给定笔画的一些坐标（x，y），如何按顺序平滑笔画？

Question

我目前正在做一个项目，我需要在给定一些有序的笔画坐标的情况下创建一个平滑的笔画图像。假设我有一些要点

import numpy as np

X = np.array([1, 3, 6, 8, 5])

Y = np.array([1, 8, 4, 4, 1])

plt.plot(X, Y)

但我想要的是制作一个平滑的点集合来绘制这个（这只是一张手绘图片，我想你明白了）：

我见过这个问题，它只适用于函数（一个 x 只输出一个 y）。但是我需要一个关系（不是函数）的样条。先感谢您。

Answer 1

参见柴金算法。Chaikin 算法是一种直接处理控制多边形的几何算法。曲线生成方案基于“角切割”，其中算法通过从原始角上切掉角来生成新的控制多边形。下图说明了这个想法，其中通过切断第一个序列的角，将初始控制多边形细化为第二个多边形（稍微偏移）。这是一个示例实现。"""polygoninterpolation.pyChaikin's Algorith for curveshttp://graphics.cs.ucdavis.edu/~joy/GeometricModelingLectures/Unit-7-Notes/Chaikins-Algorithm.pdf"""import mathimport randomfrom graphics import *class MultiLine:    def __init__(self, points=None, rgb_color=(255, 255, 255), width=1):        self.lines = []        if points is None:            self.points = []        else:            self.points = points            self._build_lines()        self.rgb_color = rgb_color        self.width = width    def add_point(self):        self.points.append(point)    def _build_lines(self):        for idx, point in enumerate(self.points[:-1]):            self.lines.append(Line(self.points[idx], self.points[idx + 1]))    def draw(self, win):        for line in self.lines:            line.setOutline(color_rgb(*self.rgb_color))            line.setWidth(self.width)            line.draw(win)def get_chaikin(points, factor=4):    new_points = []   # [points[0]]    for idx in range(len(points) - 1):        p1, p2 = points[idx], points[idx+1]        p_one_qtr, p_three_qtr = get_quarter_points(p1, p2, factor)        new_points.append(p_one_qtr)        new_points.append(p_three_qtr)    return new_points   # + [points[-1]]  # for a closed polygondef get_quarter_points(p1, p2, factor=4):    n = factor    qtr_x = (p2.x - p1.x) / n    qtr_y = (p2.y - p1.y) / n    return Point(p1.x + qtr_x, p1.y + qtr_y), \           Point(p1.x + (n-1) * qtr_x, p1.y + (n-1) * qtr_y)win = GraphWin("My Window", 500, 500)win.setBackground(color_rgb(0, 0, 0))# points0 = [Point(250, 20),#            Point(20, 400),#            Point(480, 400)]# points0 = [Point(20, 400),#            Point(35, 200),#            Point(250, 100),#            Point(400, 150),#            Point(450, 350),#            Point(380, 450)]# points0 = [Point(20, 400),#            Point(35, 200),#            Point(250, 100),#            Point(400, 150),#            Point(220, 170),#            Point(310, 190),#            Point(180, 270),#            Point(450, 230),#            Point(440, 440),#            Point(380, 450)]points0 = [Point(random.randrange(500), random.randrange(500)) for _ in range(random.randrange(3, 80))]x_line0 = MultiLine(points0)# x_line0.draw(win)points1 = get_chaikin(points0)x_line1 = MultiLine(points1, rgb_color=(200, 200, 200), width=1)# x_line1.draw(win)points2 = get_chaikin(points1)x_line2 = MultiLine(points2, rgb_color=(200, 200, 200), width=1)# x_line2.draw(win)points3 = get_chaikin(points2)x_line3 = MultiLine(points3, rgb_color=(200, 200, 200), width=1)# x_line3.draw(win)points4 = get_chaikin(points3)x_line4 = MultiLine(points4, rgb_color=(200, 200, 200), width=1)# x_line4.draw(win)points5 = get_chaikin(points4)x_line5 = MultiLine(points5, rgb_color=(200, 200, 200), width=1)x_line5.draw(win)# poly0 = Polygon(points0)# poly0.setOutline(color_rgb(0, 255, 0))# poly0.setWidth(1)# poly0.draw(win)## points1 = get_chaikin(points0 + [points0[0]])# poly1 = Polygon(points1)# poly1.setOutline(color_rgb(0, 255, 0))# poly1.setWidth(1)# poly1.draw(win)## points2 = get_chaikin(points1 + [points1[0]])# poly2 = Polygon(points2)# poly2.setOutline(color_rgb(0, 255, 0))# poly2.setWidth(1)# poly2.draw(win)## points3 = get_chaikin(points2 + [points2[0]])# poly3 = Polygon(points3)# poly3.setOutline(color_rgb(0, 255, 0))# poly3.setWidth(1)# poly3.draw(win)## points4 = get_chaikin(points3 + [points3[0]])# poly4 = Polygon(points4)# poly4.setOutline(color_rgb(0, 255, 0))# poly4.setWidth(1)# poly4.draw(win)## points5 = get_chaikin(points4 + [points4[0]])# poly5 = Polygon(points5)# poly5.setOutline(color_rgb(0, 255, 0))# poly5.setWidth(2)# poly5.draw(win)print("done")print(win.getMouse())win.close()