Repairing and meshing imperfect shapes with Delaunay refinement

Abstract

As a direct consequence of software quirks, designer errors, and representation flaws, often three-dimensional shapes are stored in formats that introduce inconsistencies such as small gaps and overlaps between surface patches. We present a new algorithm that simultaneously repairs imperfect geometry and topology while generating Delaunay meshes of these shapes. At the core of this approach is a meshing algorithm for input shapes that are piecewise smooth complexes (PSCs), a collection of smooth surface patches meeting at curves non-smoothly or in non-manifold configurations. Guided by a user tolerance parameter, we automatically merge nearby components while building a Delaunay mesh that has many of these errors fixed. Experimental evidence is provided to show the results of our algorithm on common computer-aided design (CAD) formats. Our algorithm may also be used to simplify shapes by removing small features which would require an excessive number of elements to preserve them in the output mesh.

A tool for ship hull surface healing and domain preparation for downstream applications

“…Therefore, geometric data models that have been created by mesh generation software or imported from external CAD systems have to satisfy quality constraints which usually impede automatic mesh generation (Wang et al, 2007). The quality constraints required by mesh generators usually include globally continues (C 0 continuity) and consistent representation of geometric models (Busaryev et al, 2009;Butlin and Stops, 1996). Therefore it is necessary to adapt/repair the geometrical entities by changing their mathematical description while maintaining the same geometrical shape (Wang et al, 2007).…”

“…Many algorithms developed to clean geometric inconsistencies were tolerance driven and require user's interaction which takes significant time. Busaryev et al (2009) develop an algorithm that simultaneously repairs imperfect geometry and topology while generating Delaunay meshes. They were able to fix many errors in their user input tolerance driven algorithm.…”

“…These boundaries are often represented as composite parametric surfaces, or employ a discrete representation in terms of triangular facets. Ideally the CAD software generates at least watertight (C 0 continuity) which is then stored in a format that maintains both a geometric description of each patch as well as topological connectivity between patches (Busaryev et al, 2009). In addition to generating and storing geometrical and topological data, the capability of exchanging information with other systems in a large range of formats is also one the most important requirement for CAD system.…”

3D Anatomical Shape Atlas Construction Using Mesh Quality Preserved Deformable Models

“…Though pre-processing techniques using mesh smoothing methods such as [2,24,25] can alleviate the problem to some degree, it is still highly possible that the mesh is degenerate during shape deformation. Thus it is desirable to design a unified framework to consider shape deformation and mesh quality simultaneously.…”

A BREP Model and Mesh Errors Detecting Tool: TopoVisu

“…Busaryev, Dey and Levine [2] present an algorithm based on the merging of areas with small defects (gaps, overlaps, and intersections) through protecting balls, directly on the BREP model, and then to mesh the model using these protecting balls. But with this method, there is a risk to have similar problems to the approach using only tolerances to close a BREP model.…”