• Surface modeling: polygons, meshes, data structures, adjacency matrix (3 hours)
• Properties of triangles, meshes, and surfaces: normal, curvature, homeomorphism, topology, barycentric coordinates, valence, degree (3 hours)
• Visualization of surface properties, mesh processing tools, mathematical tools: HSV color space, least-squares minimization, staggered grids, Jacobian (3 hours)
• Convex hull, bounding volume (3 hours)
• Quality of polygons and meshes: vertex position, vertex split, edge collapse (3 hours)
• Surface processing: smoothing, filtering, subdivision (3 hours)
• Surface deformation: free-form deformation, Laplacian surface editing, gradient-based editing (3 hours)
• Animation by surface deformation: blend shapes, skeletal animation, linear blend skinning, dual quaternions (3 hours)
• Textures and surface parameterization (3 hours)
• Distortion measurements (3 hours)
• Surface reconstruction and triangulation: point cloud, Delaunay, Poisson surface reconstruction, marching cubes (3 hours)
• Distances: L₀, L₁, L₂, L_inf, Dijkstra, geodesic, Hausdorff (3 hours)
• Curves and surfaces: Bézier, BSpline, subdivision surfaces, implicit surfaces (3 hours)

The list of topics and sequence of topics may vary. The hours listed are approximate and for informational purposes only.

There are no scheduled laboratory periods. 

As part of the course, the student will implement techniques for mesh/surface modeling and processing. This takes the form of a personal project and a presentation of the project. The student must complete this work individually.