M-reps: Deformable Solid Modeling for Graphics & Simulation, Using Medially-Defined Multifigural Objects

M-reps定义了一种多尺度的图形建模和渲染方法，取代传统的多边形和基于样条曲线的边界表示（B-reps）与实体建模范式的基础上，通过网格的中间图元-硅藻。 每个网格定义了一个突起、一个缩进或一个单独的关联图形，这些图形在有向图中分组以创建完整的对象。 每个硅藻代表一个宽度为r的实心区域的中心，在硅藻的相关表面区域及其与相邻硅藻的连接上定义了宽度比例公差。 因此，一个硅藻网格定义了一个宽度比例公差内的图形边界，并提供了一个宽度比例的数字的内侧表面的采样。这个项目将进行四个主要领域的研究，以开发和展示的潜力M-reps：1.增强当前的建模工具和技术，将图形层次结构，CSG风格的布尔结构，边界公差和宽度比例纳入建模过程;2.添加专门的硅藻用于在M-rep模型中创建尖锐的边缘、拐角和折痕;3.实现一个新的渲染系统，该系统将隐式表面渲染与基于比例的模型相结合，以提供基于图像比例的自动简化;以及4.探索将边界位移和图像纹理映射到中间隐含表面的技术。

M-reps define a multiscale approach to graphics modeling and rendering, replacing traditional polygonal and spline-based boundary representations (B-reps) with a solid modeling paradigm based on medial representation by meshes of medial primitives----diatoms. Each mesh defines a protrusion, an indentation, or a separate associated figure, and these figures are grouped in directed graphs to create complete objects. Each diatom represents the center of a solid region of width r, with a width-proportional tolerance defined on the diatom's associated surface regions and on its links to neighboring diatoms. Thus, a diatom mesh defines the figural boundary to within a width-proportional tolerance, and provides a width-proportional sampling of the figure's medial surface.This project will undertake four main areas of research to develop and demonstrate the potential of M-reps:1. augmenting current modeling tools and techniques to incorporate figural hierarchies, CSG-style boolean construction, boundary tolerances and width-proportionality into the modeling process;2. adding specialized diatoms for creating sharp edges, corners, and creases in M-rep models;3. implementing a new rendering system which combines implicit surface rendering with scale-based models to provide automatic simplification based on image-scale; and4. exploring techniques for mapping boundary displacements and image textures to the medially implied surface.