Transforms a polynomial in canonical basis into bezier basis and vice-versa

canon2bezier.py

from typing import Tuple    
import sympy as sp
import numpy as np

def Bezier2Canonical(degree: int) -> np.ndarray:
    """
    Returns a transformation matrix between the basis
        Bezier -> Canonical
    """
    matrix = np.zeros((degree+1, degree+1), dtype="object")
    matrix = sp.Matrix(matrix)
    for i in range(degree+1):
        coef0 = sp.binomial(degree, i)
        for j in range(degree+1-i):
            coef1 = sp.binomial(degree-i, j)
            value = coef0 * coef1
            matrix[degree-i, i+j] = -value if j%2 else value 
    matrix = np.array(matrix, dtype="object")
    return matrix

def extract_canon_coefs(poly, var: sp.Symbol, degree: int) -> Tuple:
    """
    Given a poly like: 1 + 3*x + 4*x^2 + 0*x^3 + 2*x^4 + 0*x^5
    Then, this function returns
        [1, 3, 4, 0, 2, 0]
    For specified degree
    """
    coefs = sp.Poly(poly, var).all_coeffs()[::-1]
    coefs += [0]*(degree+1-len(coefs))
    return tuple(coefs)

if __name__ == "__main__":
    
    degree = 4
    bezier2canonical = Bezier2Canonical(degree)
    canonical2bezier = sp.Matrix(bezier2canonical).inv()
    canonical2bezier = np.array(canonical2bezier, dtype="object")

    u = sp.symbols("u", real=True)
    expr = -2*u # (1+u**2)**2
    can_coefs = extract_canon_coefs(expr, u, degree)
    print("can_coefs = ")
    print(can_coefs)

    bez_coefs = canonical2bezier @ can_coefs
    print("bez_coefs = ")
    print(bez_coefs)