Skeleton-based Generalized Cylinder Deformation under the Relative Curvature Condition

Abstract

Deformation of a generalized cylinder with a parameterized shape change of its centerline is a non-trivial task when the surface is represented as a high-resolution triangle mesh, particularly when self-intersection and local distortion are to be avoided. We introduce a deformation approach that satisfies these properties based on the skeleton (densely sampled centerline and cross sections) of a generalized cylinder. Our approach uses the relative curvature condition to extract a reasonable centerline for a generalized cylinder whose orthogonal cross sections will not intersect. Given the desired centerline shape as a parametric curve, the displacements on the cross sections are determined while controlling for twisting effects, and under this constraint a vertex-wise displacement field is calculated by minimizing a quadratic surface bending energy. The method is tested on complicated generalized cylindrical objects. In particular, we discuss one application of the method for human colon (large intestine) visualization.