数字“5”的曲线轮廓的数据为49,597,149,597,149,597,345,597, 345,597,361,597,365,599,368,606, 368,606,406,695,368,606,406,695, 406,695,397,702,406,695,397,702, 397,702,382,681,372,676,351,676, 351,676,351,676,351,676,142,676, 142,676,33,439,142,676,33,439, 33,449,32,438,43,436,32,434, 32,434,32,438,32,436,32,434, 44,426,74,426,109,420,149,408, 149,408,269,372,324,310,324,208, 324,208,324,112,264,37,185,37, 185,37,165,37,149,44,119,66, 119,66,86,90,65,99,42,99, 42,99,14,99,0,87,0,62, 0,62,0,24,46,0,121,0, 121,0,205,0,282,27,333,78, 333,78,378,123,399,180,399,256, 399,256,399,327,381,372,333,422, 333,422,288,468,232,491,112,512, 112,512,112,512,149,597,149,597 对以上数据借助hermite插值相关算法绘制平滑的的数字“5”的字体轮廓曲线（Python实现） （已知构造hermite插值参数曲线的相关公式，利用这两个公式进行插值： x(t)=[2*(x0-x1)+(a0+a1)]*t^3+[3*(x1-x0)-(a1+2*a0)]*t^2+a0*t+x0 y(t)=[2*(y0-y1)+(b0+b1)]*t^3+[3*(y1-y0)-(b1+2*b0)]*t^2+b0*t+y0）

首先，我们需要将给定的点坐标分别存储在两个列表中，即x和y坐标。

x = [49, 597, 149, 597, 149, 597, 345, 597, 345, 597, 361, 597, 365, 599, 368, 606, 368, 606, 406, 695, 368, 606, 406, 695, 406, 695, 397, 702, 406, 695, 397, 702, 397, 702, 382, 681, 372, 676, 351, 676, 351, 676, 351, 676, 142, 676, 142, 676, 33, 439, 142, 676, 33, 439, 33, 449, 32, 438, 43, 436, 32, 434, 32, 434, 32, 438, 32, 436, 32, 434, 44, 426, 74, 426, 109, 420, 149, 408, 149, 408, 269, 372, 324, 310, 324, 208, 324, 208, 324, 112, 264, 37, 185, 37, 185, 37, 165, 37, 149, 44, 119, 66, 119, 66, 86, 90, 65, 99, 42, 99, 42, 99, 14, 99, 0, 87, 0, 62, 0, 62, 0, 24, 46, 0, 121, 0, 121, 0, 205, 0, 282, 27, 333, 78, 333, 78, 378, 123, 399, 180, 399, 256, 399, 256, 399, 327, 381, 372, 333, 422, 333, 422, 288, 468, 232, 491, 112, 512, 112, 512, 112, 512, 149, 597, 149, 597]
y = [597, 597, 345, 597, 345, 597, 345, 597, 345, 597, 345, 597, 345, 599, 368, 606, 368, 606, 406, 695, 368, 606, 406, 695, 406, 695, 397, 702, 406, 695, 397, 702, 397, 702, 382, 681, 372, 676, 351, 676, 351, 676, 351, 676, 142, 676, 142, 676, 33, 439, 142, 676, 33, 439, 33, 449, 32, 438, 43, 436, 32, 434, 32, 434, 32, 438, 32, 436, 32, 434, 44, 426, 74, 426, 109, 420, 149, 408, 149, 408, 269, 372, 324, 310, 324, 208, 324, 208, 324, 112, 264, 37, 185, 37, 185, 37, 165, 37, 149, 44, 119, 66, 119, 66, 86, 90, 65, 99, 42, 99, 42, 99, 14, 99, 0, 87, 0, 62, 0, 62, 0, 24, 46, 0, 121, 0, 121, 0, 205, 0, 282, 27, 333, 78, 333, 78, 378, 123, 399, 180, 399, 256, 399, 256, 399, 327, 381, 372, 333, 422, 333, 422, 288, 468, 232, 491, 112, 512, 112, 512, 112, 512, 149, 597, 149, 597]

接下来，我们将通过hermite插值方法来平滑这些数据点。我们需要定义一个函数来计算x和y坐标的插值值。

def hermite_interpolation(x0, x1, a0, a1, y0, y1, b0, b1, t):
    """
    计算Hermite插值值
    """
    return (2*(x0-x1)+(a0+a1))*t**3 + (3*(x1-x0)-(a1+2*a0))*t**2 + a0*t + x0, (2*(y0-y1)+(b0+b1))*t**3 + (3*(y1-y0)-(b1+2*b0))*t**2 + b0*t + y0

接下来，我们需要为每个数据点计算插值点，并将这些插值点存储在两个新的列表中。

import numpy as np

x_new, y_new = [], []
for i in range(len(x) - 1):
    x0, x1 = x[i], x[i+1]
    y0, y1 = y[i], y[i+1]
    if i == 0:
        a0, b0 = x[i+2] - x[i], y[i+2] - y[i]
    else:
        a0, b0 = x[i] - x[i-1], y[i] - y[i-1]
    if i == len(x) - 2:
        a1, b1 = x[i+1] - x[i-1], y[i+1] - y[i-1]
    else:
        a1, b1 = x[i+2] - x[i+1], y[i+2] - y[i+1]
    for j in np.linspace(0, 1, num=10, endpoint=True):
        x_j, y_j = hermite_interpolation(x0, x1, a0, a1, y0, y1, b0, b1, j)
        x_new.append(x_j)
        y_new.append(y_j)

最后，我们可以使用Matplotlib库绘制平滑的数字“5”的字体轮廓曲线。

import matplotlib.pyplot as plt

plt.plot(x_new, y_new)
plt.show()

完整的代码如下：

import numpy as np
import matplotlib.pyplot as plt

x = [49, 597, 149, 597, 149, 597, 345, 597, 345, 597, 361, 597, 365, 599, 368, 606, 368, 606, 406, 695, 368, 606, 406, 695, 406, 695, 397, 702, 406, 695, 397, 702, 397, 702, 382, 681, 372, 676, 351, 676, 351, 676, 351, 676, 142, 676, 142, 676, 33, 439, 142, 676, 33, 439, 33, 449, 32, 438, 43, 436, 32, 434, 32, 434, 32, 438, 32, 436, 32, 434, 44, 426, 74, 426, 109, 420, 149, 408, 149, 408, 269, 372, 324, 310, 324, 208, 324, 208, 324, 112, 264, 37, 185, 37, 185, 37, 165, 37, 149, 44, 119, 66, 119, 66, 86, 90, 65, 99, 42, 99, 42, 99, 14, 99, 0, 87, 0, 62, 0, 62, 0, 24, 46, 0, 121, 0, 121, 0, 205, 0, 282, 27, 333, 78, 333, 78, 378, 123, 399, 180, 399, 256, 399, 256, 399, 327, 381, 372, 333, 422, 333, 422, 288, 468, 232, 491, 112, 512, 112, 512, 112, 512, 149, 597, 149, 597]
y = [597, 597, 345, 597, 345, 597, 345, 597, 345, 597, 345, 597, 345, 599, 368, 606, 368, 606, 406, 695, 368, 606, 406, 695, 406, 695, 397, 702, 406, 695, 397, 702, 397, 702, 382, 681, 372, 676, 351, 676, 351, 676, 351, 676, 142, 676, 142, 676, 33, 439, 142, 676, 33, 439, 33, 449, 32, 438, 43, 436, 32, 434, 32, 434, 32, 438, 32, 436, 32, 434, 44, 426, 74, 426, 109, 420, 149, 408, 149, 408, 269, 372, 324, 310, 324, 208, 324, 208, 324, 112, 264, 37, 185, 37, 185, 37, 165, 37, 149, 44, 119, 66, 119, 66, 86, 90, 65, 99, 42, 99, 42, 99, 14, 99, 0, 87, 0, 62, 0, 62, 0, 24, 46, 0, 121, 0, 121, 0, 205, 0, 282, 27, 333, 78, 333, 78, 378, 123, 399, 180, 399, 256, 399, 256, 399, 327, 381, 372, 333, 422, 333, 422, 288, 468, 232, 491, 112, 512, 112, 512, 112, 512, 149, 597, 149, 597]

def hermite_interpolation(x0, x1, a0, a1, y0, y1, b0, b1, t):
    """
    计算Hermite插值值
    """
    return (2*(x0-x1)+(a0+a1))*t**3 + (3*(x1-x0)-(a1+2*a0))*t**2 + a0*t + x0, (2*(y0-y1)+(b0+b1))*t**3 + (3*(y1-y0)-(b1+2*b0))*t**2 + b0*t + y0

x_new, y_new = [], []
for i in range(len(x) - 1):
    x0, x1 = x[i], x[i+1]
    y0, y1 = y[i], y[i+1]
    if i == 0:
        a0, b0 = x[i+2] - x[i], y[i+2] - y[i]
    else:
        a0, b0 = x[i] - x[i-1], y[i] - y[i-1]
    if i == len(x) - 2:
        a1, b1 = x[i+1] - x[i-1], y[i+1] - y[i-1]
    else:
        a1, b1 = x[i+2] - x[i+1], y[i+2] - y[i+1]
    for j in np.linspace(0, 1, num=10, endpoint=True):
        x_j, y_j = hermite_interpolation(x0, x1, a0, a1, y0, y1, b0, b1, j)
        x_new.append(x_j)
        y_new.append(y_j)

plt.plot(x_new, y_new)
plt.show()