44 lines
1.0 KiB
Python
44 lines
1.0 KiB
Python
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"""
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"""
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tsequence = tuple([t / 20.0 for t in range(21)])
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beziers = {}
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def pascal_row(n):
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""" Returns n-th row of Pascal's triangle
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"""
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result = [1]
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x, numerator = 1, n
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for denominator in range(1, n // 2 + 1):
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x *= numerator
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x /= denominator
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result.append(x)
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numerator -= 1
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if n & 1 == 0:
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result.extend(reversed(result[:-1]))
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else:
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result.extend(reversed(result))
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return result
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def make_bezier(n):
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""" Bezier curves:
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http://en.wikipedia.org/wiki/B%C3%A9zier_curve#Generalization
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"""
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try:
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return beziers[n]
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except KeyError:
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combinations = pascal_row(n - 1)
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result = []
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for t in tsequence:
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tpowers = (t ** i for i in range(n))
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upowers = ((1 - t) ** i for i in range(n - 1, -1, -1))
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coefs = [c * a * b for c, a, b in zip(combinations,
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tpowers, upowers)]
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result.append(coefs)
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beziers[n] = result
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return result
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