Jacobi Fiber Surfaces for Bivariate Reeb Space Computation

摘要: This paper presents an efficient algorithm for the computation of Reeb space input bivariate piecewise linear scalar function f defined on a tetrahedral mesh. By extending and generalizing algorithmic concepts from univariate case to one, we report first practical, output-sensitive exact such space. The starts by identifying Jacobi set , analogs critical points in case. Next, is computed segmenting mesh along new notion Fiber Surfaces, analog contours We additionally present simplification heuristic that enables progressive coarsening Our simple implement most its computations can be trivially parallelized. performance numbers demonstrating orders magnitude speedups over previous approaches, enabling time tractable spaces practice. Moreover, unlike range-based quantization approaches (such as Joint Contour Net), our parameter-free. demonstrate utility approach using semi-automatic segmentation tool data. In particular, introduce continuous scatterplot peeling, technique which reduction cluttering scatterplot, interactively selecting features project. provide VTK-based C++ implementation used reproduction purposes or development based visualization techniques.