bze.py
6.5 KB
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
# coding=utf-8
#author: 4N
#createtime: 2020/10/16
#email: nheweijun@sina.com
import numpy as np
def bezier_curve(p0, p1, p2, p3, inserted):
"""
三阶贝塞尔曲线
p0, p1, p2, p3 - 点坐标，tuple、list或numpy.ndarray类型
inserted - p0和p3之间插值的数量
"""
assert isinstance(p0, (tuple, list, np.ndarray)), u'点坐标不是期望的元组、列表或numpy数组类型'
assert isinstance(p0, (tuple, list, np.ndarray)), u'点坐标不是期望的元组、列表或numpy数组类型'
assert isinstance(p0, (tuple, list, np.ndarray)), u'点坐标不是期望的元组、列表或numpy数组类型'
assert isinstance(p0, (tuple, list, np.ndarray)), u'点坐标不是期望的元组、列表或numpy数组类型'
if isinstance(p0, (tuple, list)):
p0 = np.array(p0)
if isinstance(p1, (tuple, list)):
p1 = np.array(p1)
if isinstance(p2, (tuple, list)):
p2 = np.array(p2)
if isinstance(p3, (tuple, list)):
p3 = np.array(p3)
points = list()
for t in np.linspace(0, 1, inserted + 2):
points.append(p0 * np.power((1 - t), 3) + 3 * p1 * t * np.power((1 - t), 2) + 3 * p2 * (1 - t) * np.power(t,
2) + p3 * np.power(
t, 3))
return np.vstack(points)
def smoothing_base_bezier(date_x, date_y, k=0.5, inserted=10, closed=False):
"""
基于三阶贝塞尔曲线的数据平滑算法
date_x - x维度数据集，list或numpy.ndarray类型
date_y - y维度数据集，list或numpy.ndarray类型
k - 调整平滑曲线形状的因子，取值一般在0.2~0.6之间。默认值为0.5
inserted - 两个原始数据点之间插值的数量。默认值为10
closed - 曲线是否封闭，如是，则首尾相连。默认曲线不封闭
"""
assert isinstance(date_x, (list, np.ndarray)), u'x数据集不是期望的列表或numpy数组类型'
assert isinstance(date_y, (list, np.ndarray)), u'y数据集不是期望的列表或numpy数组类型'
if isinstance(date_x, list) and isinstance(date_y, list):
assert len(date_x) == len(date_y), u'x数据集和y数据集长度不匹配'
date_x = np.array(date_x)
date_y = np.array(date_y)
elif isinstance(date_x, np.ndarray) and isinstance(date_y, np.ndarray):
assert date_x.shape == date_y.shape, u'x数据集和y数据集长度不匹配'
else:
raise Exception(u'x数据集或y数据集类型错误')
# 第1步：生成原始数据折线中点集
mid_points = list()
for i in range(1, date_x.shape[0]):
mid_points.append({
'start': (date_x[i - 1], date_y[i - 1]),
'end': (date_x[i], date_y[i]),
'mid': ((date_x[i] + date_x[i - 1]) / 2.0, (date_y[i] + date_y[i - 1]) / 2.0)
})
if closed:
mid_points.append({
'start': (date_x[-1], date_y[-1]),
'end': (date_x[0], date_y[0]),
'mid': ((date_x[0] + date_x[-1]) / 2.0, (date_y[0] + date_y[-1]) / 2.0)
})
# 第2步：找出中点连线及其分割点
split_points = list()
for i in range(len(mid_points)):
if i < (len(mid_points) - 1):
j = i + 1
elif closed:
j = 0
else:
continue
x00, y00 = mid_points[i]['start']
x01, y01 = mid_points[i]['end']
x10, y10 = mid_points[j]['start']
x11, y11 = mid_points[j]['end']
d0 = np.sqrt(np.power((x00 - x01), 2) + np.power((y00 - y01), 2))
d1 = np.sqrt(np.power((x10 - x11), 2) + np.power((y10 - y11), 2))
k_split = 1.0 * d0 / (d0 + d1)
mx0, my0 = mid_points[i]['mid']
mx1, my1 = mid_points[j]['mid']
split_points.append({
'start': (mx0, my0),
'end': (mx1, my1),
'split': (mx0 + (mx1 - mx0) * k_split, my0 + (my1 - my0) * k_split)
})
# 第3步：平移中点连线，调整端点，生成控制点
crt_points = list()
for i in range(len(split_points)):
vx, vy = mid_points[i]['end'] # 当前顶点的坐标
dx = vx - split_points[i]['split'][0] # 平移线段x偏移量
dy = vy - split_points[i]['split'][1] # 平移线段y偏移量
sx, sy = split_points[i]['start'][0] + dx, split_points[i]['start'][1] + dy # 平移后线段起点坐标
ex, ey = split_points[i]['end'][0] + dx, split_points[i]['end'][1] + dy # 平移后线段终点坐标
cp0 = sx + (vx - sx) * k, sy + (vy - sy) * k # 控制点坐标
cp1 = ex + (vx - ex) * k, ey + (vy - ey) * k # 控制点坐标
if crt_points:
crt_points[-1].insert(2, cp0)
else:
crt_points.append([mid_points[0]['start'], cp0, mid_points[0]['end']])
if closed:
if i < (len(mid_points) - 1):
crt_points.append([mid_points[i + 1]['start'], cp1, mid_points[i + 1]['end']])
else:
crt_points[0].insert(1, cp1)
else:
if i < (len(mid_points) - 2):
crt_points.append([mid_points[i + 1]['start'], cp1, mid_points[i + 1]['end']])
else:
crt_points.append([mid_points[i + 1]['start'], cp1, mid_points[i + 1]['end'], mid_points[i + 1]['end']])
crt_points[0].insert(1, mid_points[0]['start'])
# 第4步：应用贝塞尔曲线方程插值
out = list()
for item in crt_points:
group = bezier_curve(item[0], item[1], item[2], item[3], inserted)
out.append(group[:-1])
out.append(group[-1:])
out = np.vstack(out)
return out.T[0], out.T[1]
if __name__ == '__main__':
import matplotlib.pyplot as plt
x = np.array([2, 4, 4, 3, 2])
y = np.array([2, 2, 4, 3, 4])
plt.plot(x, y, 'ro')
x_curve, y_curve = smoothing_base_bezier(x, y, k=0.3, closed=True)
print(x_curve)
print(y_curve)
plt.plot(x_curve, y_curve, label='$k=0.3$')
# x_curve, y_curve = smoothing_base_bezier(x, y, k=0.4, closed=True)
# plt.plot(x_curve, y_curve, label='$k=0.4$')
# x_curve, y_curve = smoothing_base_bezier(x, y, k=0.5, closed=True)
# plt.plot(x_curve, y_curve, label='$k=0.5$')
# x_curve, y_curve = smoothing_base_bezier(x, y, k=0.6, closed=True)
# plt.plot(x_curve, y_curve, label='$k=0.6$')
plt.legend(loc='best')
plt.show()