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I have an algorithm that implements an uniform resample process throughout a Bézier curve. This is done using a chord parametrization process.

However, the results achieved do not accomplish my needs. I have noticed a lack in the algorithm: regions of high curvature are simpler, with less information (samples), and does not represent the original curve with precision.

What I actually need is an algorithm to resample the Bézier curve such that more samples are located in regions with high curvature. But other constraint must me respected: I need a specific number of points in the resampled curve.

Any suggestion?

Thank in advance!

João Paulo Navarro
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1 Answers1

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I assume that the curve to be resampled is itself a piece-wise (cubic) bezier curve. Then a variation of the Ramer-Douglas-Peucker algorithm may do what you want. The algorithm as described in the link can be generalized because of the following facts:

  1. The extremal values of a projection of a bezier curve can easily be found (at least for quadratic and cubic curves).
  2. A Bezier curve can be split at any point into two shorter bezier curves.

The stopping criterium for resampling can be a combination of number of resample points and maximal allowed error.

WimC
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