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Adaptive Composite B-Spline Grid Generation for Interactive 3D Visualizations

Published

Author(s)

Bonita V. Saunders, Qiming Wang, Brian Antonishek

Abstract

We describe an adaptive grid generation technique based on the composition of tensor product B-spline mappings, T and Phi, where Phi maps the unit square onto itself and T maps the unit square onto the desired physical domain. Variational methods are used to adjust the T and Phi coefficients to move grid points on the physical domain in response to adaptive criteria. The introduction of Phi makes it possible to move boundary points without disturbing the accuracy of the boundary approximation. The effectiveness of the method on both convex and nonconvex domains suggests it can be used for a variety of 2D applications, but our immediate goal is to develop computational grids for the rendering of complex mathematical function surfaces on the web.
Proceedings Title
IMACS Series in Computational and Applied Mathematics (Special Volume)
Volume
18
Conference Dates
October 22-26, 2012
Conference Location
Las Palmas de Gran Canaria, -1
Conference Title
MASCOT12/ISGG2012(International IMACS Workshop and Bi-annual International Society for Grid Generation
Conference)

Keywords

Adaptive grid generation, Tensor product B-splines, 3D visualization
Created January 22, 2014, Updated February 19, 2017