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#!/usr/bin/python
def choose(n, k):
r = 1
for i in range(1, k+1):
r = (r*(n-k+i))/i
return r
def W(n, j, k):
q = (n+1)/2.
if((n & 1) == 0 and j == q and k == q):
return 1
if(k > n-k):
return W(n, n-j, n-k)
assert((k <= q))
if(k >= q):
return 0
# assert(!(j >= n-k));
if(j >= n-k):
return 0
# assert(!(j < k));
if(j < k):
return 0
return float(choose(n-2*k-1, j-k)) / choose(n,j);
# this produces a degree 2q bezier from a degree k sbasis
def sbasis_to_bezier(B, q):
if(q == 0):
q = len(B)
n = q*2
result = [0.0 for i in range(n)]
if(q > len(B)):
q = len(B)
n -= 1
for k in range(q):
for j in range(n-k+1):
result[j] += (W(n, j, k)*B[k][0] +
W(n, n-j, k)*B[k][1])
return result
def lerp(a, b, t):
return (1-t)*a + t*b
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