Beizer BSpline

UII

# coding = utf-8
import numpy as np
from matplotlib import pyplot as plt
import math
# bezier
# TODO: LUT
def B(n, k, t):
    up = 1
    down = 1
    for i in range(k):
        up *= (n - i)
        down *= (i + 1)
    left = 1
    for i in range(k):
        left *= t
    right = 1
    for i in range(n - k):
        right *= (1 - t)
    return up / down * left * right
def bezier(c, num_resample=100):  # Bezier曲线公式转换，获取x和y
    # bezier
    n = c.shape[0] - 1
    ts = np.linspace(0, 1, num_resample)
    line = np.zeros((num_resample, 2))
    for i in range(ts.shape[0]):
        t = ts[i]
        pt = 0
        for k in range(n + 1):
            pt += (B(n, k, t) * c[k])
        line[i] = pt
    return line
# bezier End
# bspline
def deboor(r, i, t, u, c, k):
    if r == 0:
        return c[i - 1]
    omega = (t - u[i]) / (u[i + k - r] - u[i] + 1e-7)
    return (1 - omega) * deboor(r - 1, i - 1, t, u, c, k) + \
             omega * deboor(r - 1, i, t, u, c, k)
def bspline(c, num_resample=100, k=3):
    # c = np.concatenate([c, c[-1].reshape(-1, 2)])
    n = c.shape[0]  # for travel 0...n
    m = n + k + 1  # m > 2k
    u = [i for i in range(m + 1)]
    u = np.array(u)
    u[:k] = k
    u[-(k+1):] = m - k
    line = []
    t = k
    step = (n + 1 - t) / (num_resample - 1)
    while t <= (n + 1 + 1e-5):
        i = math.floor(t)
        if i == m - k:
            i = m - k - 1
        line.append(deboor(k - 1, i, t, u, c, k))
        t += step
    return np.vstack(line)
# bspline End
class MyB:
    def __init__(self, line):
        self.line = line
        self.index_02 = None  # 保存拖动的这个点的索引
        self.press = None  # 状态标识，1为按下，None为没按下
        self.pick = None  # 状态标识，1为选中点并按下,None为没选中
        self.motion = None  # 状态标识，1为进入拖动,None为不拖动
        self.xs = list()  # 保存点的x坐标
        self.ys = list()  # 保存点的y坐标
        self.cidpress = line.figure.canvas.mpl_connect('button_press_event', self.on_press)  # 鼠标按下事件
        self.cidrelease = line.figure.canvas.mpl_connect('button_release_event', self.on_release)  # 鼠标放开事件
        self.cidmotion = line.figure.canvas.mpl_connect('motion_notify_event', self.on_motion)  # 鼠标拖动事件
        self.cidpick = line.figure.canvas.mpl_connect('pick_event', self.on_picker)  # 鼠标选中事件
    def on_press(self, event):  # 鼠标按下调用
        if event.inaxes != self.line.axes: return
        self.press = 1
    def on_motion(self, event):  # 鼠标拖动调用
        if event.inaxes != self.line.axes: return
        if self.press is None: return
        if self.pick is None: return
        if self.motion is None:  # 整个if获取鼠标选中的点是哪个点
            self.motion = 1
            x = self.xs
            xdata = event.xdata
            ydata = event.ydata
            index_01 = 0
            for i in x:
                if abs(i - xdata) < 0.02:  # 0.02 为点的半径
                    if abs(self.ys[index_01] - ydata) < 0.02: break
                index_01 = index_01 + 1
            self.index_02 = index_01
        if self.index_02 is None: return
        self.xs[self.index_02] = event.xdata  # 鼠标的坐标覆盖选中的点的坐标
        self.ys[self.index_02] = event.ydata
        self.draw()
    def on_release(self, event):  # 鼠标按下调用
        if event.inaxes != self.line.axes: return
        if self.pick == None:  # 如果不是选中点，那就添加点
            self.xs.append(event.xdata)
            self.ys.append(event.ydata)
        if self.pick == 1 and self.motion != 1:  # 如果是选中点，但不是拖动点，那就降阶
            x = self.xs
            xdata = event.xdata
            ydata = event.ydata
            index_01 = 0
            for i in x:
                if abs(i - xdata) < 0.02:
                    if abs(self.ys[index_01] - ydata) < 0.02: break
                index_01 = index_01 + 1
            self.xs.pop(index_01)
            self.ys.pop(index_01)
        self.draw()
        self.pick = None  # 所有状态恢复，鼠标按下到稀放为一个周期
        self.motion = None
        self.press = None
        self.index_02 = None
    def on_picker(self, event):  # 选中调用
        self.pick = 1
    def draw(self):  # 绘图
        self.line.clear()  # 不清除的话会保留原有的图
        self.line.axis([0, 1, 0, 1])  # x和y范围0到1
        control_points = np.array([self.xs, self.ys]).T
        k = 4
        if control_points.shape[0] >= k:
            line = self.b(control_points, k, 100)  # B样条曲线
            self.line.plot(line[:, 0], line[:, 1])
        self.line.scatter(self.xs, self.ys, color='b', s=200, marker="o", picker=5)  # 画点
        # self.line.plot(self.xs, self.ys, color='r')  # 画线
        self.line.figure.canvas.draw()  # 重构子图
    def b(self, c, k=3, num_resample=100):  # Bezier曲线公式转换，获取x和y
        # line = bezier(c, num_resample)
        line = bspline(c, num_resample, k)
        return line
fig = plt.figure(2, figsize=(12, 6))  # 创建第2个绘图对象,1200*600像素
ax = fig.add_subplot(111)  # 一行一列第一个子图
ax.set_title('My B')
myBezier = MyB(ax)
plt.xlabel('X')
plt.ylabel('Y')
plt.show()

• 绘图交互代码来源：B样条曲线——de Boor递推算法实现