Approximate implicitization of planar curves by piecewise rational approximation of the distance function

We present an approximate implicitization method for planar curves. The computed implicit representation is a piecewise rational approximation of the distance function to the given parametric curve. The proposed method consists of four main steps: quadratic B–spline approximation of the given parametric curve, data reduction, segments–wise implicitization, multiplying with suitable polynomial factors. These segments are joined such that the collection generate a global Cr spline function which

• Type: Journal
• Year: 2007
• Where: AAECC
• Authors: Mohamed Shalaby, Bert Jüttler, Josef Schicho
• Keywords: AAECC 2007, Algorithms, Approximate Implicitization Method, Computed Implicit Representation, Parametric Curve