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The PolynomialCurves2d module is devoted to the manipulation of planar smooth curves parameterized by polynomial for each coordinate.

A polynomial curve is represented by 3 row vectors:

  • the bounds of the parametrization
  • the coefficients for the x coordinate (in increasing degree)
  • the coefficients for the y coordinate (in increasing degree)


 C = {[0 1], [3 4], [0 1 -1]};

represents the curve defined by:

 x(t) = 3 + 4*t;
 y(t) = t - t*t;

for t belonging to the interval [0 1].

As each coordinate are given by polynoms, it is possible to compute various parameters like curvature, normal, or the exact geodesic length of the curve.

For most functions, parameters are given as three separate arguments. Sometimes, only the 2 parameters corresponding to the X and Y coefficients are required.