presents the first unified account of the four major areas of application where number theory plays a fundamental role, namely cryptography, coding theory, quasi-Monte Carlo methods, and pseudorandom number generation, allowing the authors to delineate the manifold links and interrelations between these areas.

A Beginner's Guide to Essential Mathematics, Data Structures and Algorithms used in Game Programming applied in Unity