3D Projection in pygame

Question

I'm trying to create a simple 3d rendering of a cube. As in this video from the Coding Train: https://www.youtube.com/watch?v=p4Iz0XJY-Qk on minute 14. I got stuck at one point. Since I'm pretty new to all of this, I'm not exactly sure what's causing my issue. When I start the project, the cube rotates as I want it to, but moves away from the screen to the left and it looks like it's making a circle.

import pygame
import numpy as np
import os
import math

WHITE = (255,255,255)
width, height = 700, 700
screen = pygame.display.set_mode((width, height))
clock = pygame.time.Clock()

points = []
angle = 0

points.append(np.array([[300], [250], [1]]))
points.append(np.array([[300], [350], [1]]))
points.append(np.array([[400], [250], [1]]))
points.append(np.array([[400], [350], [1]]))

projectionMatrix = np.array([[1, 0, 0],
                             [0, 1, 0]])

while True:
    clock.tick(30)
    screen.fill((0,0,0))

    rotation = np.array([[math.cos(angle), -math.sin(angle)],
                         [math.sin(angle), math.cos(angle)]])

    for event in pygame.event.get():
            if event.type == pygame.QUIT:
                os._exit(1)

    for point in points:
        projected2d = np.dot(projectionMatrix, point)
        rotated = np.dot(rotation, projected2d)
        pygame.draw.circle(screen, WHITE, (int(rotated[0][0]), int(rotated[1][0])), 5)

    angle += 0.01
    pygame.display.update()

I would really appreciate any help to why this is happening and how I could fix it so it's just rotating around.

There is no bug in this code. The points rotate around the top left (0, 0). Most likely you have to look the tutorial to the end. — Rabbid76, Sep 17 '20 at 18:35
The video is in Processing. Its not python. I have the exact same matricies and he doesnt have such a problem. Thats what im asking. Why is it rotating? — , Sep 17 '20 at 18:50
p5.js uses a different coordinate system. In p5.js (0, 0) can be translated to the center of the screen. — Rabbid76, Sep 17 '20 at 18:50

Rabbid76 · Accepted Answer · 2020-09-17T19:27:12.047

There is no bug in this code. The points rotate around the top left (0, 0). Note, In 3D mode, p5.js uses a different coordinate system than pygame.

If you want to rotate the dots around the centre of the window, then define the points in range [-1, 1] (normalized device space:

points.append(np.matrix([ 0.5,  0.5, 1]))
points.append(np.matrix([ 0.5, -0.5, 1]))
points.append(np.matrix([-0.5,  0.5, 1]))
points.append(np.matrix([-0.5, -0.5, 1]))

Define a projection matrix from the range[-1, 1] to window space:

projectionMatrix = np.matrix([[height/2, 0, width/2],
                              [0, height/2, height/2]])

Specify a 3x3 rotation matrix:

rotation = np.array([[math.cos(angle), -math.sin(angle), 0],
                     [math.sin(angle), math.cos(angle), 0],
                     [0, 0, 1]])

First rotate the points, then project it to the window:

projected2d = projectionMatrix * rotation * point.reshape((3, 1))

Complete example:

import pygame
import numpy as np
import os
import math

WHITE = (255,255,255)
width, height = 400, 300
screen = pygame.display.set_mode((width, height))
clock = pygame.time.Clock()

points = []
angle = 0

points.append(np.matrix([ 0.5,  0.5, 1]))
points.append(np.matrix([ 0.5, -0.5, 1]))
points.append(np.matrix([-0.5,  0.5, 1]))
points.append(np.matrix([-0.5, -0.5, 1]))

projectionMatrix = np.matrix([[height/2, 0, width/2],
                             [0, height/2, height/2]])

while True:
    clock.tick(30)
    screen.fill((0,0,0))

    rotation = np.matrix([[math.cos(angle), -math.sin(angle), 0],
                         [math.sin(angle), math.cos(angle), 0],
                         [0, 0, 1]])

    for event in pygame.event.get():
            if event.type == pygame.QUIT:
                os._exit(1)

    for point in points:
        projected2d = projectionMatrix * rotation * point.reshape((3, 1))
        pygame.draw.circle(screen, WHITE, (int(projected2d[0][0]), int(projected2d[1][0])), 5)

    angle += 0.01
    pygame.display.update()

3D Projection in pygame

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