4DCANAS v0.2.0 - Advanced 4D Visualization and Simulation Suite

Overview

4DCANAS is a comprehensive Python library for 4D mathematics, physics simulation, visualization, and VR/AR applications. It provides powerful tools for working with 4D objects, real-time rendering, physics engines, AI-assisted development, and game creation.

Installation

pip install 4DCANAS

For development with VR support:

pip install 4DCANAS[torch,tensorflow,viz]

Features

Complete 4D Mathematics Library
2D/3D/4D Rendering Engines
Advanced Physics Simulation (Gravity, EM, Dark Energy, Quantum)
Full VR/AR Support (All Major Headsets)
AI Assistant (MEROAI) for Development
Game Engine for Interactive Experiences
File I/O Support (OBJ, JSON, PLY, GLTF)
Professional Export Tools
Real-time Visualization
Shape Generation and Analysis

Quick Start

Basic 4D Tesseract

from 4DCANAS import Tesseract, AdvancedVisualizer4D

tesseract = Tesseract(size=1.0)
tesseract.rotate([0.1, 0.2, 0.15, 0.05])
projected, edges = tesseract.get_3d_projection()

visualizer = AdvancedVisualizer4D()
vertices_4d = [v.coords for v in tesseract.vertices]
fig = visualizer.multi_projection_view(vertices_4d, edges)

AI Assistant

from 4DCANAS import start_chat

start_chat()

Or programmatically:

from 4DCANAS import MEROAIAssistant

assistant = MEROAIAssistant()
response = assistant.chat("How do I create a rotating tesseract?")
print(response)

4D Mathematics

Point4D Operations

from 4DCANAS import Point4D, Vector4D

p1 = Point4D(1.0, 2.0, 3.0, 4.0)
p2 = Point4D(5.0, 6.0, 7.0, 8.0)

distance = p1.distance_to(p2)
projected_3d = p1.project_3d(method='perspective')
p3 = p1 + p2
p4 = p1 * 2.0

Vector4D Operations

v1 = Vector4D(1.0, 0.0, 0.0, 0.0)
v2 = Vector4D(0.0, 1.0, 0.0, 0.0)

dot_product = v1.dot(v2)
angle = v1.angle_to(v2)
normalized = v1.normalize()
projected = v1.project_onto(v2)
reflected = v1.reflect_about(v2)

Tesseract Creation and Manipulation

from 4DCANAS import Tesseract, Rotation4D

tesseract = Tesseract(center=Point4D(0, 0, 0, 0), size=2.0)

tesseract.rotate([0.1, 0.2, 0.15, 0.05, 0.03, 0.02])
tesseract.translate(Vector4D(1.0, 0.0, 0.0, 0.0))
tesseract.scale(1.5)

projections = tesseract.to_3d_projections()
orthogonal_proj = projections['orthogonal']
perspective_proj = projections['perspective']
stereographic_proj = projections['stereographic']

4D Rotations

from 4DCANAS import Rotation4D, Point4D

rotation = Rotation4D([np.pi/4, np.pi/6, np.pi/8, np.pi/12])
point = Point4D(1.0, 0.0, 0.0, 0.0)
rotated = rotation.apply(point)

composed = rotation.compose(Rotation4D([0.1, 0.2, 0.0, 0.0]))
inverse = rotation.inverse()

2D Rendering

from 4DCANAS import Renderer2D
import numpy as np

renderer = Renderer2D(width=1920, height=1080)

points = [
    np.array([-0.5, -0.5]),
    np.array([0.5, -0.5]),
    np.array([0.5, 0.5]),
    np.array([-0.5, 0.5])
]
edges = [(0, 1), (1, 2), (2, 3), (3, 0)]

canvas = renderer.render_lines_2d(points, edges)
canvas_points = renderer.render_points_2d(points, colors=[1.0, 0.8, 0.6, 0.9])
canvas_circle = renderer.render_circle_2d(np.array([0.0, 0.0]), 0.3)

3D Rendering

from 4DCANAS import Renderer3D
import numpy as np

renderer = Renderer3D(width=1920, height=1080)

renderer.set_camera(
    position=np.array([3.0, 3.0, 3.0]),
    target=np.array([0.0, 0.0, 0.0]),
    up=np.array([0.0, 1.0, 0.0])
)

vertices = [
    np.array([-1.0, -1.0, -1.0]),
    np.array([1.0, -1.0, -1.0]),
    np.array([1.0, 1.0, -1.0]),
    np.array([-1.0, 1.0, -1.0]),
    np.array([-1.0, -1.0, 1.0]),
    np.array([1.0, -1.0, 1.0]),
    np.array([1.0, 1.0, 1.0]),
    np.array([-1.0, 1.0, 1.0])
]

edges = [
    (0, 1), (1, 2), (2, 3), (3, 0),
    (4, 5), (5, 6), (6, 7), (7, 4),
    (0, 4), (1, 5), (2, 6), (3, 7)
]

canvas = renderer.render_lines_3d(vertices, edges)
canvas_points = renderer.render_points_3d(vertices)

faces = [
    [0, 1, 2, 3],
    [4, 5, 6, 7],
    [0, 1, 5, 4],
    [2, 3, 7, 6],
    [0, 3, 7, 4],
    [1, 2, 6, 5]
]
wireframe = renderer.render_wireframe_3d(vertices, faces)

4D Visualization

from 4DCANAS import AdvancedVisualizer4D, Tesseract
import matplotlib.pyplot as plt

visualizer = AdvancedVisualizer4D(figsize=(16, 12))

tesseract = Tesseract(size=1.0)
vertices_4d = [v.coords for v in tesseract.vertices]
edges = tesseract.edges

fig = visualizer.multi_projection_view(vertices_4d, edges)

fig = visualizer.visualize_with_lighting(
    vertices_4d,
    edges,
    light_position=np.array([2, 2, 2]),
    ambient_light=0.3
)

def shape_generator(t):
    tesseract_copy = Tesseract(size=1.0)
    tesseract_copy.rotate([t * 0.5, t * 0.3, t * 0.2, t * 0.1])
    vertices = [v.coords for v in tesseract_copy.vertices]
    return vertices, tesseract_copy.edges

animation = visualizer.time_evolution_animation(
    shape_generator,
    time_steps=100,
    interval=50
)

plt.show()

Physics Simulation

Basic Physics Engine

from 4DCANAS import Physics4DEngine
import numpy as np

engine = Physics4DEngine(
    gravity_vector=np.array([0, -9.81, 0, 0]),
    damping=0.99,
    time_step=0.001,
    solver='rk4'
)

engine.add_particle(
    position=np.array([0.0, 10.0, 0.0, 0.0]),
    velocity=np.array([1.0, 0.0, 0.0, 0.0]),
    mass=1.0,
    charge=0.0
)

engine.add_particle(
    position=np.array([0.0, 0.0, 0.0, 0.0]),
    velocity=np.array([0.0, 0.0, 0.0, 0.0]),
    mass=100.0,
    charge=0.0
)

for step in range(1000):
    engine.update(0.016)
    if step % 60 == 0:
        positions = [p.position for p in engine.particles]
        print(f"Step {step}: Particle 1 at {positions[0]}")

Relativity Simulation

from 4DCANAS import RelativityEngine4D

rel_engine = RelativityEngine4D(c=299792458.0)

velocity = np.array([0.9 * 299792458.0, 0.0, 0.0])
gamma = rel_engine.lorentz_factor(velocity)
energy = rel_engine.relativistic_energy(1.0, velocity)
momentum = rel_engine.relativistic_momentum(1.0, velocity)

event1 = np.array([0.0, 0.0, 0.0, 0.0])
event2 = np.array([1.0, 1.0, 0.0, 0.0])
interval = rel_engine.spacetime_interval(event1, event2)

transformed = rel_engine.lorentz_transform(event2, velocity)

Quantum Mechanics

from 4DCANAS import QuantumMechanics4D

qm = QuantumMechanics4D()

def harmonic_potential(x):
    return 0.5 * np.sum(x**2)

initial_state = np.random.randn(100).astype(complex)
initial_state = initial_state / np.linalg.norm(initial_state)

states = qm.schrodinger_equation_solver(
    potential=harmonic_potential,
    initial_state=initial_state,
    dt=1e-6,
    steps=1000
)

prob_density = qm.probability_density(states[-1])
expectation = qm.expectation_value(states[-1], np.diag(np.arange(100)))

VR/AR Support

VR Setup

from 4DCANAS import VRSession, VRDeviceType, Tesseract
import numpy as np

session = VRSession(VRDeviceType.OCULUS_QUEST_2)
session.start()

tesseract = Tesseract(size=1.0)

while session.active:
    tesseract.rotate([0.01, 0.0, 0.0, 0.0])
    vertices_4d = [v.coords for v in tesseract.vertices]
    edges = tesseract.edges
    
    left_view, right_view = session.render_frame(vertices_4d, edges)
    
    session.update(0.016)

session.stop()

Supported VR Devices

Oculus Quest / Quest 2 / Quest 3
Oculus Rift / Rift S
HTC Vive / Vive Pro / Vive Cosmos / Vive Pro 2
Valve Index
PlayStation VR / PSVR 2
Windows Mixed Reality
HP Reverb / Reverb G2
Pico Neo / Pico 4
Varjo Aero / XR-3
Meta Quest Pro
Apple Vision Pro
Generic SteamVR / OpenXR

AR System

from 4DCANAS import ARSystem
import numpy as np

ar = ARSystem(camera_resolution=(1920, 1080))

point_4d = np.array([1.0, 1.0, 1.0, 1.0])
camera_pose = np.eye(4)
projected_2d = ar.project_4d_to_ar(point_4d, camera_pose)

planes = ar.detect_planes()
anchor_id = ar.create_anchor(np.array([0.0, 0.0, 0.0]))

AI Assistant

Chat Interface

from 4DCANAS import start_chat

start_chat()

Programmatic Usage

from 4DCANAS import MEROAIAssistant

assistant = MEROAIAssistant(use_g4f=True)

response = assistant.chat("How do I create a physics simulation with gravity?")
print(response)

code = assistant.generate_code("create a rotating tesseract with VR support")
print(code)

explanation = assistant.explain_concept("4d rotation")
print(explanation)

info = assistant.get_library_info()
print(f"Library: {info['name']} v{info['version']}")

Game Engine

Basic Game

from 4DCANAS import GameEngine4D, VRDeviceType
import numpy as np

engine = GameEngine4D(vr_device=VRDeviceType.OCULUS_QUEST_2, use_physics=True)

engine.add_game_object(
    obj_id='player',
    position_4d=np.array([0.0, 0.0, 0.0, 0.0]),
    shape_type='tesseract',
    scale=1.0,
    physics_enabled=True,
    mass=1.0
)

engine.add_game_object(
    obj_id='enemy',
    position_4d=np.array([5.0, 0.0, 0.0, 0.0]),
    shape_type='tesseract',
    scale=0.5
)

def update_callback(dt):
    engine.translate_object('player', np.array([0.01, 0.0, 0.0, 0.0]))

engine.on_update(update_callback)

engine.run(max_frames=1000, target_fps=60.0)

Game Library

from 4DCANAS import GameLibrary, GameEngine4D, VRDeviceType

library = GameLibrary()

def my_game(engine):
    engine.add_game_object('object1', np.array([0, 0, 0, 0]), 'tesseract')
    engine.add_game_object('object2', np.array([2, 0, 0, 0]), 'tesseract')
    
    def game_update(dt):
        engine.rotate_object('object1', np.array([0.01, 0, 0, 0, 0, 0]))

library.register_game('my_game', my_game)

engine = GameEngine4D(vr_device=VRDeviceType.HTC_VIVE)
library.create_game('my_game', engine)
engine.run()

File Handling

Loading Files

from 4DCANAS import FileHandler4D

handler = FileHandler4D()

shape_obj = handler.load_file('model.obj')
shape_json = handler.load_file('data.json')
shape_ply = handler.load_file('points.ply')
shape_gltf = handler.load_file('scene.gltf')

tesseract = handler.convert_to_tesseract(shape_obj, target_size=2.0)

Saving Files

from 4DCANAS import FileHandler4D, Tesseract

handler = FileHandler4D()
tesseract = Tesseract(size=1.0)

shape = {
    'vertices': [v.coords for v in tesseract.vertices],
    'edges': tesseract.edges,
    'type': 'tesseract'
}

handler.save_file(shape, 'output.obj', format='obj')
handler.save_file(shape, 'output.json', format='json')
handler.save_file(shape, 'output.ply', format='ply')
handler.save_file(shape, 'output.gltf', format='gltf')

Export Formats

from 4DCANAS import AdvancedExportTools, Tesseract

tesseract = Tesseract(size=1.0)
shape = {
    'vertices': [v.coords for v in tesseract.vertices],
    'edges': tesseract.edges,
    'type': 'tesseract'
}

AdvancedExportTools.quick_export(shape, format='obj', filename='tesseract.obj')
AdvancedExportTools.quick_export(shape, format='json', filename='tesseract.json')
AdvancedExportTools.quick_export(shape, format='gltf', filename='tesseract.gltf')
AdvancedExportTools.quick_export(shape, format='ply', filename='tesseract.ply')

Advanced Examples

Complete VR Experience with Physics

from 4DCANAS import (
    VRSession, VRDeviceType, Tesseract, 
    Physics4DEngine, GameEngine4D
)
import numpy as np

game = GameEngine4D(
    vr_device=VRDeviceType.META_QUEST_3,
    use_physics=True
)

game.add_game_object(
    'tesseract1',
    np.array([0.0, 0.0, 0.0, 0.0]),
    'tesseract',
    1.0,
    physics_enabled=True,
    mass=1.0
)

def game_loop():
    game.update(0.016)
    canvas = game.render('vr')

game.run(target_fps=72.0)

AI-Powered Shape Generation

from 4DCANAS import AutoGenerator4D, DeepAnalyzer4D, AdvancedVisualizer4D

generator = AutoGenerator4D()
analyzer = DeepAnalyzer4D()
visualizer = AdvancedVisualizer4D()

shapes = []
for seed in range(10):
    shape = generator.generate_shape("complex rotating polytope", seed=seed)
    analysis = analyzer.analyze_shape(shape['vertices'], shape['edges'])
    
    if analysis['aesthetic_score'] > 0.7:
        shapes.append(shape)
        fig = visualizer.multi_projection_view(
            shape['vertices'],
            shape['edges']
        )

Multi-dimensional Visualization Pipeline

from 4DCANAS import (
    Tesseract, Renderer2D, Renderer3D, Renderer4D,
    AdvancedVisualizer4D
)

tesseract = Tesseract(size=1.0)
tesseract.rotate([0.1, 0.2, 0.15, 0.05])

vertices_4d = [v.coords for v in tesseract.vertices]
edges = tesseract.edges

renderer_2d = Renderer2D(1920, 1080)
renderer_3d = Renderer3D(1920, 1080)
renderer_4d = Renderer4D(1920, 1080)

vertices_2d = [v[:2] for v in vertices_4d]
vertices_3d = [v[:3] for v in vertices_4d]

canvas_2d = renderer_2d.render_lines_2d(vertices_2d, edges)
canvas_3d = renderer_3d.render_lines_3d(vertices_3d, edges)
canvas_4d = renderer_4d.render_4d(vertices_4d, edges)

API Reference

Core Classes

Point4D(x, y, z, w) - 4D point with projection methods
Vector4D(x, y, z, w) - 4D vector with operations
Tesseract(center, size) - 4D hypercube
Rotation4D(angles) - 4D rotation matrices
Matrix4D(matrix) - 4x4 matrix operations
Quaternion4D(w, x, y, z) - 4D quaternions

Physics Classes

Physics4DEngine() - Physics simulation engine
RelativityEngine4D(c) - Relativistic calculations
QuantumMechanics4D() - Quantum mechanics solver
Particle4D - Particle data structure

Rendering Classes

Renderer2D(width, height) - 2D rendering
Renderer3D(width, height) - 3D rendering
Renderer4D(width, height) - 4D rendering
AdvancedVisualizer4D() - Advanced visualization

VR Classes

VRSession(device_type) - VR session management
VRSystem(device_type) - VR device interface
VRRenderer(vr_system) - VR rendering
ARSystem() - AR system

AI Classes

MEROAIAssistant(use_g4f) - AI assistant
ChatBot(assistant) - Chat interface

Game Classes

GameEngine4D(vr_device, use_physics) - Game engine
GameObject - Game object data
GameLibrary() - Game library

File Handling

FileHandler4D() - File I/O operations

Performance Tips

Use np.float64 for precision in 4D calculations
Batch operations when possible
Use Physics4DEngine.simulate() for long simulations
Enable GPU acceleration where available
Cache projections for static objects
Use appropriate projection methods for your use case

Contributing

Contributions welcome! Areas of interest:

Additional 4D shapes
Physics simulations
Visualization methods
VR/AR improvements
Performance optimizations

License

MIT License

Author

MERO (mero@ps.com)

Version

0.2.0

Support

For questions and support:

Use MEROAI assistant: from 4DCANAS import start_chat; start_chat()
Check documentation and examples
Review test files for usage patterns

Name		Name	Last commit message	Last commit date
Latest commit History 1 Commit
README.md		README.md
__init__.py		__init__.py
ai.py		ai.py
ai_assistant.py		ai_assistant.py
algorithms.py		algorithms.py
cli.py		cli.py
core.py		core.py
export.py		export.py
file_handler.py		file_handler.py
game_engine.py		game_engine.py
physics.py		physics.py
pyproject.toml		pyproject.toml
rendering_2d_3d.py		rendering_2d_3d.py
setup.py		setup.py
test_2d.py		test_2d.py
test_3d.py		test_3d.py
test_4d.py		test_4d.py
test_ai_assistant.py		test_ai_assistant.py
test_file_handler.py		test_file_handler.py
test_game_engine.py		test_game_engine.py
test_physics.py		test_physics.py
test_vr.py		test_vr.py
visualization.py		visualization.py
vr.py		vr.py

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4DCANAS v0.2.0 - Advanced 4D Visualization and Simulation Suite

Overview

Table of Contents

Installation

Features

Quick Start

Basic 4D Tesseract

AI Assistant

4D Mathematics

Point4D Operations

Vector4D Operations

Tesseract Creation and Manipulation

4D Rotations

2D Rendering

3D Rendering

4D Visualization

Physics Simulation

Basic Physics Engine

Relativity Simulation

Quantum Mechanics

VR/AR Support

VR Setup

Supported VR Devices

AR System

AI Assistant

Chat Interface

Programmatic Usage

Game Engine

Basic Game

Game Library

File Handling

Loading Files

Saving Files

Export Formats

Advanced Examples

Complete VR Experience with Physics

AI-Powered Shape Generation

Multi-dimensional Visualization Pipeline

API Reference

Core Classes

Physics Classes

Rendering Classes

VR Classes

AI Classes

Game Classes

File Handling

Performance Tips

Contributing

License

Author

Version

Support

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