Is there a library or function in python to compute Catmull-Rom spline from three points ?
What I need in the end are the x,y coordinates of points along the spline, provided that they are always equidistant of a given amount t along the spline (say, the spline curve is 3 units long and I want the x,y coordinates at spline length 0, 1, 2 and 3)
Nothing really exciting. I am writing it by myself, but if you find something nice, It would be great for testing (or to save time)
3 points ? Catmull-Rom is defined for 4 points, say p_1 p0 p1 p2; a cubic curve goes from p0 to p1, and outer points p_1 and p2 determine the slopes at p0 and p1. To draw a curve through some points in an array P, do something like this:
for j in range( 1, len(P)-2 ): # skip the ends for t in range( 10 ): # t: 0 .1 .2 .. .9 p = spline_4p( t/10, P[j-1], P[j], P[j+1], P[j+2] ) # draw p def spline_4p( t, p_1, p0, p1, p2 ): """ Catmull-Rom (Ps can be numpy vectors or arrays too: colors, curves ...) """ # wikipedia Catmull-Rom -> Cubic_Hermite_spline # 0 -> p0, 1 -> p1, 1/2 -> (- p_1 + 9 p0 + 9 p1 - p2) / 16 # assert 0 <= t <= 1 return ( t*((2-t)*t - 1) * p_1 + (t*t*(3*t - 5) + 2) * p0 + t*((4 - 3*t)*t + 1) * p1 + (t-1)*t*t * p2 ) / 2
One can use piecewise quadratic curves through 3 points -- see Dodgson, Quadratic Interpolation for Image Resampling. What do you really want to do ?