Particle Systems for Efficient and Accurate High-Order Finite Element Visualization
Particle Systems for Efficient and Accurate High-Order Finite Element Visualization
复制标题
用于高效、准确的高阶有限元可视化的粒子系统
DOI：
10.1109/tvcg.2007.1048
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发表时间：
2007
影响因子：
5.2
通讯作者：
R. Whitaker
中科院分区：
文献类型：
--
作者：
Miriah D. Meyer;B. Nelson;R. Kirby;R. Whitaker
可视化已经成为仿真管道的一个重要组成部分，为科学家和工程师提供了他们模型的视觉直觉。然而，利用高阶有限元方法进行空间细分的模拟对传统的等值面可视化技术提出了挑战。高阶有限元等值面通常由参考空间中的基函数定义，通过坐标变换得到世界空间解，而该解不一定具有闭型逆。因此，像行进立方体和光线追踪这样的世界空间等值面呈现方法必须执行嵌套的根查找，这在计算上是昂贵的。因此，我们建议用粒子系统来可视化这些等值面。我们提出了一个框架，允许粒子在参考空间中采样等值面，避免了在评估基函数时从世界空间中进行昂贵的位置逆映射。粒子在参考空间等值面上的分布由来自世界空间等值面的几何信息控制，如曲面梯度和曲率。得到的粒子分布可以均匀分布，也可以适应世界空间表面特征。这为这些具有挑战性的数据集提供了紧凑、高效和准确的等值面表示。
Visualization has become an important component of the simulation pipeline, providing scientists and engineers a visual intuition of their models. Simulations that make use of the high-order finite element method for spatial subdivision, however, present a challenge to conventional isosurface visualization techniques. High-order finite element isosurfaces are often defined by basis functions in reference space, which give rise to a world-space solution through a coordinate transformation, which does not necessarily have a closed-form inverse. Therefore, world-space isosurface rendering methods such as marching cubes and ray tracing must perform a nested root finding, which is computationally expensive. We thus propose visualizing these isosurfaces with a particle system. We present a framework that allows particles to sample an isosurface in reference space, avoiding the costly inverse mapping of positions from world space when evaluating the basis functions. The distribution of particles across the reference space isosurface is controlled by geometric information from the world-space isosurface such as the surface gradient and curvature. The resulting particle distributions can be distributed evenly or adapted to accommodate world-space surface features. This provides compact, efficient, and accurate isosurface representations of these challenging data sets.