What most of us take for granted when using CAD/CAM/CAE technologies had to come from somewhere, correct? By that I mean the mathematics that underlie and drive all CAx applications. From the basic math numerical models are derived as the output of systems. The output of these systems are geometric shape descriptions of modeled objects. As these systems were being developed a new branch of mathematics, known as geometric modeling, was created – and that’s what the book, Geometric Modeling, is all about.
Fundamentally, geometric modeling studies the methods used to construct and control numerical geometric models of real and imaginary objects.
Geometric modeling is entirely dependent of several areas of mathematics, but primarily differential geometry (that employs differential and integral calculus and linear algebra for developing planes, curves, and surfaces in 3D Euclidean space) and numerical methods (to find numerical approximations – the more precise the approximation, the better the model).
How basic math becomes numerical modeling that becomes geometric modeling is the subject of a new book, Geometric Modeling, by Dr. Nikolay Golovanov. The book is based on the author’s experience gained throughout his career, and especially during the development of the ASCON Group’s C3D geometric kernel as a principal architect.
In a nutshell, the book outlines the methods of geometric modeling, including methods for constructing curves, surfaces, and solids. It describes the algorithms and data structures behind geometric objects. It also presents the principles of the interconnections between the elements of geometric models. Finally, the book examines some of the applications of geometric models, such as determining model physical characteristics, rendering, simulation, etc.