3D Playground - Python 3D engine.

TL;DR: Basic 3D world playground with animations and camera completely from scratch using 2D surface/canvas.

This implementation / API only for demonstration and playground purposes based on Perspective projection.
Can be used on top of any 2d graphics engine/lib(frame buffers, sdl and etc.)

Not implemented features due to low performance:

• Face clipping not implemented, vertices clipping ignored too
• Flat shading and Gouraud shading not implemented.
• Z-buffering

models.Model API is open demonstration of MVP model and is definitely a good starting point/topic for 3D graphics.

Also you can plot any function on 3D scene.

• Install
• How to use
• Model View Projection
  • Projection
  • Camera
    • Camera scene example
• Mesh and Wireframe
• Rasterization
• 3D Plotting
• Basic Wavefront .obj format support
• Model API
• Trajectory API
• Pygame Example

Install

pip install play3d

How to use

There is only one requirement - to provide 2D pixel and line renderer(drawer)

As current example uses pygame,

pip install pygame==2.0.1 # recommended version
# You have to install sdl lib separately
# for Mac OS:
brew install sdl2 sdl2_gfx sdl2_image sdl2_mixer sdl2_net sdl2_ttf

from play3d.three_d import Device
import pygame

# our adapter will rely on pygame renderer
put_pixel = lambda x, y, color: pygame.draw.circle(screen, color, (x, y), 1)
# we certainly can draw lines ourselves using put_pixel three_d.drawline
# but implementation below - much faster
line_adapter = lambda p1, p2, color: pygame.draw.line(screen, color, (p1[x], p1[y]), (p2[x], p2[y]), 1)

width, height = 1024, 768 # should be same as 2D provider 
Device.viewport(width, height)
Device.set_renderer(put_pixel, line_adapter)
screen = pygame.display.set_mode(Device.get_resolution())

That's all we need for setting up environment. Now we can create and render model objects by calling Model.draw() at each frame update (See Example)
To create model you can simply pass 3D world vertices as 2-d list Model(data=data)

It is possible to provide faces as 2d array Model(data=data, faces=faces). Face index starts from 1. Only triangles supported. For more information see below.

Simply by providing 3D (or 4D homogeneous where w=1) data vertices list - Model transforms this coordinates from 3D world space to projected screen space

from play3d.models import Model

# our 2D library renderer setup.. See above.

# Cube model. Already built-in `models.Cube`  
cube = Model(position=(0, 0, 0),
                 data=[
                    [-1, 1, 1, 1],
                    [1, 1, 1, 1],
                    [-1, -1, 1, 1],
                    [1, -1, 1, 1],
                    [-1, 1, -1, 1],
                    [1, 1, -1, 1],
                    [1, -1, -1, 1],
                    [-1, -1, -1, 1]
                ])
while True: # your render lib/method
    cube.draw()

Model View Projection

models.Model and three_d.Camera implements all MVP(See Model.draw).

Projection

Here we use perspective projection matrix
Z axis of clipped cube(from frustum) mapped to [-1, 1] and our camera directed to -z axis (OpenGL convention)
Projection Matrix can be tuned there (aspect ratio, FOV and etc.) \

Camera.near = 1
Camera.far = 10
Camera.fov = 60
Camera.aspect_ratio = 3/4

World camera

By OpenGL standard we basically move our scene. Facing direction considered when we move our camera in case of rotations(direction vector will be transformed too)
Camera can be moved through three_d.Camera API:

from play3d.three_d import Camera
camera = Camera.get_instance()

# move camera to x, y, z with 0.5 step considering facing direction
camera['x'] += 0.5
camera['y'] += 0.5
camera['z'] += 0.5

camera.move(0.5, 0.5, 0.5) # identical above

# rotate camera to our left on XZ plane
camera.rotate('y', 2) # 

Camera keys example

Mesh and Wireframe

To exploit mesh one should provide both data and faces. Face represents triple group of vertices index referenced from data. Face index starts from 1.
By default object rendered as wireframe

from play3d.models import Model
triangle = Model(position=(-5, 3, -4),
                 data=[
                     [-3, 1, -7, 1],
                     [-2, 2, -7, 1],
                     [-1, 0, -7, 1],
                 ], faces=[[1, 2, 3]])

Rasterization

By default if data and faces provided, rasterization will be enabled.
For rasterization we use - standard slope algorithm with horizontal filling lines.

from play3d.models import Model

white = (230, 230, 230)
suzanne = Model.load_OBJ('suzanne.obj.txt', position=(-4, 2, -6), color=white, rasterize=True)
suzanne_wireframe = Model.load_OBJ('suzanne.obj.txt', position=(-4, 2, -6), color=white)
suzanne.rotate(0, -14)
suzanne_wireframe.rotate(0, 14)

3D plotting

You can plot any function you want by providing parametric equation as func(*parameters) -> [x, y, z]. For example, sphere and some awesome wave both polar and parametric equations(Sphere built-in as Models.Sphere):

import math
from play3d.models import Plot

def fn(phi, theta):

    return [
        math.sin(phi * math.pi / 180) * math.cos(theta * math.pi / 180),
        math.sin(theta * math.pi / 180) * math.sin(phi * math.pi / 180),
        math.cos(phi * math.pi / 180)
    ]

sphere_model = Plot(func=fn, allrange=[0, 360], position=(-4, 2, 1), color=(0, 64, 255))

blow_your_head = Plot(
    position=(-4, 2, 1), color=(0, 64, 255),
    func=lambda x, t: [x, math.cos(x) * math.cos(t), math.cos(t)], allrange=[0, 2*math.pi], interpolate=75
)

OBJ format

Wawefront format is widely used as a standard in 3D graphics

You can import your model here. Only vertices and faces supported.
Model.load_OBJ(cls, path_or_url, wireframe=False, **all_model_kwargs)

You can find examples here github.com/alecjacobson/common-3d-test-models

You might have to normalize(scale and etc.)each .obj sample differently
Only vertices and faces are supported.

Model.load_OBJ('beetle.obj.txt', wireframe=True, color=white, position=(-2, 2, -4), scale=3)

Models API

Models.Model

Fields	Description
position	tuple=(0, 0, 0) with x, y, z world coordinates
scale	integer(=1)
color	tuple (255, 255, 255)
data	list[[x, y, z, [w=1]]] - Model vertices(points)
faces	list[[A, B, C]] - Defines triangles See: Mesh and Wireframe
rasterize	bool(=True) - Rasterize - "fill" an object
shimmering	bool(=False) - color flickering/dancing

# Initial Model Matrix
model.matrix = Matrix([
                          [1 * scale, 0, 0, 0],
                          [0, 1 * scale, 0, 0],
                          [0, 0, 1 * scale, 0],
                          [*position, 1]
                      ])

Methods

• model_obj @ translate(x, y, z)

  translates object's model matrix (in world space)

• rotate(self, angle_x, angle_y=0, angle_z=0)

  Rotates object relative to particular axis plane. First object translated from the world space back to local origin, then we rotate the object

• route(self, trajectory: 'Trajectory', enable_trace=False)

  Set the function-based trajectory routing for the object.

  • trajectory Trajectory - trajectory state
  • enable_trace bool - Keep track of i.e. draw trajectory path (breadcrumbs)

Trajectory API

Models.Trajectory

Fields	Description
func	func Parametrized math function which takes *args and returns world respective coordinates tuple=(x, y, z)

To move our object through defined path we can build Trajectory for our object. You can provide any parametric equation with args.
World coordinates defined by func(*args) tuple output.

Example

import math

from play3d.models import Sphere, Trajectory
white = (230, 230, 230)
moving_sphere = Sphere(position=(1, 3, -5), color=white, interpolate=50)
moving_sphere.route(Trajectory.ToAxis.Z(speed=0.02).backwards())

whirling_sphere = Sphere(position=(1, 3, -5), color=white, interpolate=50)
# Already built-in as Trajectory.SineXY(speed=0.1)
whirling_sphere.route(Trajectory(lambda x: [x, math.sin(x)], speed=0.1))


while True: # inside your "render()"
    moving_sphere.draw()
    whirling_sphere.draw()

Pygame example

import logging
import sys

import pygame

from play3d.models import Model, Grid
from pygame_utils import handle_camera_with_keys # custom keyboard handling - moving camera 
from play3d.three_d import Device, Camera
from play3d.utils import capture_fps

logging.basicConfig(stream=sys.stdout, level=logging.INFO)

black, white = (20, 20, 20), (230, 230, 230)


Device.viewport(1024, 768)
pygame.init()
screen = pygame.display.set_mode(Device.get_resolution())

# just for simplicity - array access, we should avoid that
x, y, z = 0, 1, 2

# pygame sdl line is faster than default one
line_adapter = lambda p1, p2, color: pygame.draw.line(screen, color, (p1[x], p1[y]), (p2[x], p2[y]), 1)
put_pixel = lambda x, y, color: pygame.draw.circle(screen, color, (x, y), 1)

Device.set_renderer(put_pixel, line_renderer=line_adapter)

grid = Grid(color=(30, 140, 200), dimensions=(30, 30))

# be aware of different scaling of .obj samples. Only vertices and faces supported! 
suzanne = Model.load_OBJ(
  'https://raw.githubusercontent.com/OpenGLInsights/OpenGLInsightsCode/master/Chapter%2026%20Indexing%20Multiple%20Vertex%20Arrays/article/suzanne.obj',
  position=(3, 2, -7), color=white, rasterize=True)
beetle = Model.load_OBJ(
  'https://raw.githubusercontent.com/alecjacobson/common-3d-test-models/master/data/beetle.obj',
   wireframe=False, color=white, position=(0, 2, -11), scale=3)
beetle.rotate(0, 45, 50)

camera = Camera.get_instance()
# move our camera up and back a bit, from origin
camera.move(y=1, z=2)


@capture_fps
def frame():
    if pygame.event.get(pygame.QUIT):
        sys.exit(0)

    screen.fill(black)
    handle_camera_with_keys()  # to move our camera - walk, can be ignored
    grid.draw()
    beetle.draw()
    suzanne.rotate(0, 1, 0).draw()
    pygame.display.flip()


while True:

    frame()