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polynomialCurves2d
dlegland edited this page Mar 3, 2016
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The polynomialCurves2d module of the MatGeom library provides functions for the manipulation of planar smooth curves that can be parameterized by polynomials for each x and y 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)
Example:
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 is represented by a polynomial, it is easy 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.
polynomialCurveCentroid - Compute the centroid of a polynomial curve
polynomialCurveProjection - Projection of a point on a polynomial curve
polynomialCurveLength - Compute the length of a polynomial curve
polynomialCurvePoint - Compute point corresponding to a position
polynomialCurvePosition - Compute position on a curve for a given length
polynomialCurveDerivative - Compute derivative vector of a polynomial curve
polynomialCurveNormal - Compute the normal of a polynomial curve
polynomialCurveCurvature - Compute the local curvature of a polynomial curve
polynomialCurveCurvatures - Compute curvatures of a polynomial revolution surface
polynomialCurveFit - Fit a polynomial curve to a series of points
polynomialCurveSetFit - Fit a set of polynomial curves to a segmented image
drawPolynomialCurve - Draw a polynomial curve approximation
polynomialDerivate - Derivate a polynomial
polyfit2 - Polynomial approximation of a curve