Contouring Curved Quadratic Elements

Wiley, D. F.; Childs, H. R.; Gregorski, B. F.; Hamann, B.; Joy, K. I.

Contouring Curved Quadratic Elements

Files

167-176.pdf (2.63 MB)

Date

2003

Authors

Wiley, D. F.
Childs, H. R.
Gregorski, B. F.
Hamann, B.
Joy, K. I.

Publisher

The Eurographics Association

Abstract

We show how to extract a contour line (or isosurface) from quadratic elements - specifically from quadratic triangles and tetrahedra. We also devise how to transform the resulting contour line (or surface) into a quartic curve (or surface) based on a curved-triangle (curved-tetrahedron) mapping. A contour in a bivariate quadratic function defined over a triangle in parameter space is a conic section and can be represented by a rational-quadratic function, while in physical space it is a rational quartic. An isosurface in the trivariate case is represented as a rational-quadratic patch in parameter space and a rational-quartic patch in physical space. The resulting contour surfaces can be rendered efficiently in hardware.

        @inproceedings{10.2312:VisSym/VisSym03/167-176
,
booktitle = {Eurographics / IEEE VGTC Symposium on Visualization
},
editor = {G.-P. Bonneau and S. Hahmann and C. D. Hansen
},
title = {{Contouring Curved Quadratic Elements
}},
author = {Wiley, D. F. and 
Childs, H. R. and 
Gregorski, B. F. and 
Hamann, B. and 
Joy, K. I.
},
year = {2003
},
publisher = {The Eurographics Association
},
ISSN = {1727-5296
},
ISBN = {3-905673-01-0
},
DOI = {10.2312/VisSym/VisSym03/167-176
}
}