Contouring Curved Quadratic Elements

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Date
2003
Journal Title
Journal ISSN
Volume Title
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.
Description

        
@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
} }
Citation