CGGS: Computer Graphics: Geometry and Simulation

Welcome to Computer Graphics: Geometry and Simulation

Learning Outcomes

On successful completion of this course, you should be able to: 

1. identify and isolate geometric problems and produce an algorithm to fit
2. implement basic methods in geometry and simulation which would be adequate for either further research or as an initial knowledge to find work in the relevant industry (examples of advanced industry that uses this core knowledge: 3D printing, architectural design, medical imaging, weather simulations, robotics)
3. use software and tools (this year we will use C++ + Eigen) to implement geometric algorithms and test their results
4. identify, fix, and test for possible issues with geometric algorithms in a way that transcends just 'software bugs' but rather problems with a geometric context

• Overview: geometry and simulation in digital applications. 
• Elemental digital representations of geometry: simplicial meshes, point clouds, voxelizations, implicit functions, neural fields
• Elementary principles of discrete simulation: strain and stress tensors, force equations, time integration.
• Geometry acquisition and reconstruction: classical (least-squares based) and modern (neural-network based) algorithms.
• Discrete shape analysis: curvatures, topology, differential operators.
• Finite-element spaces for simulation and analysis, including basic PDEs like elasticity, Stokes equation, and Poisson equation.
• Simulation of rigid bodies with collisions.
• Modern deep-learning techniques for geometry and simulation, such as physics-informed neural networks, graph neural networks, and implicit representations (e.g., signed distance fields)
• Practical aspects of implementation and debugging in geometry: we will discuss how to identify, critically analyse, and improve performance in geometric methods, with emphasis on pitfalls and basic principles in implementation and design.