Lecture at graduate school of information science and technology in the university of Tokyo, spring semester, 2023

For Slack and GitHub Classroom invitations

• https://itc-lms.ecc.u-tokyo.ac.jp/lms/course?idnumber=20214860-10810F01

Dr. Nobuyuki Umetani

• email: [email protected]
• url: https://www.nobuyuki-umetani.com/
• lab's website: https://cgenglab.github.io/en/

• Monday 2rd period, 10:25pm - 12:10pm

Computer-generated images are everywhere in movies, video games, and VR. This course is an introduction to the techniques to animate objects in computer graphics based on the law of physics. The aim of the course is to get familiar with applied mathematics such as linear algebra, vector analysis, partial differential equations, variational principle, optimization, and numerical analysis through the animation techniques for particle systems, rigid bodies, elastic bodies. There are C++/Python programming assignments to acquire research-oriented graphics programming skills.

Topics:

• mass-spring simulation
• rigid body simulation
• elastic body simulation
• cloth and hair modeling & simulation
• collision-detection using spatial hashing
• finite boundary method

• [1] Introduction
• [2] Data Structure
• [3] Cpp
• [4] Git
• [5] Newtonian Mechanics
• [6] Time Integration
• [7] Jagged Array
• [8] Principal Component Analysis
• [9] Collision Detection
• [10] Jacobian and Hessian
• [11] Vector Differentiation
• [12] Mass-Spring System
• [13] Optimization
• [14] Variational Integration
• [15] Matrix Data Structure
• [16] Linear System Solver
• [17] Optimization with Constraints
• [18] Rotation
• [19] Grid & Mesh Interpolation
• [20] Angular Velocity
• [21] Rigid Body Approximation
• [22] Equation of Rigid Body
• [23] Lagrangian Mechanics
• [24] Tensor
• [25] Finite Element Method

• 20% lecture attendance
  • Attendance is counted based on writing a secret keyword on LMS. The keyword is announced for each lecture.
• 80% small assignments
  • see below

There are many small programming assignments. To do the assignments, you need to create your own copy of this repository through GitHub Classroom. These assignements needs to be submitted using pull request functionality of the GitHub. Look at the following document.

How to Submit the Assignments

Task ID	Title	Thumbnail
task00	Building C++ Program with CMake
task01	Implicit Time Integration
task02	Linear Momentum Conservation
task03	Acceleration of N-body Simulation
task04	Accelerated Nearest Search using Kd-Tree
task05	Gradient Descent for Mass-Spring Simulation
task06	Dynamic Mass-spring System using Variational Euler Time Integration
task07	Solving Laplace Equation with Gauss-Seidel Method
task08	Controlling Volume of a Mesh using Lagrange-Multiplier Method
task09	Rotation and Energy Minimization
task10	Simulation of Rigid Body Precession

• Do the assignment by yourself. Don't share the assignments with others.
• Don't post the answers of the assignment on Slack
• Late submission of an assignment is subject to grade deduction
• Score each assignment will not be open soon (instructor needs to adjust weights of the score later)

• Ten Min Physics (Youtube channel)
• Physically Based Modeling: Principles and Practice, Siggraph '97 Course notes by Dr. Baraff
• Physics-Based Animation by Kenny Erleben et al. (free textobook about rigid body dynamics)
• Dynamic Deformables: Implementation and Production Practicalities, SIGGRAPH 2020 Courses
• Awesome Computer Graphics (GitHub)
• Skinning: Real-time Shape Deformation SIGGRAPH 2014 Course

• Physics-based Animation 2021S
• Applied Computer Graphics 2022S