Unstructured tetrahedral mesh quality analysis using an interactive haptic and visual interface

Abstract.

The problem of interactively probing a mesh to determine its quality is described for three-dimensional unstructured tetrahedral meshes. Mesh quality as a function of individual element error is defined for a specific class of problems. The importance of analyzing mesh quality within a geometrical representation of the mesh is discussed. The problems encountered when attempting to visualize the geometric and error information for a visually complex mesh are identified and used to motivate a design for an interactive user interface for mesh quality analysis. The primary intended user of such a system is one who is interested in per-element mesh quality, such as the developer of mesh generating software or the persons charged with generating a good quality mesh for a specific problem; however, it may also be used by end users of meshes to see the main problem areas of the mesh and to compare various available meshing strategies. The interface provides the user with necessary information about element quality in a form which allows the user to isolate “bad” mesh elements and analyze the individual contributions of element shape, orientation, geometric neighborhood, and solution behavior. The availability of this information when combined with a haptic device allows the user to easily identify poor quality mesh regions. A prototype implementation of the interface was constructed and used to examine two meshes in detail. This was done in part reflexively, to determine the feasibility of this approach to mesh quality analysis. It was also done in the interests of our larger goals, to try to determine the main contributers to poor element quality in the two meshes. User analysis of the problem meshes is presented along with visual output from the interface. A formal user study was not performed; however, informal results and timings are used to show the speed and effectiveness of the interface.