Contour trees and small seed sets for isosurface traversal
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
The visualization toolkit (2nd ed.): an object-oriented approach to 3D graphics
The visualization toolkit (2nd ed.): an object-oriented approach to 3D graphics
A simple recursive tessellator for adaptive surface triangulation
Journal of Graphics Tools
A High Accuracy Volume Renderer for Unstructured Data
IEEE Transactions on Visualization and Computer Graphics
The Application Visualization System: A Computational Environment for Scientific Visualization
IEEE Computer Graphics and Applications
Compatible Triangulations of Spatial Decompositions
VIS '04 Proceedings of the conference on Visualization '04
Ray-Tracing Polymorphic Multidomain Spectral/hp Elements for Isosurface Rendering
IEEE Transactions on Visualization and Computer Graphics
Embarrassingly parallel mesh refinement by edge subdivision
Engineering with Computers
Triangulating point set surfaces with bounded error
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Computational 3D ultrasound volumetric rendering; an object oriented open-sources approach
ACS'11 Proceedings of the 11th WSEAS international conference on Applied computer science
Efficient parallel vectors feature extraction from higher-order data
EuroVis'11 Proceedings of the 13th Eurographics / IEEE - VGTC conference on Visualization
Hi-index | 0.00 |
The finite element method is an important, widely used numerical technique for solving partial differential equations. This technique utilizes basis functions for approximating the geometry and the variation of the solution field over finite regions, or elements, of the domain. These basis functions are generally formed by combinations of polynomials. In the past, the polynomial order of the basis has been low—typically of linear and quadratic order. However, in recent years so-called p and hp methods have been developed, which may elevate the order of the basis to arbitrary levels with the aim of accelerating the convergence of the numerical solution. The increasing complexity of numerical basis functions poses a significant challenge to visualization systems. In the past, such systems have been loosely coupled to simulation packages, exchanging data via file transfer, and internally reimplementing the basis functions in order to perform interpolation and implement visualization algorithms. However, as the basis functions become more complex and, in some cases, proprietary in nature, it becomes increasingly difficult if not impossible to reimplement them within the visualization system. Further, most visualization systems typically process linear primitives, in part to take advantage of graphics hardware and, in part, due to the inherent simplicity of the resulting algorithms. Thus, visualization of higher-order finite elements requires tessellating the basis to produce data compatible with existing visualization systems. In this paper, we describe adaptive methods that automatically tessellate complex finite element basis functions using a flexible and extensible software framework. These methods employ a recursive, edge-based subdivision algorithm driven by a set of error metrics including geometric error, solution error, and error in image space. Further, we describe advanced pretessellation techniques that guarantees capture of the critical points of the polynomial basis. The framework has been designed using the adaptor design pattern, meaning that the visualization system need not reimplement basis functions, rather it communicates with the simulation package via simple programmatic queries. We demonstrate our method on several examples, and have implemented the framework in the open-source visualization system VTK.