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 method in geometry and simulation which would be adequate for either further re-search or as an initial knowledge to find work in the relevant industry (example of advanced industry that uses this core knowledge: 3D printing, architectural design, medical imaging, weather simulations, robotics)
3. use software and tools (e.g., Python and C++) 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 'soft-ware 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.