Neural Networks
Deep learning fundamentals, forward/backward propagation, and optimization.
Mathematical foundations of neural networks including forward propagation, backpropagation, and gradient descent.
Comprehensive study of activation functions, loss functions, and optimization algorithms.
Analysis of regularization techniques including L1/L2 regularization and dropout for preventing overfitting.
Theoretical understanding of training dynamics, convergence, and generalization in deep learning systems.
Mesh Representations
A review of commonly used mesh representations and their trade-offs.
Comprehensive analysis of mesh data structures including face-based, edge-based, and vertex-based representations.
Memory consumption and performance trade-offs between adjacency lists, indexed face sets, and connectivity structures.
Edge-based representations: winged-edge, half-edge, and directed-edge data structures for efficient mesh traversal.
Render-optimized approaches including corner tables and hybrid geometric-topological representations.
Monte Carlo Light Transport
Light transport, Monte Carlo methods, and MCML.
Deep dive into radiometry, light transport theory, reflectance distribution functions, and Monte Carlo methods.
Comprehensive study of the Monte Carlo Multi-Layered (MCML) algorithm for accurate simulation of photon propagation.
Theoretical foundations of subsurface scattering and the radiative transfer equation.
Analysis of material properties and their effects on light transport in complex mediums.
Skin Rendering
Real-time physically-based skin rendering with subsurface scattering.
Advanced shading techniques for real-time rendering of human skin combining surface reflection and subsurface scattering.
Implementation of physically-based reflectance models including Kelemen/Szirmay-Kalos specular BRDF and Cook-Torrance approximations.
Screen-space and texture-space diffusion approaches for real-time subsurface scattering using Gaussian approximations.
Translucency effects and transmittance modeling using translucent shadow maps and attenuation functions.