G1 rational blend interpolatory schemes: A comparative study

Interpolation of triangular meshes is a subject of great interest in many computer graphics related applications, as, for example, gaming and realtime rendering. One of the main approaches to interpolate the positions and normals of the mesh vertices is the use of parametric triangular Bézier patches. As it is well known, any method aiming at constructing a parametric, tangent plane (G1) continuous surface has to deal with the vertex consistency problem. In this article, we propose a comparison of three methods appeared in the nineties that use a particular technique called rational blend to avoid this problem. Together with these three methods we present a new scheme, a cubic Gregory patch, that has been inspired by one of them. Our comparison includes an analysis of their computational costs on CPU and GPU, a study of their capabilities of approximating analytic surfaces and their response to different surface interrogation methods on arbitrary triangle meshes with a low triangle count that actually occur in their real-world use.

We compare three recently appeared methods for local parametric G1 interpolation of triangular meshes that use a particular technique called rational blend. Together with these three methods we present a new scheme, a cubic Gregory patch, that has been inspired by one of them. The comparison is based on an analysis of their computational costs on CPU and GPU, a study of their capability of reproducing analytic surfaces and their response to surface interrogation methods.Figure optionsDownload as PowerPoint slideHighlights
► Compared schemes: hybrid parametric patch (degree 3), PNG1 triangles (degree 3), Walton and Meek’s Gregory patch (degree 4).
► CubicWM-B1: a new cubic Gregory patch inspired by Walton and Meek’s patch.
► Best performance on GPU: cubicWM-B1; best on CPU: Walton and Meek’s patch.
► Best sphere and torus approximation: Walton and Meek’s and cubicWM-B1 patch. Best behaviour on arbitrary meshes: PNG1.
► Stability problems for hybrid parametric patch on arbitrary meshes.