Algorithmic Computer Animation & Physics Simulation
A comprehensive suite of physics-based simulation and character animation modules bridging theoretical mathematics with interactive graphics. This collection features custom numerical solvers, rigid body dynamics, inverse kinematics, and deep reinforcement learning.
Key Implementations
- Spline Interpolation: Implemented Bezier, B-spline, and Catmull-Rom splines to generate smooth keyframe trajectories.
- Physics Integrators: Built and compared numerical integration methods—including Explicit Euler, Midpoint, RK4, and Implicit Euler—for accurate free-fall modeling.
- Tinkertoy Constraints: Modeled 2D structural constraints and linkages.
- Rigid Body Dynamics: Developed a rigid body simulator from scratch, handling positional updates, collision detection, and energy loss via the coefficient of restitution.
- Inverse Kinematics (IK): Created an IK solver utilizing Jacobian computation and gradient-based optimization to retarget human motion capture data onto a 3D character.
- Deep Reinforcement Learning: Formulated a Markov Decision Process for a CartPole balancing task and trained an autonomous agent using Deep Q-Learning (DQN).
Technologies Used: Python, PyBullet, SciPy, Gymnasium, Stable Baselines3.