Real-time GPU rendering of piecewise algebraic surfaces
Real-time GPU rendering of piecewise algebraic surfaces
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DOI：
10.1145/1179352.1141939
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发表时间：
2006-07
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通讯作者：
Charles T. Loop;J. Blinn
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作者：
Charles T. Loop;J. Blinn
我们考虑由Bézier四面体定义的代数曲面的实时GPU渲染问题。这些表面直接根据其多项式表示进行渲染，而不是近似三角形的集合，从而消除了镶嵌伪影并减少了内存使用。这种算法的关键步骤是计算每个像素的一元多项式系数;该多项式的真实的根对应于表面上可能可见的点。我们的方法利用了GPU计算的优势，并且非常高效。此外，我们计算这些系数的伯恩斯坦的形式，以最大限度地提高稳定性的根查找，并提供着色器实例的早期退出测试的基础上，这些系数的符号。求解根是使用解析技术来完成的，这些技术可以很好地映射到SIMD架构，但将我们限制在四阶代数曲面。一般的框架可以扩展到高阶数值求根。
We consider the problem of real-time GPU rendering of algebraic surfaces defined by Bézier tetrahedra. These surfaces are rendered directly in terms of their polynomial representations, as opposed to a collection of approximating triangles, thereby eliminating tessellation artifacts and reducing memory usage. A key step in such algorithms is the computation of univariate polynomial coefficients at each pixel; real roots of this polynomial correspond to possibly visible points on the surface. Our approach leverages the strengths of GPU computation and is highly efficient. Furthermore, we compute these coefficients in Bernstein form to maximize the stability of root finding, and to provide shader instances with an early exit test based on the sign of these coefficients. Solving for roots is done using analytic techniques that map well to a SIMD architecture, but limits us to fourth order algebraic surfaces. The general framework could be extended to higher order with numerical root finding.