Parallel Smoothing of Quad Meshes

For use in real-time applications, we present a fast algorithm for converting a quad mesh to a smooth, piecewise polynomial surface on the Graphics Processing Unit (GPU). The surface has well-defined normals everywhere and closely mimics the shape of Catmull-Clark subdivision surfaces. It consists of bi-cubic splines wherever possible, and a new class of patches – c-patches – where a vertex has a valence different from 4. The algorithm fits well into parallel streams so that meshes with 12,000 input quads, of which 60 % have one or more non-4-valent vertices, are converted, evaluated and rendered with 9 × 9 resolution per quad at 50 frames per second. The GPU computations are ordered so that evaluation avoids pixel dropout