如何平滑类似于 d3 的 curveCardinal 方法实现的闭合线的边缘？

所以，这就是我最终做到的。我决定在每两个现有数据点之间引入新点。下图显示了我如何添加这些新点。红色是我拥有的数据。使用凸包计算数据点的几何中心并从每个点绘制线（用蓝线显示）。将这些线分成两半并连接结果点（绿线）。绿线的中心是添加的新点。

以下是实现此目的的函数：

def midpoint(p1, p2, sf=1):
    """Calculate the midpoint, with an optional 
    scaling-factor (sf)"""
    xm = ((p1[0]+p2[0])/2) * sf
    ym = ((p1[1]+p2[1])/2) * sf
    return (xm, ym)

def star_curv(old_x, old_y):
    """ Interpolates every point by a star-shaped curve. It does so by adding
    "fake" data points in-between every two data points, and pushes these "fake"
    points towards the center of the graph (roughly 1/4 of the way).
    """

    try:
        points = np.array([old_x, old_y]).reshape(7, 2)
        hull = ConvexHull(points)
        x_mid = np.mean(hull.points[hull.vertices,0])
        y_mid = np.mean(hull.points[hull.vertices,1])
    except:
        x_mid = 0.5
        y_mid = 0.5

    c=1
    x, y = [], []
    for i, j in zip(old_x, old_y):
        x.append(i)
        y.append(j)
        try:
            xm_i, ym_i = midpoint((i, j),
                                  midpoint((i, j), (x_mid, y_mid)))

            xm_j, ym_j = midpoint((old_x[c], old_y[c]),
                                  midpoint((old_x[c], old_y[c]), (x_mid, y_mid)))

            xm, ym = midpoint((xm_i, ym_i), (xm_j, ym_j))
            x.append(xm)
            y.append(ym)
            c += 1
        except IndexError:
            break


    orig_len = len(x)
    x = x[-3:-1] + x + x[1:3]
    y = y[-3:-1] + y + y[1:3]


    t = np.arange(len(x))
    ti = np.linspace(2, orig_len + 1, 10 * orig_len)

    kind='quadratic'
    xi = interp1d(t, x, kind=kind)(ti)
    yi = interp1d(t, y, kind=kind)(ti)

    return xi, yi

这是它的外观：

import numpy as np
import matplotlib.pyplot as plt
from scipy.interpolate import interp1d
from scipy.spatial import ConvexHull

x = [0.5, 0.13, 0.4, 0.5, 0.6, 0.7, 0.5]
y = [1.0, 0.7, 0.5, 0.2, 0.4, 0.6, 1.0]

xi, yi = star_curv(x, y)

fig, ax = plt.subplots()
ax.plot(xi, yi, 'g')

ax.plot(x, y, 'k', alpha=0.5)
ax.scatter(x, y, color='r')

当数据点更对称时，结果尤其明显，例如以下 x, y 值给出下图中的结果：

x = [0.5, 0.32, 0.34, 0.5, 0.66, 0.65, 0.5]
y = [0.71, 0.6, 0.41, 0.3, 0.41, 0.59, 0.71]

此处介绍的插值与默认的 interp1d 插值之间的比较。