In graphics and animation applications, two of the problems are: (1) representation of an analytic curve by a discrete set of sampled points and (2) determining the similarity between two parametric curves. It is necessary to measure the accuracy of approximation and to have a metric to calculate the disparity between two parametric curves. Both of these problems have been associated with the reparameterization of the curves with respect to arc length. One of the methods uses Gaussian Quadrature to determine the arc length parameterization [Guenter and Parent 1990], while another interesting technique is a simple approximation method [Fritsch and Nielson 1990]. There are various ways to compute the similarity between two curves. For 2D Cartesian curves, max norm yields a satisfactory distance metric. For parametric curves, Euclidean norm is frequently used. Arc length is reasonable parameterization, but explicit arc length parameterization is not easy to compute for arbitrary parametric curves. We give a new technique for discretizing parametric curves. These sampled points can be used to approximate curves, determine arc length parameterization, and similarity between them. This technique is accurate, robust and simpler to implement. Comparisons of the previous methods with the new one is presented.
C. Sabharwal, "An Intelligent Approach To Discrete Sampling Of Parametric Curves," Proceedings of the ACM Symposium on Applied Computing, pp. 397 - 401, Association for Computing Machinery (ACM), Mar 1993.
The definitive version is available at https://doi.org/10.1145/162754.162947
Article - Conference proceedings
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01 Mar 1993