Abstract: Methods of modeling a three-dimensional surface structure include partitioning three-dimensional object data into regions of a Morse complex and generating a feature skeleton having a plurality of smooth edges and a plurality of vertices separating the regions of the Morse complex. Operations are also performed to thicken the feature skeleton by replacing the plurality of smooth edges with corresponding pairs of curves that locate longitudinal boundaries of transitions between primary regions of the feature skeleton. The thickening operations may also include replacing each of the plurality of vertices with a corresponding loop of edges, using setback-type vertex blends.

Abstract: Embodiments automatically generate an accurate network of watertight NURBS patches from polygonal models of objects while automatically detecting and preserving character lines thereon. These embodiments generate from an initial triangulation of the surface, a hierarchy of progressively coarser triangulations of the surface by performing a sequence of edge contractions using a greedy algorithm that selects edge contractions by their numerical properties. Operations are also performed to connect the triangulations in the hierarchy using homeomorphisms that preserve the topology of the initial triangulation in the coarsest triangulation. A desired quadrangulation of the surface can then be generated by homeomorphically mapping edges of a coarsest triangulation in the hierarchy back to the initial triangulation. This quadrangulation is topologically consistent with the initial triangulation and is defined by a plurality of quadrangular patches.