Raymarched Clouds
Language: OpenGL
I created a cloud-like effect by raymarching through octaves of simplex noise, with a nested raymarch towards the light source to create shadows. This was implemented as a custom shader in Substance Designer.
Pathtracer
Language: C++
A path tracing renderer assignment for the Computer Graphics course at Carnegie Mellon. It can render diffuse, reflective, and refractive materials. Global illumination is done via Monte Carlo path tracing with Russian Roulette to terminate the paths. The renderer can use .exr files as environment maps to add light to scenes. It also generates a Bounding Volume Hierarchy for each mesh to accelerate triangle mesh intersection.
Crowd Simulation
Language: C#
I read the paper ‘A Synthetic-Vision Based Steering Approach for Crowd Simulation’ (SIGGRAPH 2010) by Ondrej et al. and attempted to replicate their results with a C# script in Unity. The paper describes an algorithm to simulate obstacle avoidance in humans by creating a synthetic optic flow for each individual. Each individual continuously calculates the change in bearing angle between themselves and all obstacles in their field of vision, turning to eliminate the danger of collision as well as slowing down if collision is imminent. Using this method, Ondrej et al. were able to show the emergence of patterns within crowds and eliminate deadlocks.
When implementing the algorithm, I had to make some adjustments such as changing model parameters. Some parameters chosen in the paper didn't work well in my simulation, most likely due to differences in scale, and had to be adjusted.
Flocking Simulation
Language: C++, Python
I created a flocking simulation in C++ for my final project in the Computer Graphics course at Dartmouth. The program simulates flocking behavior, following the Boids model established by Craig Reynolds. The particles in the program all obey rules of cohesion, alignment, and separation. The resulting behavior simulates the movement of animals groups such as flocks of birds or schools of fish.
I later wrote a new version of this script in Python to run in Maya, and added goal steering behavior. The above video is a demo created in Maya using the script.
Mathematical Model
I formulated a mathematical model based on this flocking simulation for a 2 week research project in my applied math course. A poster detailing my research can be viewed by clicking on the image above.
Viscoelastic Fluid Simulation
Engine: Unity Language: C#
For a project in my Technical Animation course at Carnegie Mellon, I read the paper 'Particle-based Viscoelastic Fluid Simulation' by Clavet et al. (2005), and implemented it in Unity. The goal of this paper was to improve the traditional Lagrangian fluid simulation method by introducing a new procedure to enforce incompressibility and anti-clustering, called double density relaxation. The double density relaxation prevents clustering by taking into account density as well as a new term called near-density, which creates a repulsive force between neighboring particles. Viscoelasticity is a combination of elasticity, plasticity, and viscosity. Elasticity is created by inserting springs between particles, which apply displacement to the particles depending on the spring’s rest length and stiffness constant. Plasticity is determined by the extent to which the springs change their rest length as the fluid moves.
Using this algorithm, I was able to simulate a variety of fluid behaviors. I ran simulations ranging from 300 to 10,000 particles. For 300 particles, I was able to achieve an frame rate of around 20fps, allowing the fluid to be interactible.
FABRIK IK Solver
Engine: Unity Language: C#
For a project in my Technical Animation course at Carnegie Mellon, I read the paper 'FABRIK: A fast, iterative solver for the Inverse Kinematics problem' by Aristidou & Lasenby (2011), and implemented it in Unity. This paper describes a new algorithm to solve for joint positions in an inverse kinematic system. The method is called Forward and Backward Reaching Inverse Kinematics, and computes joint positions by locating positions on a line instead of solving for rotational angles. The result is efficient and produces reliable results. I implemented the algorithm for a single chain as well as a chain with multiple end effectors.
Cloth Simulation
Engine: Unity Language: C#
A spring-mass cloth simulation script written for my Technical Animation course at Carnegie Mellon. It can perform four different integration methods, which can affect the cloth appearance and the maximum allowable timestep for the simulation.