bspline with out numpy

bspline.py

#import numpy as np
# cv = list of 2d control vertices
# n = number of samples (default: 100)
# d = curve degree (default: cubic = 3)
# closed = is the curve closed (periodic) or open? (default: open)
def bspline(cv, n=100, d=3, closed=False):
    # Create a range of u values
    count = len(cv)
    knots = None
    u = None
    if not closed:
        u = [ (float(i/(n-1)) * (count-d)) for i in range(0,n) ] # keep u=0 relative to 1st cv
        knots = [0]*d + [ a for a in range(count-d+1)] + [count-d]*d 
    else:
        u = [ ((float(i)/(n-1) * count) - (0.5 * (d-1))) % count for i in range(0,n) ] # keep u=0 relative to 1st cv
        knots = [i for i in range(0-d,count+d+d-1) ] 
    # Simple Cox - DeBoor recursion
    def coxDeBoor(u, k, d):
        # Test for end conditions
        if (d == 0):
            if (knots[k] <= u and u < knots[k+1]):
                return 1
            return 0

        Den1 = knots[k+d] - knots[k]
        Den2 = knots[k+d+1] - knots[k+1]
        Eq1  = 0;
        Eq2  = 0;

        if Den1 > 0:
            Eq1 = ((u-knots[k]) / Den1) * coxDeBoor(u,k,(d-1))
        if Den2 > 0:
            Eq2 = ((knots[k+d+1]-u) / Den2) * coxDeBoor(u,(k+1),(d-1))
        return Eq1 + Eq2

    # Sample the curve at each u value
    samples = [ [0,0] for i in range(n) ]
    for i in range(n):
        if not closed:
            if u[i] == count-d:
                samples[i] = cv[-1]
            else:
                for k in range(count):
                    coxDeBoor_factor = coxDeBoor(u[i],k,d)
                    samples[i] = [ component[0] + coxDeBoor_factor * component[1]
                                  for component in zip(samples[i],cv[k]) ]
                    
        else:
            for k in range(count+d):
                coxDeBoor_factor = coxDeBoor(u[i],k,d)
                samples[i] = [ component[0] + coxDeBoor_factor * component[1]
                              for component in zip(samples[i],cv[k%count]) ]

    return samples




if __name__ == "__main__":
    from  graph import *
    
    cv = [[ 230,  195],
               [ 380, 230],
               [ 750, 187],
               [ 630, 520],
               [ 427, 790],
               [ 260, 507],
               [ 183, 308],
               [ 145,  200]]
    canvasSize(900,900)
    windowSize(900,900)
    for mult in [1,2,10]:
        splined_cv = bspline(cv, n=len(cv) * mult , d=2, closed=True)
        splined_cv = [ [v[0],v[1]] for v in splined_cv ]
        orig_cv = [ [v[0],v[1]] for v in cv  ]
        brushColor("#dee9af"); penColor("black"); penSize(1)
        polyline(splined_cv)

    penColor("red"); penSize(2)
    orig_cv.append(orig_cv[0])
    polyline(orig_cv)
    run()