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Table of contents

Bezier techniques. Interpolation and approximation. Bspline representation.

Mathematics and Visualization

Bezier and Bspline representations. Bspline techniques.

Cubic splines (Bezier curves) using linear algebra - Wild Linear Algebra 24 - NJ Wildberger

Uniform subdivision. Tensor product surfaces.

ISBN 13: 9783642078422

Constructing smooth surfaces. Stationary subdivision for regular nets. Stationary subdivision for arbitrary nets. Multivariate splines.

Metadata Show full item record. In this paper we extend this concept also for visualization.

Post-processing and visualization techniques for isogeometric analysis results

The presented post-processing and visualization techniques thereby strengthen the relation between geometry, analysis and visualization. This is achieved by facilitating the same mathematical function space used for geometry and analysis also for post-processing and visualization purposes. During non-linear analysis derivatives are incrementally computed and stored with different basis function representations.

We introduce and investigate projection methods to be able to use the same function space for both displacements and stresses without loss of accuracy. The typically used unrelated fictitious finite element mesh representation for visualization purposes are easily replaced without changing the underlying geometry as well as the algorithmic data structure.

CAD/CAM Machine Drawing and Computer Graphics 3(1+2)

In this paper we have developed and investigated an accurate, efficient and practical post-processing pipeline for visualization of isogeometric analysis results. We have tested four different projection methods. Furthermore, the use of GPU shader programming to enable efficient and pixel-accurate visualization is detailed.

The performance of the four different projection techniques has been tested on manufactured problems as well as on realistic benchmark problems.