如何按顺序给定笔划的一些坐标（x，y）来平滑笔划？

Question

我目前正在做一个项目，我需要创建一个笔画图像，在给定笔画的一些有序坐标的情况下进行平滑处理。假设我有一些积分

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，我想你明白了）：

我看到了 this 仅适用于函数的问题（一个 x 只会输出一个 y）。但是我需要一个关系样条（不是函数）。提前谢谢你。

Answer 1

参见chaikin's algorithm。

柴金算法是一种直接作用于控制多边形的几何算法。曲线生成方案基于“切角”算法通过切掉原始多边形的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.py
Chaikin's Algorith for curves
http://graphics.cs.ucdavis.edu/~joy/GeometricModelingLectures/Unit-7-Notes/Chaikins-Algorithm.pdf
"""
import math
import random
from 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 polygon


def 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()

Answer 2

您可以使用来自 scipy.interpolate 的 B 样条曲线（splprep 和 splev）：

import numpy as np
from scipy.interpolate import splprep, splev
import matplotlib.pyplot as plt

X = np.array([1, 3, 6, 8, 5])
Y = np.array([1, 8, 4, 4, 1])
pts = np.vstack((X, Y))
# Find the B-spline representation of an N-dimensional curve
tck, u = splprep(pts, s=0.0)
u_new = np.linspace(u.min(), u.max(), 1000)
# Evaluate a B-spline
x_new, y_new = splev(u_new, tck)

plt.plot(x_new, y_new, 'b--')
plt.show()

这将为您提供类似的内容：

您可以使用 splprep 参数来改变结果。您可以在此 Whosebug .

中找到更多详细信息

Answer 3

上面的答案很优雅，但是这里尝试"hacky"解决方案，那就不那么顺利了

X_new = []
Y_new = []
for i in range(4):
    line1 = [X[i],Y[i]] + np.expand_dims(np.linspace(0,1,10),-1)*np.array([X[i+1] - X[i], Y[i+1] - Y[i]])

    line_normal = [- Y[i+1] + Y[i], X[i+1] - X[i]]
    line_normal = line_normal/np.sqrt(np.dot(line_normal, line_normal))

    line1_noisy = line1 + line_normal * 0.2*(np.random.rand(10,1) - 0.5)
    X_new.append(line1_noisy[:,0])
    Y_new.append(line1_noisy[:,1])
X_new = np.stack(X_new).reshape(-1)
Y_new = np.stack(Y_new).reshape(-1)
plt.plot(X_new, Y_new)

如何按顺序给定笔划的一些坐标（x，y）来平滑笔划？

How to smooth out a stroke, given some coordinates (x, y) of the stroke in order?

python

geometry

numpy

matplotlib

bspline