Contouring curved quadratic elements
David F. Wiley, Henry R. Childs, Benjamin F. Gregorski, Bernd Hamann, Kenneth I. Joy · eScholarship (California Digital Library) · 2003
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.