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Projecting points onto planar parametric curves by local biarc approximation

Abstract : This paper proposes a geometric iteration algorithm for computing point projection and inversion on planar parametriccurves based on local biarc approximation. The iteration begins with initial estimation of the projection of theprescribed test point. For each iteration, we construct a biarc that locally approximates a segment on the originalcurve starting from the current projective point. Then we compute the projective point for the next iteration, as well asthe parameter corresponding to it, by projecting the test point onto this biarc. The iterative process terminates whenthe projective point satisfies the required precision. Examples demonstrate that our algorithm converges faster and isless dependent on the choice of the initial value compared to the traditional geometric iteration algorithms based onsingle-point approximation.
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Submitted on : Thursday, December 19, 2013 - 4:08:59 AM
Last modification on : Tuesday, June 1, 2021 - 2:34:07 PM
Long-term archiving on: : Thursday, March 20, 2014 - 11:41:53 AM


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  • HAL Id : hal-00920672, version 1


Hai-Chuan Song, Xin Xu, Kan-Le Shi, Jun-Hai Yong. Projecting points onto planar parametric curves by local biarc approximation. Computers and Graphics, Elsevier, 2014. ⟨hal-00920672⟩



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