The topic of this week is to visualize scalar and vector fields on surfaces. As an example, we will consider the mean curvature of a triangle mesh. The triangle mesh is an unstructured grid which discretizes a surface. The chapter on curvature in triangle meshes, see reference below, explains how to compute the mean curvature normal given a triangle mesh representation of a surface. The mean curvature normal is a vector field on the surface. The dot product of the mean curvature normal with the (normalized) surface normal is the mean curvature, which is a scalar field on the surface. An example where the mean curvature normal and the mean curvature are computed for the Stanford Bunny triangle mesh is available in a lecture example. Modify this example to visualize the mean curvature (normal) in different ways using the techniques described in DV and in the lecture.
| DV | Chapter 5 and Sections 6-6.2 and 6.6. Scalar visualization and vector visualization. |
| suppl. | Bærentzen, J. A., Gravesen, J., Anton, F., and Aanæs, H. Curvature in Triangle Meshes. In Guide to Computational Geometry Processing, Chapter 8, pp. 143-158, Springer, 2012. |