Contouring Curved Quadratic Elements

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. Categories and Subject Descriptors (according to ACM CCS): I.4.10 [Image Representation]: Volumetric I.3.5 [Computational Geometry and Object Modeling]: Curve, surface, solid, and object representations

• Type: Conference
• Year: 2003
• Where: VISSYM
• Authors: David F. Wiley, Henry R. Childs, Benjamin F. Gregorski, Bernd Hamann, Kenneth I. Joy
• Keywords: Contour, Contour Line, Parameter Space, VISSYM 2003, Visualization