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101 lines
2.9 KiB
101 lines
2.9 KiB
1 year ago
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import utils.b_spline.BaseFunction as bf
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import numpy as np
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def curve_interpolation(D, N, k, param, knot):
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'''
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Given a set of N data points, D0, D1, ..., Dn and a degree k,
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find a B-spline curve of degree k defined by N control points
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that passes all data points in the given order.
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:param D: data points (N x 2)
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:param N: the number of data points
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:param k: degree
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:param param: parameters
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:param knot: knot vector
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:return: control points (N x 2)
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'''
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Nik = np.zeros((N, N))
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for i in range(N):
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for j in range(N):
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Nik[i][j] = bf.BaseFunction(j, k+1, param[i], knot)
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Nik[N-1][N-1] = 1
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print(Nik)
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Nik_inv = np.linalg.inv(Nik)
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print(Nik_inv)
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P = []
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for i in range(len(D)):
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P.append(np.dot(Nik_inv, D[i]).tolist())
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print(P)
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return P
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def curve_approximation(D, N, H, k, param, knot):
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'''
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Given a set of N data points, D0, D1, ..., Dn, a degree k,
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and a number H, where N > H > k >= 1, find a B-spline curve
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of degree k defined by H control points that satisfies the
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following conditions:
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1. this curve contains the first and last data points;
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2. this curve approximates the data polygon in the sense
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of least square;
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:param D: data points (N x 2)
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:param H: the number of control points
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:param k: degree
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:param param: parameters
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:param knot: knot vector
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:return: control points (H x 2)
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'''
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P = []
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if H >= N or H <= k:
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print('Parameter H is out of range')
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return P
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for idx in range(len(D)):
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P_ = np.zeros((1, H))
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P_[0][0] = D[idx][0]
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P_[0][H-1] = D[idx][N-1]
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Qk = np.zeros((N - 2, 1))
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Nik = np.zeros((N, H))
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for i in range(N):
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for j in range(H):
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Nik[i][j] = bf.BaseFunction(j, k+1, param[i], knot)
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# print(Nik)
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for j in range(1, N - 1):
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Qk[j - 1] = D[idx][j] - Nik[j][0] * P_[0][0] - Nik[j][H - 1] * P_[0][H - 1]
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N_part = Nik[1: N - 1, 1: H - 1]
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# print(N_part)
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Q = np.dot(N_part.transpose(), Qk)
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# print(Q)
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M = np.dot(np.transpose(N_part), N_part)
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P_[0][1:H - 1] = np.dot(np.linalg.inv(M), Q).transpose()
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P.append(P_.tolist()[0])
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return P
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def curve(P, N, k, param, knot):
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'''
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Calculate B-spline curve.
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:param P: Control points
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:param N: the number of control points
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:param k: degree
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:param param: parameters
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:param knot: knot vector
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:return: data point on the b-spline curve
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'''
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Nik = np.zeros((len(param), N))
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for i in range(len(param)):
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for j in range(N):
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Nik[i][j] = bf.BaseFunction(j, k+1, param[i], knot)
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Nik[len(param)-1][N - 1] = 1
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# print(Nik)
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# D = np.dot(Nik, P)
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D = []
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for i in range(len(P)):
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D.append(np.dot(Nik, P[i]).tolist())
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# print(D)
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return D
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