Lattice Lighting

这项研究涉及一种用于计算和渲染的创新晶格，称为六方密堆积（HCP）晶格，用于各种3D和4D波动现象模拟，如照明，声学和断层扫描。HCP晶格用于追踪光子的反射、折射和散射，以在计算机图形中渲染参与介质、次表面散射和其他全局照明效果。它可以跟踪波前，以模拟目前图形中无法实现的光学效应，例如非均匀介质中的连续折射，复杂物体中的衍射，光波的干涉和多普勒效应。 它还可以扩展到跟踪除光和电磁波之外的其他类型的波，例如声音和超声波。HCP晶格对这些应用和各种其他应用具有广泛的影响，例如在粒子物理学中，HCP晶格跟踪并与各种小粒子相互作用，使其能够模拟许多波动现象。它比笛卡尔格和其他格具有独特的优点，包括：（1）HCP格提供了3D和4D中连续函数的最佳采样。在3D中，它只需要29.3%的笛卡尔晶格样本;然而，它最均匀地分布它们。HCP/HCP对在频率和空间（或时空）共域都是最优的。(2)它提供了更好的角度离散化精度，因为它的网站有12个最近的邻居。(3)3D HCP晶格的任何两个相邻体素共享2D菱形面;因此，在相邻连接中没有模糊性，大大简化了对象体素化。(4)站点链接是径向对称的，并且两个相邻站点之间的所有距离都相同。这使得简单的径向滤波器和精确的插值。(5)它支持灵活的，分层的和自适应的HCP晶格。(6)计算在图形处理单元（GPU）和GPU集群上加速良好，同时跟踪数千个粒子。

This research involves an innovative lattice for computation and rendering, called hexagonal closed packing (HCP) lattice, for a variety of 3D and 4D wave phenomena simulations, such as lighting, acoustics and tomography. The HCP lattice is used to trace photons reflected, refracted and scattered for rendering participating media, subsurface scattering, and other global illumination effects in computer graphics. It can trace the wavefront for simulating optical effects currently unavailable in graphics, such as continuous refraction in inhomogeneous media, diffraction in complex objects, interference of light waves, and Doppler effects. It can also be extended to trace other kinds of waves besides light and electromagnetic waves, such as sound and ultrasound. The HCP lattice has the potential for a broad impact on these applications and a variety of other applications, such as in particle physics.The HCP lattice traces and interacts with a variety of small particles, enabling it to simulate many wave phenomena. It has unique advantages over Cartesian and other lattices, including: (1) The HCP lattice provides optimal sampling of a continuous function in 3D and 4D. In 3D, it requires only 29.3% of Cartesian lattice samples; yet, it distributes them most uniformly. The HCP/HCP pair is optimal in both frequency and space (or spacetime) co-domains. (2) It provides better accuracy in angular discretization, since its sites have 12 nearest neighbors. (3) Any two neighboring voxels of a 3D HCP lattice share a 2D rhombic face; thus, there is no ambiguity in neighbor-connectivity, greatly simplifing object voxelization. (4) The site links are radially symmetric, and all distances between two neighboring sites are identical. This makes simple radial filters and accurate interpolation. (5) Its supports flexible, hierarchical and adaptive HCP lattices. (6) The computations accelerate well on graphics processing units (GPUs) and GPU clusters, tracing thousands of particles simultaneously.