Python 3D Orbital Physics Engine

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Project Overview

A custom-built 3D rendering and physics engine written in pure Python. This project demonstrates a from-scratch implementation of the graphics pipeline (rasterization, matrix transformations) and Newtonian orbital mechanics without relying on external game engines or 3D libraries (like OpenGL or Unity).

Features

1. Custom Graphics Pipeline

• Software Rasterizer: Implements 3D-to-2D projection, viewport scaling, and wireframe/filled polygon rendering using Pygame only for the final pixel buffer.
• Matrix Mathematics: Custom Matrix4 and Vector3 classes handling Translation, Rotation, Scaling, and Perspective Projection.
• Visuals: Supports flat shading (Dot Product lighting), back-face culling, and z-depth sorting (Painter's Algorithm).

2. Physics Simulation

• Newtonian Gravity: Implements Universal Gravitation ($F = G \frac{m_1 m_2}{r^2}$) for realistic orbital trajectories.
• Collision Detection: Simple radial collision detection with surface constraint resolution.
• Vector Visualization: Real-time rendering of Velocity, Gravity, and Heading vectors for debugging flight forces.

3. Flight Systems

• 5-DOF Control: Full pitch, yaw, and thrust controls.
• Time Warp: Dynamic time-step simulation allowing 1x to 50x simulation speeds.
• Instrumentation: Heads-Up Display (HUD) showing altitude, orbital velocity, and camera modes.

Controls

Key	Action
W / S	Pitch Nose Down / Up
Mouse	Look Around (Yaw / Pitch)
R	Reset Time Warp (1x)
T	Time Warp (10x)
Y	Time Warp (50x)
V	Toggle Physics Vector Overlay
C	Switch Camera Mode (Chase / Follow / Free)
ESC	Exit Simulation

Technical Implementation

The engine uses a Right-Handed Coordinate System. The core loop performs the following steps:

1. Physics Step: Applies gravity forces and updates velocity/position vectors.
2. Camera Step: Generates the View Matrix based on camera mode (Euler Angles).
3. Pipeline Step:
   • Transforms local mesh vertices to World Space.
   • Applies View and Projection matrices.
   • Performs Perspective Division ($x/w, y/w$).
   • Rasterizes triangles to the screen buffer.

Dependencies

• Python 3.x
• Pygame (for window management and 2D drawing primitives)