Spline Command

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Spline( <List of Points> )
Creates a cubic spline through all points.
Spline( <List of Points>, <Order ≥ 3> )
Creates a spline with given order through all points.
Spline( <List of Points>, <Order ≥ 3>, <Weight Function> )
Creates a spline with given order through all points. The weight function says what should be the difference of t values for point Pi and Pi+1 given their difference Pi+1 - Pi = (x, y). To get the spline you expect from "function" algorithm you should use abs(x)+0*y, to get the GeoGebra's default spline you can use sqrt(x^2+y^2).
Note: The choice of default makes the result behave nicely when transformed, making sure that Rotate(Spline(list), a) gives the same as Spline(Rotate(list, a)).

Comments

The result of the spline command is a curve. Spline algorithm is used for x and y coordinates separately: first we determine values of t that correspond to the points (based on Euclidian distances between the points), then we find cubic splines as functions t->x and t->y.

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