Detecting Critical Regions in Scalar Fields

Abstract

Trivariate data is commonly visualized using isosurfaces or direct volume rendering. When exploring scalar fields by isosurface extraction it is often difficult to choose isovalues that convey "useful" information. The significance of visualizations using direct volume rendering depends on the choice of good transfer functions. Understanding and using isosurface topology can help in identifying "relevant" isovalues for visualization via isosurfaces and can be used to automatically generate transfer functions. Critical isovalues indicate changes in topology of an isosurface: the creation of new surface components, merging of surface components or the formation of holes in a surface component. Interesting isosurface behavior is likely to occur at and around critical isovalues. Current approaches to detect critical isovalues are usually limited to isolated critical points. Data sets often contain regions of constant value (i.e., mesh edges, mesh faces, or entire mesh cells). We present a method that detects critical points, critical regions and corresponding critical isovalues for a scalar field defined by piecewise trilinear interpolation over a uniform rectilinear grid. We describe how to use the resulting list of critical regions/points and associated values to examine trivariate data.