python - Pygame rotating cubes around axis

Question

I have been playing around with the example of a rotating cube here. I have generated 2 cubes that should rotate around the Y-axis. However, it doesn't seem to work as expected and I can't figure out what the problem of it is.

Here is a working code example:

import sys
import math
import pygame

from pygame.math import Vector3
from enum import Enum


class Color(Enum):
    BLACK = (0, 0, 0)
    SILVER = (192,192,192)


class Cube():

    def __init__(self, vectors, screen_width, screen_height, initial_angle=25):
        self._vectors = vectors
        self._angle = initial_angle
        self._screen_width = screen_width
        self._screen_height = screen_height

        # Define the vectors that compose each of the 6 faces
        self._faces  = [(0,1,2,3),
                       (1,5,6,2),
                       (5,4,7,6),
                       (4,0,3,7),
                       (0,4,5,1),
                       (3,2,6,7)]

        self._setup_initial_positions(initial_angle)

    def _setup_initial_positions(self, angle):
        tmp = []
        for vector in self._vectors:
            rotated_vector = vector.rotate_x(angle).rotate_y(angle)#.rotateZ(self.angle)
            tmp.append(rotated_vector)

        self._vectors = tmp

    def transform_vectors(self, new_angle):
        # It will hold transformed vectors.
        transformed_vectors = []

        for vector in self._vectors:
            # Rotate the point around X axis, then around Y axis, and finally around Z axis.
            mod_vector = vector.rotate_y(new_angle)
            # Transform the point from 3D to 2D
            mod_vector = self._project(mod_vector, self._screen_width, self._screen_height, 256, 4)
            # Put the point in the list of transformed vectors
            transformed_vectors.append(mod_vector)

        return transformed_vectors

    def _project(self, vector, win_width, win_height, fov, viewer_distance):
        factor = fov / (viewer_distance + vector.z)
        x = vector.x * factor + win_width / 2
        y = -vector.y * factor + win_height / 2
        return Vector3(x, y, vector.z)

    def calculate_average_z(self, vectors):
        avg_z = []
        for i, face in enumerate(self._faces):
            # for each point of a face calculate the average z value
            z = (vectors[face[0]].z + 
                 vectors[face[1]].z + 
                 vectors[face[2]].z + 
                 vectors[face[3]].z) / 4.0
            avg_z.append([i, z])

        return avg_z

    def get_face(self, index):
        return self._faces[index]

    def create_polygon(self, face, transformed_vectors):
        return [(transformed_vectors[face[0]].x, transformed_vectors[face[0]].y), 
                (transformed_vectors[face[1]].x, transformed_vectors[face[1]].y),
                (transformed_vectors[face[2]].x, transformed_vectors[face[2]].y),
                (transformed_vectors[face[3]].x, transformed_vectors[face[3]].y),
                (transformed_vectors[face[0]].x, transformed_vectors[face[0]].y)]


class Simulation:
    def __init__(self, win_width=640, win_height=480):
        pygame.init()

        self.screen = pygame.display.set_mode((win_width, win_height))

        self.clock = pygame.time.Clock()

        cube = Cube([
            Vector3(0, 0.5, -0.5),
            Vector3(0.5, 0.5, -0.5),
            Vector3(0.5, 0, -0.5),
            Vector3(0, 0, -0.5),
            Vector3(0, 0.5, 0),
            Vector3(0.5, 0.5, 0),
            Vector3(0.5, 0, 0),
            Vector3(0, 0, 0)
        ], win_width, win_height)

        cube2 = Cube([
            Vector3(0.5, 0.5, -0.5),
            Vector3(1, 0.5, -0.5),
            Vector3(1, 0, -0.5),
            Vector3(0.5, 0, -0.5),
            Vector3(0.5, 0.5, 0),
            Vector3(1, 0.5, 0),
            Vector3(1, 0, 0),
            Vector3(0.5, 0, 0)
        ], win_width, win_height)

        self._angle = 30

        self._cubes = [cube, cube2]

    def run(self):
        while True:
            for event in pygame.event.get():
                if event.type == pygame.QUIT:
                    pygame.quit()
                    sys.exit()

            self.clock.tick(50)
            self.screen.fill(Color.BLACK.value)

            for cube in self._cubes:
                transformed_vectors = cube.transform_vectors(self._angle)
                avg_z = cube.calculate_average_z(transformed_vectors)

                # Draw the faces using the Painter's algorithm:
                # Distant faces are drawn before the closer ones.
                for avg_z in sorted(avg_z, key=lambda x: x[1], reverse=True):
                    face_index = avg_z[0]
                    face = cube._faces[face_index]
                    pointlist = cube.create_polygon(face, transformed_vectors)

                    pygame.draw.polygon(self.screen, Color.SILVER.value,pointlist)
                    pygame.draw.polygon(self.screen, Color.BLACK.value, pointlist, 3)
                    # break 

            self._angle += 1

            pygame.display.flip()

if __name__ == "__main__":
    Simulation().run()

Both cubes should rotate around the Y-axis in this example. For the future I'd like to have a solution so they can rotate around any axis.

Answer 1

It is not sufficient to sort the faces of each cube separately by its depth. You've to sort the faces of all objects of the entire scene by its depth.

Create a list of tuples, which consists of the projected (transformed) points ofa face and the average depth (z value):

polygons = []
for cube in self._cubes:
    transformed_vectors = cube.transform_vectors(self._angle)
    avg_z = cube.calculate_average_z(transformed_vectors)
    for z in avg_z:
        face_index = z[0]
        face = cube._faces[face_index]
        pointlist = cube.create_polygon(face, transformed_vectors)
        polygons.append((pointlist, z[1]))

Draw the faces of all objects in (reverse) sorted order:

for poly in sorted(polygons, key=lambda x: x[1], reverse=True):
    pygame.draw.polygon(self.screen, Color.SILVER.value,poly[0])
    pygame.draw.polygon(self.screen, Color.BLACK.value, poly[0], 3)

---

Minimal example: repl.it/@Rabbid76/PyGame-3D

import math
import pygame

def project(vector, w, h, fov, distance):
    factor = math.atan(fov / 2 * math.pi / 180) / (distance + vector.z)
    x = vector.x * factor * w + w / 2
    y = -vector.y * factor * w + h / 2
    return pygame.math.Vector3(x, y, vector.z)

def rotate_vertices(vertices, angle, axis):
    return [v.rotate(angle, axis) for v in vertices]
def scale_vertices(vertices, s):
    return [pygame.math.Vector3(v[0]*s[0], v[1]*s[1], v[2]*s[2]) for v in vertices]
def translate_vertices(vertices, t):
    return [v + pygame.math.Vector3(t) for v in vertices]
def project_vertices(vertices, w, h, fov, distance):
    return [project(v, w, h, fov, distance) for v in vertices]

class Mesh():

    def __init__(self, vertices, faces):
        self.__vertices = [pygame.math.Vector3(v) for v in vertices]
        self.__faces = faces

    def rotate(self, angle, axis):
        self.__vertices = rotate_vertices(self.__vertices, angle, axis)
    def scale(self, s):
        self.__vertices = scale_vertices(self.__vertices, s)
    def translate(self, t):
        self.__vertices = translate_vertices(self.__vertices, t)

    def calculate_average_z(self, vertices):
        return [(i, sum([vertices[j].z for j in f]) / len(f)) for i, f in enumerate(self.__faces)]

    def get_face(self, index):
        return self.__faces[index]
    def get_vertices(self):
        return self.__vertices

    def create_polygon(self, face, vertices):
        return [(vertices[i].x, vertices[i].y) for i in [*face, face[0]]]
       
class Scene:
    def __init__(self, mehses, fov, distance):
        self.meshes = mehses
        self.fov = fov
        self.distance = distance 
        self.euler_angles = [0, 0, 0]

    def transform_vertices(self, vertices, width, height):
        transformed_vertices = vertices
        axis_list = [(1, 0, 0), (0, 1, 0), (0, 0, 1)]
        for angle, axis in reversed(list(zip(list(self.euler_angles), axis_list))):
            transformed_vertices = rotate_vertices(transformed_vertices, angle, axis)
        transformed_vertices = project_vertices(transformed_vertices, width, height, self.fov, self.distance)
        return transformed_vertices

    def draw(self, surface):
        
        polygons = []
        for mesh in self.meshes:
            transformed_vertices = self.transform_vertices(mesh.get_vertices(), *surface.get_size())
            avg_z = mesh.calculate_average_z(transformed_vertices)
            for z in avg_z:
            #for z in sorted(avg_z, key=lambda x: x[1], reverse=True):
                pointlist = mesh.create_polygon(mesh.get_face(z[0]), transformed_vertices)
                polygons.append((pointlist, z[1]))
                #pygame.draw.polygon(surface, (128, 128, 192), pointlist)
                #pygame.draw.polygon(surface, (0, 0, 0), pointlist, 3)

        for poly in sorted(polygons, key=lambda x: x[1], reverse=True):
            pygame.draw.polygon(surface, (128, 128, 192), poly[0])
            pygame.draw.polygon(surface, (0, 0, 0), poly[0], 3)
        

vertices = [(-1,-1,1), (1,-1,1), (1,1,1), (-1,1,1), (-1,-1,-1), (1,-1,-1), (1,1,-1), (-1,1,-1)]
faces = [(0,1,2,3), (1,5,6,2), (5,4,7,6), (4,0,3,7), (3,2,6,7), (1,0,4,5)]

cube_origins = [(-1, -1, 0), (0, -1, 0), (1, -1, 0), (1, 0, 0), (1, 1, 0), (0, 1, 0), (-1, 1, 0), (-1, 0, 0)]
meshes = []
for origin in cube_origins:
    cube = Mesh(vertices, faces)
    cube.scale((0.5, 0.5, 0.5))
    cube.translate(origin)
    meshes.append(cube)

scene = Scene(meshes, 90, 5)

pygame.init()
window = pygame.display.set_mode((400, 300))
clock = pygame.time.Clock()

run = True
while run:
    clock.tick(60)
    for event in pygame.event.get():
        if event.type == pygame.QUIT:
            run = False

    window.fill((255, 255, 255))
    scene.draw(window)
    scene.euler_angles[1] += 1
    pygame.display.flip()

pygame.quit()