Approximating Material Interfaces During Data Simplification
We present a new method for simplifying large data sets that contain material interfaces. Material interfaces embedded in the meshes of computational data sets are often a source of error for simplification algorithms because they represent discontinuities in the scalar or vector fields over a cell. By representing material interfaces explicitly in a data simplification process, we are able to provide separate field representations for each material over a single cell and, thus, to represent the fields much more accurately. Our algorithm uses a multiresolution tetrahedral mesh supporting fast coarsening and refinement capabilities and error bounds for feature preservation. We represent a material interface or other surface of discontinuity as the zero set of a signed distance function. This representation makes it possible to maintain continuity of the surface across cell boundaries. It also makes it possible to represent more complex interface structures within a cell, such as T-intersections. Within a cell, a field is represented on either side of the surface of discontinuity by separate linear functions. These functions are determined by true and ''ghost'' values of the field at the vertices of the cell. By requiring that each vertex have only one ghost value for a given field and material, we are able to avoid introducing spurious discontinuities in the fields at cell boundaries. The use of linear functions determined by ghost values makes it unnecessary to divide the original cells in the mesh along the surface of discontinuity, avoiding the resultant introduction of complex cell types and field representations. It also decouples the field representation from the representation of the surface of discontinuity, making it easier to represent fields when the material interfaces are more complex. Both the signed distance function that defines the surface of discontinuity and the ghost values that determine the field representations are handled very simply during refinement and coarsening of the mesh ensuring that all spurious discontinuities can be avoided with a minimum of computation and programming effort. We have applied our algorithm to simplification of a test problem from a well known fluid dynamics code with excellent results. Graphical and numerical results are presented. Furthermore, our multiresolution representation can be applied to other kinds of surfaces, e.g. isosurfaces.
- Research Organization:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- W-7405-ENG-48
- OSTI ID:
- 15013473
- Report Number(s):
- UCRL-JC-145747; TRN: US200601%%477
- Resource Relation:
- Conference: NSF/DOE Lake Tahoe Workshop on Hierarchical Approximation and Geometrical Methods for Scientific Visualization, Tahoe City, CA, Oct 15 - Oct 17, 2000
- Country of Publication:
- United States
- Language:
- English
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