This paper describes a hidden curve algorithm specifically designed for sculptured surfaces. A technique is described to extract the visible curves for a given scene without the need to approximate the surface by polygons. This algorithm produces higher quality results than polygon based algorithms, as most of the output set has an exact representation. Surface coherence is used to speed up the process. Although designed for sculptured surfaces, this algorithm is also suitable for polygonal data.
a) (b) Figure 1: (a) 10000 freeform geometric models (chess pieces) falling into a pile, where the same models share a common BVH of Coons patches approximating the given freeform NURBS surfaces within an error bound 10 −5 , where the unit length is taken as the largest side length of the minimum bounding box of the model, and (b) the minimum distance computation between a flying B58 model and a complex dynamic scene with many Utah teapots falling to the playground. AbstractWe present a compact representation for the bounding volume hierarchy (BVH) of freeform NURBS surfaces using Coons patches. Following the Coons construction, each subpatch can be bounded very efficiently using the bilinear surface determined by the four corners. The BVH of freeform surfaces is represented as a hierarchy of Coons patch approximation until the difference is reduced to within a given error bound. Each leaf node contains a single Coons patch, where a detailed BVH for the patch can be represented very compactly using two lists (containing curve approximation errors) of length proportional only to the height of the BVH. We demonstrate the effectiveness of our compact BVH representation using several experimental results from real-time applications in collision detection and minimum distance computation for freeform models. jects [Samet 2006]. Real-time algorithms for polygonal meshes employ various different types of BVHs that are built in a preprocessing stage of the geometric computation [Akenine-Möller et al. 2008]. The BVH for a polygonal mesh usually requires a much larger memory space compared to the original model itself [Yoon and Manocha 2006]. Thus it is an important subject of research to develop compact representations for BVH structures.Freeform geometric models are more compact than polygonal meshes. The BVH structure of freeform geometry can be generated by recursively subdividing the freeform surfaces [Johnson and Cohen 1998]. Nevertheless, it is unclear, in general, where to stop the recursive subdivision and how to proceed with the geometric computation when we reach the leaf level. In this paper, we address these two important issues and propose a compact BVH construction scheme for freeform geometry that is based on the special structure of the Coons patch. 169:8 • Y.-J. Kim et al.
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