Deformable Solid Modeling via Medial Sampling and Displacement Subdivision

Discrete m-reps use tolerance-based, sampled medial skeleta as an underlying framework for boundaries defined by displaced subdivision surfaces. They provide local and global shape information, combining the strengths of multiscale skeletal modeling with the multi-resolution, deformation and shading properties afforded by subdivision surfaces. Hierarchically linked medial figures allow figural, object-based deformation, and their stability of object representation with respect to boundary perturbation shows advantages of tolerance-based medial representations over Blum axis and Voronoi-based skeletal models. M-rep models provide new approaches to traditional computer graphics modeling, to physically based modeling and simulation, and to image-analysis, segmentation and display, by combining local and object-level deformability and by explicitly including object-scale, tolerance and hierarchical level-of-detail. Sampled medial representations combine the solid modeling capabilities of constructive solid geometry with the flexibility of traditional b-reps, to which they add multiscale medial and boundary deformations parameterized by an object-based coordinate system. This thesis research encompassed conceptual development on discrete m-reps and their implementation for MIDAG (the Medical Image Display and Analysis Group) at UNC-Chapel Hill. Prototype and application code was created to support the following: medial atoms in 3D that included a quaternion frame to establish a local coordinate system; data structures for medial mesh topologies; a new algorithm for interpolating Catmull-Clark subdivision surfaces for m-rep boundaries; a medially based coordinate system parameterizing the m-rep boundary, interior, and local exterior; displacement texturing and displacement meshing of m-rep boundaries; methods of medially based deformation; figure/subfigure blending by implicit surface methods or (with Qiong Han) using remeshing of subdivision boundaries; and C++ code libraries for m-rep modeling in geometric design and image-segmentation applications.