D. J. Walton
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Index Terms
- Turning point preserving planar interpolation
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Reviews
Andrew Timothy Thornton
A useful technique is described for fitting a curve to a set of points that are known to be the turning points of the curve, such that the curve passes through all of these points and the curve is not self-intersecting unless its parent is. This technique is particularly useful in cartographic applications for fitting curves to contour lines. The basic technique is to create a pair of quadratic Be´ zier curves between each pair of points, with zero curvature and a common tangent vector where they meet. The tangents at the turning points are defined through interpolation, so only one more item of information is needed to define the two curves. Minimum arc length was tried, but proved to be too expensive to compute although very robust; minimizing the deviation from the chord, for instance by making the common tangent vector parallel to the chord, is robust and fast, but to my eye the resultant line appears too taut; lastly, a constant speed parameterization gives a slacker line, but fails when the change in chord direction at any point exceeds about 80 degrees. The technique is useful, as the self-intersection problem is solved to a much greater extent than previously. Using the minimum deviation approach, it is both fast and robust.
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