Volume Synthesis Theory and Algorithms

这个项目涉及体积合成，它的理论框架，它的基本体素化算法，从它们的几何描述合成体积(基于体素的)对象，以及它的离散渲染算法，用于可视化这些对象。本研究的三个主要目标是：(1)研究3D离散拓扑学中的体素化和离散绘制算法的理论框架，以保证在连通性、厚度、可分离性、最小化、覆盖和精度方面生成行为良好的离散表示；(2)开发和实现高效的3D直线、3D圆、曲面和实体的体素化算法，使用各种连通性、厚度和空间占有率，特别关注二进制和非二进制(模糊)体素化；以及(3)开发和实现离散算法，所述离散算法利用体积缓冲器的离散表示，使用诸如体积光线跟踪和基于模板的投影等方法来快速观看场景。

This project deals with volume synthesis, its theoretical framework, its underlying voxelization algorithms for synthesizing volumetric (voxel-based) objects from their geometric description, and its discrete rendering algorithms for visualizing these objects. The three main objectives of this research are: (1) to study the theoretical framework in 3D discrete topology for the voxelization and discrete rendering algorithms in order to guarantee the generation of a `well-behaved` discrete representation in terms of connectivity, thickness, separability, minimization, coverage, and accuracy; (2) to develop and implement efficient voxelization algorithms for 3D lines, 3D circles, surfaces, and solids, using a variety of connectivities, thicknesses, and spatial occupancies, with a specific focus on both binary and non- binary (`fuzzy`) voxelization; and (3) to develop and implement discrete algorithms that capitalize on the discrete representation of the volume buffer for fast viewing of the scene, using approaches such as volumetric ray tracing and template-based projection.