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

Principal Investigator: Stephen M. Pizer
Funding Agency: National Science Foundation
Agency Number: CCR-9910419

Abstract
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:

• augmenting current modeling tools and techniques to incorporate figural hierarchies, CSG-style boolean construction, boundary tolerances and width- proportionality into the modeling process;
• adding specialized diatoms for creating sharp edges, comers, and creases in M-rep models;
• implementing a new rendering system which combines implicit surface rendering with scale-based models to provide automatic simplification based on image-scale; and
• exploring techniques for mapping boundary displacements and image textures to the medially implied surfaces.

M-rep models will provide superior approaches to traditional computer graphics modeling and rendering, to physically-based modeling and simulation, and to image-analysis and display, by combining local and object-level deformability and by explicitly including object-scale, tolerance, and hierarchical level-of- detail in both modeling and rendering. M-reps combine the solid modeling capabilities of constructive solid geometry with the flexibility of traditional B-reps and include features and advantages found in neither.