Curves and Surfaces in Computer-Aided Geometric Design

How do computer graphics programs, CAD tools, and animation software represent smooth, complex shapes? Understanding the underlying mathematics of curves and surfaces is essential for anyone looking to build, analyze, or program modern 3D design systems. This course bridges the gap between abstract geometry and practical computation, giving you the tools to describe and manipulate shapes mathematically. You will transition from basic geometric concepts to confidently defining and analyzing complex spatial structures. What you'll learn: - Understand the fundamental mathematical definitions of parametric curves and surfaces; - Construct and manipulate Bezier curves and B-splines using control points; - Apply de Casteljau and de Boor algorithms to evaluate geometric shapes; - Analyze local properties of curves and surfaces including curvature, torsion, and tangent vectors; - Explore modern subdivision surface techniques used in contemporary 3D modeling pipelines; - Practice formulating geometric equations through clear written exercises. This course begins with foundational coordinate geometry and linear algebra concepts before progressing step-by-step through parametric representations, spline construction, and surface analysis. This course is designed for beginners in computer graphics, engineering students, and software developers with no prior background in differential geometry. Start your journey into geometric modeling today.