Lattice Lighting

本研究涉及一种用于计算和渲染的创新晶格，称为六边形封闭填充（HCP）晶格，用于各种3D和4D波现象模拟，如照明，声学和断层扫描。HCP晶格用于跟踪反射、折射和散射的光子，用于渲染参与介质、次表面散射和计算机图形学中的其他全局照明效果。它可以对波前进行跟踪，模拟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等目前在图形中无法实现的光学效应。它还可以扩展到追踪光和电磁波以外的其他种类的波，如声音和超声波。HCP晶格对这些应用和其他各种应用（如粒子物理）具有广泛影响的潜力。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现象。与笛卡尔格和其他格相比，它具有独特的优势，包括：(1)HCP格提供了三维和四维连续函数的最佳采样。在三维中，它只需要29.3%的笛卡尔晶格样本；然而，它们的分布是最均匀的。HCP/HCP对在频率和空间（或时空）共域中都是最优的。(2)由于其站点有12个最近邻，因此在角离散化方面提供了更好的精度。(3)三维HCP晶格的任意两个相邻体素共享一个二维菱形面；因此，邻域连通性没有歧义，极大地简化了物体体素化。(4)站点链接径向对称，相邻两个站点之间的所有距离相同。这使得简单的径向滤波器和精确的插值。(5)支持灵活、分层、自适应的HCP格。(6)计算在图形处理器（GPU）和GPU集群上加速良好，可以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.