Computational Geometry for Geometric Modeling and CAD

Modern engineering, manufacturing, and computer-aided design rely on precise digital representations of physical shapes. Understanding the underlying mathematics of computational geometry is essential for building robust software, running accurate simulations, and solving complex spatial problems. This text-based course guides you through the foundational math and algorithms needed to represent, analyze, and manipulate complex 3D shapes. You will transition from a theoretical understanding of geometric concepts to practical implementation strategies. Starting with fundamental definitions, you will explore how curves, surfaces, and solid models are constructed, represented, and analyzed computationally. What you'll learn: - Understand the mathematics of B-splines and Non-Uniform Rational B-Splines (NURBS) for surface modeling - Implement constructive solid geometry (CSG) and boundary representation (B-Rep) techniques - Solve complex intersection problems using non-linear solvers and interval methods - Analyze geometric robustness issues and apply modern numeric precision strategies - Master shape interrogation techniques for design, analysis, and manufacturing workflows - Discover how finite element discretization bridges the gap between geometry and physics This course begins with basic geometric terminology and coordinate systems before advancing to complex parametric curves and solid modeling paradigms. You will read detailed explanations, analyze mathematical formulations, and study algorithm logic step-by-step. This course is designed for beginners in computational geometry, including software developers, mechanical engineers, and CAD professionals who want to understand the engine behind modern design software. No advanced prior experience in geometric programming is required. Start reading today to unlock the mathematical principles of 3D computer-aided design.