Abstract We introduce a novel mid‐structure called the generalized swept mid‐structure (GSM) of a closed polygonal shape, and a framework to compute it. The GSM contains both curve and surface elements and has consistent sheet‐by‐sheet topology, versus triangle‐by‐triangle topology produced by other mid‐structure methods. To obtain this structure, a harmonic function, defined on the volume that is enclosed by the surface, is used to decompose the volume into a set of slices. A technique for computing the 1D mid‐structures of these slices is introduced. The mid‐structures of adjacent slices are then iteratively matched through a boundary similarity computation and triangulated to form the GSM. This structure respects the topology of the input surface model is a hybrid mid‐structure representation. The construction and topology of the GSM allows for local and global simplification, used in further applications such as parameterization, volumetric mesh generation and medical applications.

Ridges are extremal curves of principal curvatures on a surface that indicate salient intrinsic features of its shape. This paper presents a novel approach for extracting ridges of improved quality from isosurfaces of volumetric scalar-valued grids by converting them to implicit trivariate B-spline representations. A robust tracing approach demonstrated to extract ridges accurately from parametric B-spline surfaces is extended to extract ridges directly from the implicit representations resulting in accurate and hence smoother, connected ridge curves as compared to approaches that extract ridges directly from discrete representations. This approach can also be used to extract ridges directly from smooth representations such as isosurfaces of volumetric B-Spline CAD models and algebraic functions, and extended to extract ridges from polygonal meshes, as demonstrated in the paper. Most of the existing approaches for ridge extraction address only crests, a certain subset of the ridges on a surface. The approach presented in this paper enables extraction of all types of generic ridges on a surface thereby presenting a complete solution.

Ridges are characteristic curves of a surface that mark salient intrinsic features of its shape and are therefore valuable for shape matching, surface quality control, visualization and various other applications. Ridges are loci of points on a surface where either of the principal curvatures attain a critical value in its respective principal direction. These curves have complex behavior near umbilics on a surface, and may also pass through certain turning points causing added complexity for ridge computation. We present a new algorithm for numerically tracing ridges on B-Spline surfaces that also accurately captures ridge behavior at umbilics and ridge turning points. The algorithm traverses ridge segments by detecting ridge points while advancing and sliding in principal directions on a surface in a novel manner, thereby computing connected curves of ridge points. The output of the algorithm is a set of curve segments, some or all of which, may be selected for other applications such as those mentioned above. The results of our technique are validated by comparison with results from previous research and with a brute-force domain sampling technique.