# -*- coding: utf-8 -*-
r"""Plot a curve in three-dimensions.
"""
import numpy as np
import matplotlib.pyplot as plt


def curve(x, y, z, t_range):
    r"""Plot a curve in three-dimensions.

    :param x: the :math:`x(t)` parametric function.
    :param y: the :math:`y(t)` parametric function.
    :param z: the :math:`z(t)` parametric function.
    :param t_range: the range of the parameter :math:`t`.
    """
    ax = plt.figure().add_subplot(projection='3d')
    t = np.linspace(t_range[0], t_range[1], 1000)
    x_values = x(t)
    y_values = y(t)
    z_values = z(t)
    ax.plot(x_values, y_values, z_values, label='parametric curve')
    ax.legend()
    ax.set_xlabel('x')
    ax.set_ylabel('y')
    ax.set_zlabel('z')
    plt.show()


if __name__ == '__main__':
    a = 1
    b = 1
    w = 2 * np.pi

    def x(t):  # the parametric function x(t)
        return a * np.cos(w * t)

    def y(t):  # the parametric function y(t)
        return a * np.sin(w * t)

    def z(t):  # the parametric function z(t)
        return b * t

    curve(x, y, z, [0, 3])