QAS: Real-time quadratic approximation of subdivision surfaces

We introduce QAS, an efficient quadratic approximation of subdivision surfaces which offers a very close appearance compared to the true subdivision surface but avoids recursion, providing at least one order of magnitude faster rendering. QAS uses enriched polygons, equipped with edge vertices, and replaces them on-the-fly with low degree polynomials for interpolating positions and normals. By systematically projecting the vertices of the input coarse mesh at their limit position on the subdivision surface, the visual quality of the approximation is good enough for imposing only a single subdivision step, followed by our patch fitting, which allows real-time performances for million polygons output. Additionally, the parametric nature of the approximation offers an efficient adaptive sampling for rendering and displacement mapping. Last, the hexagonal support associated to each coarse triangle is adapted to geometry processors.