Volume Synthesis Theory and Algorithms

该项目涉及体合成，它的理论框架，它的底层体素化算法，用于从几何描述中合成体积（基于体素的）对象，以及用于可视化这些对象的离散渲染算法。本研究的三个主要目标是：(1)研究三维离散拓扑中体素化和离散渲染算法的理论框架，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)使用各种连通性，厚度和空间占用，开发和实施3D线，3D圆，曲面和固体的有效体素化算法，特别关注二进制和非二进制（“模糊”）体素化；(3)开发和实施离散算法，利用体积缓冲的离散表示来快速查看场景，使用诸如体积光线追踪和基于模板的投影等方法。

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.