4DCANAS 0.2.0

Advanced 4D Visualization and Simulation Suite

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.

Table of Contents

1. Installation
2. Features
3. Quick Start
4. 4D Mathematics
5. 2D Rendering
6. 3D Rendering
7. 4D Visualization
8. Physics Simulation
9. VR/AR Support
10. AI Assistant
11. Game Engine
12. File Handling
13. Export Formats
14. Advanced Examples
15. API Reference

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

1. Use np.float64 for precision in 4D calculations
2. Batch operations when possible
3. Use Physics4DEngine.simulate() for long simulations
4. Enable GPU acceleration where available
5. Cache projections for static objects
6. 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 ([e-mail])

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