Discrete Surface Geometry and Intrinsic Triangulations

Explore the fundamentals of discrete surface geometry and intrinsic triangulations in this 59-minute Fields Postdoc Colloquium talk by Nicholas Sharp. Delve into the world of piecewise-flat surfaces and discover how intrinsic triangulations offer a unique perspective on representing 3D shapes. Learn about the bridge between geometric theory and practical algorithms in geometric computing, starting with basic concepts and progressing to advanced topics. Examine surface meshes, gradients, vector fields, and Gaussian curvature before diving into intrinsic edge lengths and their historical context. Investigate Euclidean intrinsic triangles, cone metrics, and non-embeddable triangulations. Understand key properties, including Delaunay edge flips and refinement techniques. Explore applications in nonmanifold meshes, robustness improvements, and algorithm enhancements. No prior knowledge of the subject is required for this comprehensive introduction to discrete surface geometry and its practical implications in science and engineering.