如何在Sympy中从B样条曲线创建Bezier曲线？

from sympy import symbols, Matrix, simplify
from sympy.polys.polyfuncs import interpolate
import numpy as np

t = symbols('t')
control_points = [(0, 0), (1, 2), (3, 1), (4, 3)]  # 控制点坐标
knot_vector = [0, 0, 0, 0, 1, 1, 1, 1]  # 节点向量

n = len(control_points) - 1  # 控制点个数
m = len(knot_vector) - 1  # 节点向量长度

def generate_parametric_equations():
    M = np.zeros((m - 1, n + 1))
    equations = []
    
    for i in range(1, m - 1):
        for j in range(n + 1):
            M[i - 1, j] = (knot_vector[j + i + 1] - knot_vector[j + 1]) / (knot_vector[j + n + 2] - knot_vector[j + 1])
    
    for i in range(n + 1):
        equations.append(sum(M[:, i]) * t ** i)
    
    return equations

def generate_bezier_curve():
    equations = generate_parametric_equations()
    x_equation = simplify(interpolate(t, equations, [control_point[0] for control_point in control_points]))
    y_equation = simplify(interpolate(t, equations, [control_point[1] for control_point in control_points]))
    
    return x_equation, y_equation

x_equation, y_equation = generate_bezier_curve()
print("x(t) =", x_equation)
print("y(t) =", y_equation)