Diamond-based Models for Scientific Visualization Summary of Research

Mathematical and scientific computing problems are often approached using a divide and conquer paradigm in which a large problem domain is solved by combining results from smaller subdomains. In this very broad context, we focus on nested spatial decompositions of regularly sampled domains obtained by the regular simplex bisection scheme. Specifically, we utilize clusters of such simplices, referred to as diamonds, that must be refined concurrently to guarantee crack-free domain decompositions. This work investigates several diamond-based models for scientific visualization. First, we generalize the notion of diamonds from 2D and 3D to arbitrary dimension, and propose an implicit encoding for all geometric and hierarchical relationships. Second, we propose the supercube as a high-level primitive for diamond hierarchies. We use supercubes to compactly encode incomplete scalar fields as well as adaptive simplicial meshes extracted from the hierarchy. Finally, we introduce isodiamond hierarchies, a general framework for spatial access structures on a hierarchy of diamonds that decouples the implicit relationships of the hierarchy from the underlying scalar field.