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Approximation of subdivision surfaces for interactive applications

Subdivision surfaces are undoubtedly the most flexible smooth geometric representation. By only manipulating a carefully designed low-resolution mesh, an high-resolution smooth version is automatically generated using a set of local recursive rules applied on each coarse polygon. However, while being intensively used in CAD and SFX industries, they have not yet gained a significant interest for interactive and real-time applications. In fact, their recursive definition imposes a non-trivial CPU overhead, difficult to hide in interactive applications. We propose a new efficient approximation of subdivision surfaces which offers a very close appearance compared to the true subdivision surface while being at least one order of magnitude faster than true subdivision rendering. Our technique 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 input 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 on the CPU, allowing real-time performances even for million polygons output. Additionally, the parametric nature of the approximation allows an efficient adaptive sampling for both adaptive rendering and displacement mapping.