Physics-based Animation 4860-1081

Linux	Windows

Lecture at graduate school of information science and technology in the university of Tokyo, spring semester, 2021

ITC-LMS (for Slack and GitHub Classroom invitaitons):

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

Instructor

Dr. Nobuyuki Umetani

• email: umetani@ci.i.u-tokyo.ac.jp
• url: http://www.nobuyuki-umetani.com/
• lab's website: https://cgenglab.github.io/labpage/en/

Time

Monday 3rd period, 13:00pm - 14:30pm

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++ 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	Scribble	Slide
(1) Apr. 5	Introduction			[1], [2]
(2) Apr. 19	Data Structure data structure for simulation Implicit surface	task0 deadline: Apr.22th		[2]
(3) Apr. 26	Time Integration Newtonian-mechanics backward & forward Euler method, particle system	task1 deadline: Apr. 29th		[14], [3]
(4) Mar. 10	Broad-phase Collision Detection princepal component analysis sort & sweep method bounding volume hierarchy	task4 deadline: May. 13th		[18], [5]
(5) May. 17	Numerical Optimization Hessian & Jacobian, Newton-Raphson method	task2 deadline: May 20th		[19]
(6) May. 24	Simple Deformation Energy mass-spring system	task3 deadline: May 27th	[1], [2], [3]	[6]
(7) May. 31	Solving Large Linear System Sparse matrix data structure Conjugate gradient method	task5 deadline: June 3rd		[8],[20]
(8) Jun. 7	Optimization with Constraint Lagrange multiplier method Rigid Body Dynamics Rotation representation	task6 deadline: June 10th	[4], [5]	[9],[21]
(9) Jun. 14	Rigid Body Dynamics2 inertia tensor, angular velocity impulse based method	task7 deadline: June 17th		[10]
(10) Jun. 21	Lagrangian mechanics Variational time integration Continuum Mechanics tensor	task8 deadline: June 24th	[6], [7]	[17], [16]
(11) Jun. 28	Continuum Mechanics2 Mesh interpolation Tensor	task11 deadline: July 1st	[8], [9], [10]	[4], [12]
(12) Jul. 5	Geometric Deformation singular value decomposition, shape matching method, linear blend skinning, as-rigid-as possible deformation	task9 deadline: July 8th		[22]
(13) Jul. 12	Advanced Interpolation mean value coordinate, radial based function		[11], [12]	[23]

Grading

• 20% lecture attendance
  • Counted by attending the lecture, asking question, and making comments ...etc
  • Number of question counts: maximum 1 count for 1 lecture, 5 2 counts for entire course
  • Attendance is counted based on writing a secret keyword on LMS. The keyword is announced for each lecture.
• 80% small assignemnts
  • see below

Assignemnts

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

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 assignemnt will not be open soon (instructer needs to adjust weight of the score later)

Tasks

• task0: Make C++ Program with CMake
• task1: Particle System
• task2: Optimization
• task3: Mass-spring system
• task4: Sort & Sweep Method
• task5: Solving Large Linear System
• task6: Optimization with Constraints
• task7: Optimization of Rotation
• task8: Variational Implicit Euler
• task9: Shape Matching Method
• task11: Inertia Tensor

Slides

• [1] introduction
• [2] data_structure
• [3] time_integration
• [4] grid_mesh_interpolation
• [5] collision_detection_broad
• [6] mass_spring_system
• [8] linear_system_solver
• [9] optimization with constraints
• [10] rigid_body_dynamics
• [12] tensor
• [13] cpp language
• [14] newtonian mechanics
• [15] git+github
• [16] variational_integration
• [17] lagrangian_mechanics
• [18] pca
• [19] optimization
• [20] matrix_data_structure
• [21] rotation representation
• [22]geometric_defmormation
• [23]advanced_interpolation

Reading Material

• 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