Real-time ray casting of algebraic B-spline surfaces
Real-time ray casting of algebraic B-spline surfaces
复制标题
代数 B 样条曲面的实时光线投射
DOI：
10.1016/j.cag.2011.04.002
复制
发表时间：
2011-08-01
影响因子：
2.5
通讯作者：
Feng, Jieqing
中科院分区：
文献类型：
--
作者：
Wei, Feifei;Feng, Jieqing
分片代数B样条曲面（ABS曲面）能够对任意拓扑结构的全局光滑形状进行建模。这些曲面有可能应用于几何建模、科学可视化、计算机动画和数学图示等领域。然而，由于需要对非线性多项式系统进行大量的数值求根运算，对该曲面进行实时光线投射对于交互式应用来说仍然是一个障碍。在本文中，我们提出了一种基于GPU的ABS曲面实时光线投射方法。为了利用当代GPU强大的并行计算能力，我们采用迭代数值求根算法，例如牛顿 - 拉夫森算法和试位法算法，而非递归算法。为了促进牛顿 - 拉夫森算法或试位法算法的收敛，它们的初始猜测值是通过对同构等值面进行光栅化来确定的，并且该等值面是基于曲面区域细分的常规准则生成的。同时，采用极面来识别单根或分离不同的根，即光线与曲面的交点。作为一个重要的几何特征，轮廓曲线被精确计算到浮点精度，可应用于进一步的抗锯齿处理过程。实验结果表明，所提出的方法能够实时渲染数千个6 - 9次的分片代数曲面片。（C）2011爱思唯尔有限公司。保留所有权利。
Piecewise algebraic B-spline surfaces (ABS surfaces) are capable of modeling globally smooth shapes of arbitrary topology. These can be potentially applied in geometric modeling, scientific visualization, computer animation and mathematical illustration. However, real-time ray casting the surface is still an obstacle for interactive applications, due to the large amount of numerical root findings of nonlinear polynomial systems that are required. In this paper, we present a GPU-based real-time ray casting method for ABS surfaces. To explore the powerful parallel computing capacity of contemporary GPUs, we adopt iterative numerical root-finding algorithms, e.g., the Newton-Raphson and regula falsi algorithms, rather than recursive ones. To facilitate convergence of the Newton-Raphson or regula falsi algorithm, their initial guesses are determined through rasterization of the isotopic isosurface, and the isosurface is generated based on regular criteria for surface domain subdivision. Meanwhile, polar surfaces are adopted to identify single roots or to isolate different roots, i.e., ray and surface intersections. As an important geometric feature, the silhouette curve is elaborately computed to floating-point accuracy, which can be applied in further anti-aliasing processes. The experimental results show that the proposed method can render thousands of piecewise algebraic surface patches of degrees 6-9 in real time. (C) 2011 Elsevier Ltd. All rights reserved.