overhauser_spline_points ( points,  segment_subdivisions )

Return cubically interpolated point list. An Overhauser spline (aka Catmul-Rom spline) uses cubic segments that join at the given points and have continuous tangent vector. The tangent vector at point i equals the difference vector between points i+1 and i-1. For the end segments I use a quadratic curve.

It is assumed that the points are objects with operators +, -, and * (by float) defined. For example, NumPy arrays work. But points that are lists or tuples will not work.

cubic_segment_points (
        p1,
        t1,
        p2,
        t2,
        subdivisions,
        )

Return a sequence of points along a cubic starting at p1 with tangent t1 and ending at p2 with tangent t2.

linear_segment_points (
        p1,
        p2,
        subdivisions,
        )

Return a sequence of points along a linear segment starting at p1 and ending at p2.

arc_lengths ( points )

Return a list of arc lengths for a piecewise linear curve specified by points. The points should be objects with operator - defined such as NumPy arrays. There number of arc lengths returned equals the number of points, the first arc length being 0.

quadratic_segment_points (
        p1,
        t1,
        p2,
        subdivisions,
        )

Return a sequence of points along a quadratic starting at p1 with tangent t1 and ending at p2.