Geometric modeling
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Motion Control: Computing the Arc Length of Parametric Curves
IEEE Computer Graphics and Applications
Point-based methods for estimating the length of a parametric curve
Journal of Computational and Applied Mathematics
Modeling generalized cylinders using direction map representation
Computer-Aided Design
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This paper describes a simple technique for evaluating the length of a parametric curve. The technique approximates sections of the curve to the arc of a circle using only sample points on the curve; no computation of derivatives or other properties is required. This method is almost as quick to implement and compute as chord-length summation, but it is much more accurate. It also provides recursion criteria for adaptive sampling. An extension of the algorithm to estimate the area of a parametric surface is discussed briefly.