Orthonormal Bases

Given a standard orthornormal reference frame, consisting of the unit vectors along the x and y directions, the video below shows a naive mapping of that frame to the surface. When the surface is distorted, one can see that the frame is no longer orthonormal with respect to the metric of the space in which the surface is embedded.

In the video below we compute an orthonormal frame for each point using the square root method.

In the video below we domonstrate the texture unrolled onto a flat surface.