Fast Fiber Surface and Fiber Line Extraction for Bivariate Scalar Fields using Dual Bounding Volume Hierarchy Traversal

Fiber surfaces and fiber lines, being the preimages of a bivariate function to a so-called control polygon in the function’s range, are the adaptation of isosurfaces and isolines to bivariate scalar fields. Previous works have proposed use cases for fiber surface and fiber line extraction using algorithmically generated control polygons with many line segments, but their authors have either not presented results or noted that the computation becomes prohibitive slow. We present an algorithm that speeds up fiber surface extraction by using dual bounding volume hierarchy (BVH) traversal, as well as a variation that combines the benefits of single and dual BVH traversal. We study the influence of the number of line segments in the control polygon on the performance of single and dual BVH traversal algorithms using data sets from various application domains and types of control polygons. We find that dual BVH traversal is several times faster in test cases where single BVH traversal is slow, facilitating the interactive exploration of fiber surfaces in many cases where existing methods are too slow.