Yoga Cat

To illustrate data in computer vision, a yoga cat was scanned with the phone. Once the spacial data are acquired, one can now do various things with it, like displaying the curvature or painting in gold. Curvature is very interesting. It is seen in the picture to the right of the photograph. Places where the surface looks like a saddle (negative curvature), the surface is colored red, where the surface looks like a paraboloid (positive curvature), the surface is colored blue. We will later see this curvature in the form of the discriminant D when extremizing functions.
Here are the spacial data. They consist of two parts. There is a texture file and a mesh of triangles as well as parametrization maps which tell, where to apply the texture. To the right, we see the regions, in which the cat has been partitioned. Each region is covered by part of the texture. Mathematicians call a surface also a ``manifold" and the collection of parametrization maps an ``atlas". We will see parametrizations of surfaces in this course. Below are three screenshots taken from meshlab.
Here is a version rendered in Povray. Click on the picture for a large version: Here, we use glass: