460-4023/01 – Geometry for Computer Graphics (GPG)

The course is designed for students who will also deal with computer graphics. The goal is to deepen knowledge of geometry and mathematics for practical use in computer graphics. Further extend the knowledge studentůz kinematic geometry and creating technical curves and surfaces.

The course is intended for students who will be engaged in computer graphics, such as modeling curves and surfaces used in technical practice. Lecture Outline: 1. Basic information and review (coordinate system, vector, scalar and vector product, representation of a line and plane). Analytical geometry. 2. Introduction to the differential geometry of curves and surfaces. Tangent to a curve. The accompanying trihedron of a curve and Frenet formulas. 3. First and second curvature. 4. Polynomial curves and their properties. 5. Approximation curves (least squares method). 6. Ferguson curve, Ferguson surface. 7. Spline curves, Catmull-Rom spline. 8. Bézier curve and surface. 9. Coons B-spline curve and surface. General B-spline curve. 10. NURBS curves and surfaces. Exercise Outline: 1. Review. 2. Conversion of geometric problems into algebraic problems (determining intersections, relative positions, etc.). 3. Conic sections and quadrics. 4. Curves, surfaces, and their properties; motion along a curve. Examples of the properties of curves and surfaces. 5. Practical examples of selected curves and surfaces (polynomial curves, approximation curves, Ferguson curves, spline curves). 6. Bézier curve and surface. Properties and derivation. 7. Coons B-spline curve and surface. General B-spline curve and surface. NURBS curves and surfaces.

1. FRANCIS, S. HILL, Jr. Computer Graphics 1990. New York : Macmillian Publishing Company, a division of Macmillian, Inc. ISBN 0-02-354860-6.

Lecture, practical exercise, final project. Final project: create 3D program.