(degree, ctrlpts, **kwargs)
return pts_red
Computes the control points of the rational/non-rational spline after degree reduction.

    Implementation of Eqs. 5.41 and 5.42 of The NURBS Book by Piegl & Tiller, 2nd Edition, p.220

    Please note that degree reduction algorithm can only operate on Bezier shapes, i.e. curves, surfaces, volumes and
    this implementation does NOT compute the maximum error tolerance as described via Eqs. 5.45 and 5.46 of The NURBS
    Book by Piegl & Tiller, 2nd Edition, p.221 to determine whether the shape is degree reducible or not.

    :param degree: degree
    :type degree: int
    :param ctrlpts: control points
    :type ctrlpts: list, tuple
    :return: control points of the degree-reduced shape
    :rtype: list
Computes the control points of the rational/non-rational spline after degree reduction.
Computes the control points of the rational / non - rational spline after degree reduction .
def degree_reduction(degree, ctrlpts, **kwargs):
    """ Computes the control points of the rational/non-rational spline after degree reduction.

    Implementation of Eqs. 5.41 and 5.42 of The NURBS Book by Piegl & Tiller, 2nd Edition, p.220

    Please note that degree reduction algorithm can only operate on Bezier shapes, i.e. curves, surfaces, volumes and
    this implementation does NOT compute the maximum error tolerance as described via Eqs. 5.45 and 5.46 of The NURBS
    Book by Piegl & Tiller, 2nd Edition, p.221 to determine whether the shape is degree reducible or not.

    :param degree: degree
    :type degree: int
    :param ctrlpts: control points
    :type ctrlpts: list, tuple
    :return: control points of the degree-reduced shape
    :rtype: list
    """
    # Get keyword arguments
    check_op = kwargs.get('check_num', True)  # enable/disable input validation checks

    if check_op:
        if degree + 1 != len(ctrlpts):
            raise GeomdlException("Degree reduction can only work with Bezier-type geometries")
        if degree < 2:
            raise GeomdlException("Input spline geometry must have degree > 1")

    # Initialize variables
    pts_red = [[0.0 for _ in range(len(ctrlpts[0]))] for _ in range(degree)]

    # Fix start and end control points
    pts_red[0] = ctrlpts[0]
    pts_red[-1] = ctrlpts[-1]

    # Find if the degree is an even or an odd number
    p_is_odd = True if degree % 2 != 0 else False

    # Compute control points of degree-reduced 1-dimensional shape
    r = int((degree - 1) / 2)
    # Handle a special case when degree = 2
    if degree == 2:
        r1 = r - 2
    else:
        # Determine r1 w.r.t. degree evenness
        r1 = r - 1 if p_is_odd else r
    for i in range(1, r1 + 1):
        alpha = float(i) / float(degree)
        pts_red[i] = [(c1 - (alpha * c2)) / (1 - alpha) for c1, c2 in zip(ctrlpts[i], pts_red[i - 1])]
    for i in range(degree - 2, r1 + 2):
        alpha = float(i + 1) / float(degree)
        pts_red[i] = [(c1 - ((1 - alpha) * c2)) / alpha for c1, c2 in zip(ctrlpts[i + 1], pts_red[i + 1])]

    if p_is_odd:
        alpha = float(r) / float(degree)
        left = [(c1 - (alpha * c2)) / (1 - alpha) for c1, c2 in zip(ctrlpts[r], pts_red[r - 1])]
        alpha = float(r + 1) / float(degree)
        right = [(c1 - ((1 - alpha) * c2)) / alpha for c1, c2 in zip(ctrlpts[r + 1], pts_red[r + 1])]
        pts_red[r] = [0.5 * (pl + pr) for pl, pr in zip(left, right)]

    # Return computed control points after degree reduction
    return pts_red
def degree_reduction ( degree , ctrlpts , * * kwargs ) : # Get keyword arguments check_op = kwargs . get ( 'check_num' , True ) # enable/disable input validation checks if check_op : if degree + 1 != len ( ctrlpts ) : raise GeomdlException ( "Degree reduction can only work with Bezier-type geometries" ) if degree < 2 : raise GeomdlException ( "Input spline geometry must have degree > 1" ) # Initialize variables pts_red = [ [ 0.0 for _ in range ( len ( ctrlpts [ 0 ] ) ) ] for _ in range ( degree ) ] # Fix start and end control points pts_red [ 0 ] = ctrlpts [ 0 ] pts_red [ - 1 ] = ctrlpts [ - 1 ] # Find if the degree is an even or an odd number p_is_odd = True if degree % 2 != 0 else False # Compute control points of degree-reduced 1-dimensional shape r = int ( ( degree - 1 ) / 2 ) # Handle a special case when degree = 2 if degree == 2 : r1 = r - 2 else : # Determine r1 w.r.t. degree evenness r1 = r - 1 if p_is_odd else r for i in range ( 1 , r1 + 1 ) : alpha = float ( i ) / float ( degree ) pts_red [ i ] = [ ( c1 - ( alpha * c2 ) ) / ( 1 - alpha ) for c1 , c2 in zip ( ctrlpts [ i ] , pts_red [ i - 1 ] ) ] for i in range ( degree - 2 , r1 + 2 ) : alpha = float ( i + 1 ) / float ( degree ) pts_red [ i ] = [ ( c1 - ( ( 1 - alpha ) * c2 ) ) / alpha for c1 , c2 in zip ( ctrlpts [ i + 1 ] , pts_red [ i + 1 ] ) ] if p_is_odd : alpha = float ( r ) / float ( degree ) left = [ ( c1 - ( alpha * c2 ) ) / ( 1 - alpha ) for c1 , c2 in zip ( ctrlpts [ r ] , pts_red [ r - 1 ] ) ] alpha = float ( r + 1 ) / float ( degree ) right = [ ( c1 - ( ( 1 - alpha ) * c2 ) ) / alpha for c1 , c2 in zip ( ctrlpts [ r + 1 ] , pts_red [ r + 1 ] ) ] pts_red [ r ] = [ 0.5 * ( pl + pr ) for pl , pr in zip ( left , right ) ] # Return computed control points after degree reduction return pts_red