Wiley, D. F.Childs, H. R.Gregorski, B. F.Hamann, B.Joy, K. I.G.-P. Bonneau and S. Hahmann and C. D. Hansen2014-01-302014-01-3020033-905673-01-01727-5296https://doi.org/10.2312/VisSym/VisSym03/167-176We 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.