bse.py
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# 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
"""
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
"""
date_x = np.array(date_x)
date_y = np.array(date_y)
# 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)
})
import uuid
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:
from numpy import ndarray
group:ndarray = bezier_curve(item[0], item[1], item[2], item[3], inserted)
kk = group.tolist()
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()
group = [1,2,3,4,5]
print(group[:-1])
print(group[-1:])