B-스플라인 예제 사다리 문서의 문제 4 풀이 코드다. if __name__ == "__main__": 아래가 자체 테스트다.
"""B-스플라인 예제 사다리 문제 1~4 검증."""
from fractions import Fraction as F
def blend(u):
return [F(1, 6) * (1 - u) ** 3, F(1, 6) * (4 - 6 * u ** 2 + 3 * u ** 3),
F(1, 6) * (1 + 3 * u + 3 * u ** 2 - 3 * u ** 3), F(1, 6) * u ** 3]
def point(P, u):
b = blend(u)
return tuple(sum(bi * p[d] for bi, p in zip(b, P)) for d in range(2))
def main():
P = [(0, 0), (2, 4), (4, 4), (6, 0)]
assert blend(F(1, 2)) == [F(1, 48), F(23, 48), F(23, 48), F(1, 48)] # 문제 1
assert point(P, F(1, 2)) == (3, F(23, 6))
assert blend(F(0)) == [F(1, 6), F(4, 6), F(1, 6), 0] and point(P, F(0)) == (2, F(10, 3)) # 문제 2
Q = [(0, 0), (1, 2), (3, 3), (5, 2), (6, 0)] # 문제 3
end1 = point(Q[0:4], F(1)); start2 = point(Q[1:5], F(0))
assert end1 == start2 == (3, F(8, 3))
d = tuple(F(a - b, 2) for a, b in zip(Q[3], Q[1]))
assert d == (2, 0)
# 문제 4: 조절점 8개 → 조각 5개, p3을 쓰는 조각
segs = [list(range(i, i + 4)) for i in range(5)]
assert [i for i, s in enumerate(segs) if 3 in s] == [0, 1, 2, 3]
p0 = (1, 1)
assert point([p0, p0, p0, (4, 5)], F(0)) == p0
print("ALL CHECKS PASSED")
if __name__ == "__main__":
main()