Explicit Adaptive Tessellation based on re-parametrization on Graphics Hardware

We propose to use an explicit function for adaptive tessellation of parametric curves and surfaces. This function behaves as a new parametrization from the surface domain (or curve domain) to the domain itself; it is build using information about derivatives and curvature: a fixed tessellation may be re-arranged in an adaptive tessellation, which takes care of those parts of the curve or surface which need to be tessellated more and those which may use a poorer tessellation. We show how to produce and how to use the kernel function with four example: a simple cubic curve, a spline curve, a cubic bezièr triangle and a cubic quadrilateral patch. For every example, we compare the fixed tessellation with the adaptive one: the number of vertexes used is always the same, but the points are re-arranged in a better way. At the end we show how to use commonly known forward differencing methods to evaluate both the explicit parametrization and the curve or surface; we also show how simply this method may be implemented on common graphics cards.