Spinning Donut

donut.py

import numpy as np
import pyglet

def draw_points(points, format="v2f"):
    pyglet.graphics.draw(
        len(points),
        pyglet.gl.GL_POINTS,
        (format, tuple([x for p in points for x in p]))
    )


def rotate_x(angle):
    return [
        [1, 0, 0],
        [0, np.cos(angle), -np.sin(angle)],
        [0, np.sin(angle), np.cos(angle)]
    ]


def rotate_y(angle):
    return [
        [np.cos(angle), 0, np.sin(angle)],
        [0, 1, 0],
        [-np.sin(angle), 0, np.cos(angle)]
    ]


def rotate_z(angle):
    return [
        [np.cos(angle), -np.sin(angle), 0],
        [np.sin(angle), np.cos(angle), 0],
        [0, 0, 1]
    ]

def generate_donut_points(scale=100):
    radius = 1
    center = [1.5, 0, 0]
    circle = [
        np.array(center) + [radius * np.cos(t), radius * np.sin(t), 0]
        for t in np.linspace(0, 2 * np.pi, 50)
    ]

    return [
        scale * np.dot(rotate_y(angle), point)
        for angle in np.linspace(0, 2 * np.pi, 100)
        for point in circle
    ]


window = pyglet.window.Window(1000, 1000, caption="Donut")
center = np.array([window.height // 2, window.width // 2, 0])
rotation = np.dot(
    np.dot(
        rotate_x(np.pi / 100),
        rotate_y(np.pi / 150)
    ),
    rotate_z(np.pi / 200)
)
projection = [[1, 0, 0], [0, 1, 0]]

points = generate_donut_points()
projected = []

def update_points(value):
    global points, projected
    points = np.transpose(np.dot(rotation, np.transpose(points)))
    projected = np.transpose(np.dot(projection, np.transpose(center + points)))

@window.event
def on_draw():
    window.clear()
    draw_points(projected)


pyglet.clock.schedule_interval(update_points, 0.01)
pyglet.app.run()