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Vectorial graphics

Section that deals with techniques mostly used in relation with drawn images (images expressed by lines, contours and coloured areas rather bitmap/raster images).

  1. Introduction to Bezier curves
  2. Inflection points of a cubic Bezier
  3. 3 algorithms for fast, precision driven, piecewise degree reduction of cubic Bezier curves - in plain speak: "Approximating a cubic Bezier by quadratic Bezier segments". Some words:
    • There exists a solution for the Bezier degree reduction: google for the "Bezier degree reduction least-squares". If unable to find anything, the "3D Game Engine Design (first edition)" by Dave Eberly was recommended to me as containing a full discussion of this algorithm.
    • The discusions I had seems to indicate that, albeit more general, the least-square algorithm becomes computational expensive if applied to the adaptive subdivision. Since I haven't (yet) studied the details of the least-square algorithm for Bezier curve degree reduction, I can't compare the performance (but stay tuned... I intend to do it)
    • Finally, the reason for the article stays in the Timothée Groleau's article: when I first read it (back in 2003) I said to myself that there should be a better way.
  4. Defect comparison between midpoint quadratic apprximation of a cubic Bezier and a custom chosen quadratic - for those interested to compare the quality of midpoint approximation quadratic of a cubic Bezier with other approximating quadratics.

Downloads

Finally, after many years spent procrastinating, I managed to finish a clean room implementation for the algorithms exposed by the the first 3 articles... you can download:

 

 


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