Approximating Catmull-Clark subdivision surfaces with bicubic patches
Approximating Catmull-Clark subdivision surfaces with bicubic patches
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DOI：
10.1145/1330511.1330519
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发表时间：
2008-03
期刊：
影响因子：
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通讯作者：
Charles T. Loop;S. Schaefer
中科院分区：
文献类型：
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作者：
Charles T. Loop;S. Schaefer
我们提出了一种简单且计算高效的算法，用于使用最少数量的双三次面片来逼近Catmull - Clark细分曲面。对于控制网格的每个四边形面，我们构建一个几何面片以及一对切向面片。几何面片逼近Catmull - Clark曲面的形状和轮廓，并且除了沿着包含奇异顶点的面片边缘（在这些边缘处面片是C0连续的）外，处处光滑。为了使面片表面看起来光滑，我们提供了一对切向面片来逼近Catmull - Clark曲面的切向场。这些切向面片用于构建一个连续的法向场（通过它们的叉积），以用于着色和位移映射。使用这种二分表示法，我们能够为Catmull - Clark曲面定义一个精确的代理，该代理在具有可编程细分单元的下一代GPU架构上进行求值时是高效的。
We present a simple and computationally efficient algorithm for approximating Catmull-Clark subdivision surfaces using a minimal set of bicubic patches. For each quadrilateral face of the control mesh, we construct a geometry patch and a pair of tangent patches. The geometry patches approximate the shape and silhouette of the Catmull-Clark surface and are smooth everywhere except along patch edges containing an extraordinary vertex where the patches are C0. To make the patch surface appear smooth, we provide a pair of tangent patches that approximate the tangent fields of the Catmull-Clark surface. These tangent patches are used to construct a continuous normal field (through their cross-product) for shading and displacement mapping. Using this bifurcated representation, we are able to define an accurate proxy for Catmull-Clark surfaces that is efficient to evaluate on next-generation GPU architectures that expose a programmable tessellation unit.