Generates a uniform knot vector for NURBS evaluations

generate_knot_vector.py

import numpy as np

def generate_knot_vector(degree, num_ctrlpts, **kwargs):
    """ Generates a uniform knot vector.

    Example
    -------

    >>> generate_knot_vector(3, 7, datatype=np.float32)
    array([0.  , 0.  , 0.  , 0.  , 0.25, 0.5 , 0.75, 1.  , 1.  , 1.  , 1.  ], dtype=float32)

    :param degree: degree
    :param num_ctrlpts: number of control points
    :return: generated knot vector
    """
    dt = kwargs.get('datatype', np.float32)

    # Equation to use: m = n + p + 1
    # p: degree, n+1: number of control points; m+1: number of knots
    m = degree + num_ctrlpts + 1

    # Initialize the knot vector with zeros
    knot_vector = np.zeros(m, dtype=dt)

    # Calculate a uniform interval for middle knots
    num_segments = num_ctrlpts - (degree + 1)  # number of knots in the middle
    middle_knots = np.linspace(0.0, 1.0, num=num_segments + 2)  # add 0 and 1

    # Middle knots
    knot_vector[degree:-degree] = middle_knots

    # Last knots
    knot_vector[-degree:] = 1.0

    return knot_vector