To evaluate the difference between a three-dimensional Bézier triangle cubic interpolation and a parametric three-dimensional surface, I compute the absolute volume in between. The Bézier triangle is defined within the Bézier space (u,v,w are the barycentric coordinates) and the parametric surface is defined in the three-dimensional space (x,y are the Cartesian coordinates).
The Bézier triangle is defined by three points in between a three-dimensional cubic interpolation is computed. This triangle is meshed in 100 sub-triangles (each edge is divided into 10 parts) defined by 66 nodes. These nodes have barycentric coordinates which have a Cartesian equivalent and the absolute volume is computed by multiplying the vertical difference between nodes and the parametric surface and the planar surface of the Bézier triangle.
The goal of this seminar is to compare two ways to compute the vertical difference (at nodes or at sub-triangle barycenters) and to discuss another way to obtain similar results by limiting the computational time.