Physics-based Animation 4860-1081 2023S

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

ITC-LMS

For Slack and GitHub Classroom invitations

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

Instructor

Dr. Nobuyuki Umetani

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

Time

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

Course Description

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

Lecture Schedule

Day	Topic	Assignment	Slide
(1) Apr. 10	Introduction		[1]
(2) Apr. 17	Data Structure data structure for simulation Implicit surface	task00	[2]
(3) Apr. 24	Time Integration backward & forward Euler method, particle system	task01	[6]
(4) May 1	Newtonian Mechanics	task02	[5]
(5) May 8	Collision Detection principal component analysis sort & sweep method	task03	[9]
(6) May 15	Optimization bounding volume hierarchy Hessian & Jacobian	task04	[10]
(7) May 22	Simple Elastic Energy Newton-Raphson method mass-spring system	task05	[12]
(8) Jun. 5	Dynamic Deformation Variational time integration	task06	[14]
(9) Jun. 12	Linear System Solver Sparse matrix data structure Conjugate gradient method	task07	[17]
(10) Jun. 19	Optimization with Constraint Lagrange multiplier method	task08	[18]
(11) Jun. 26	Rotation Rotation representation	task09	[18]
(12) Jul. 3	Rigid Body Dynamics inertia tensor, angular velocity	task10	[22]
(13) Jul. 10	Continuum Mechanics tensor, finite element method		[24]

Slides

• [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

Grading

• 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

Assignments

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

Policy

• 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)

Reading Material

• 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

My Past Lectures

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