Connectivity editing for quadrilateral meshes

Abstract

Figure 1: We introduce connectivity editing operations to control irregular vertices in quadrilateral meshes. This can lead to improved results in the design of a glass structure: (a) top: the original mesh with irregular vertices as colored dots, (a) bottom: a stripe pattern applied to the mesh, (b) a rendering of the design as glass construction. In (c) and (d) we show the edited mesh. The glass panels on the roof are generated from the edges in the meshes. AbstractWe propose new connectivity editing operations for quadrilateral meshes with the unique ability to explicitly control the location, orientation, type, and number of the irregular vertices (valence not equal to four) in the mesh while preserving sharp edges. We provide theoretical analysis on what editing operations are possible and impossible and introduce three fundamental operations to move and re-orient a pair of irregular vertices. We argue that our editing operations are fundamental, because they only change the quad mesh in the smallest possible region and involve the fewest irregular vertices (i.e., two). The irregular vertex movement operations are supplemented by operations for the splitting, merging, canceling, and aligning of irregular vertices. We explain how the proposed highlevel operations are realized through graph-level editing operations such as quad collapses, edge flips, and edge splits. The utility of these mesh editing operations are demonstrated by improving the connectivity of quad meshes generated from state-of-art quadrangulation techniques.

Modeling Polyhedral Meshes with Affine Maps

“…When mesh elements become too strained, the need to remesh restarts the computation. A shape space which is either insensitive of the meshing, or easy to re-adjust, for instance by connectiv-ity editing [PZK+11], is still an open problem. As we have discussed before, it would be interesting to see if properties like concyclity, or conicality, can be totally accommodated using other types of linear spaces as well.…”