Applied Computer Graphics 4860-1084

Lecture at graduate school of information science and technology in the university of Tokyo, spring semester, 2024

UTOL (UTokyo-LMS) (for Zoom URL, Slack and GitHub Classroom invitations):

• https://utol.ecc.u-tokyo.ac.jp/lms/course?idnumber=2024_4886_4860-1084_01

Instructors

Dr. Nobuyuki Umetani

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

TA: Kenji Tojo

• url: https://kenji-tojo.github.io/

Time

Monday 2nd period, 10:25am - 12:10pm

Course Description

Computer graphics is a technology to computationally represent objects' geometry, appearance and movement. This course is an introduction to the techniques generally seen in computer graphics. The aim of the course is to get familiar with applied mathematics such as linear algebra, vector analysis, partial differential equations, numerical analysis and optimization through the topics in computer graphics. There are C++ programming assignments to acquire research-oriented graphics programming skills such as OpenGL, shader programming, Eigen matrix library, Git and cmake.

Topics:

• affine transformation & homography
• character animation (forward & inverse kinematics)
• visualization (rasterization / ray casting)
• optimization ( continuous optimization / dynamic programming )
• parametric curves & surfaces
• variational mesh deformation
• grid-based fluid simulation

Lecture Schedule

Day	Topic	Assignment	Slide
(1) Apr. 8	Introduction Didigital image		[1], [4]
(2) Apr. 15	Parametric curves / surfaces Rasterization in 2D, Digital Differential Analyzer	task01	[5] [6]
(3) Apr. 22	Parametric representation Bézier curve, polynominal	task02	[7] [8]
(5) May 7	Coordinate transformation Affine, homography transformation	task03	[9] [10] [11]
(4) May 13	Graphics pipeline depth buffer method, shading, shadow, anti aliasing	task04	[12] [13]
(6) May 20	Ray Casting 1 spatial data structure	task05	[14] [16]
(7) May 27	Ray Casting 2 Rendering equation, Monte Carlo integration	task06	[15] [17] [18] [19]
(8) June 3	Character animation Skeletal animation	task07	[21]
(9) June 10	Guest lecture by Dr. Rex West
(10) June 17	Character animation2 linear blend skinning	task08	[20]
(11) June 24	Optimization Newton-Raphson method, gradient descent		[22]
(12) July 1	Laplacian mesh deformation Sparse linear system	task09	[23] [24]
(13) July 8	Grid-based Fluid Poisson equation, Stam fluid		[25]

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

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 assignments need to be submitted using pull request functionality of the GitHub. Look at the following document.

How to Submit the Assignments

Task ID	Title	Thumbnail
task01	Rasterization of lines and polygons DDA, winding number
task02	Rasterization of parametric curves Quadratic Bézier curve, root of polynominal
task03	Perspectively-correct texture mapping rasterization of triangle, barycentric coordinate
task04	Vertex shader practice Rendering pipeline, mirror reflection, OpenGL
task05	Fragment shader practice Ray marching method, CSG modeling, implicit modeling
task06	Monte Carlo integration1 Ambient occlusion, importance sampling, BVH
task07	Monte Carlo integration2 Multiple importance sampling
task08	Skeletal Character Animation Linear blend skinning, articulated rigid body
task09	Laplacian Mesh Deformation Quadratic programming, sparse linear system

Policy

• Do the assignment by yourself. Do not share the answers of the assignments.
• Late submission of an assignment is subject to grade deduction.
• Score each assignment will not be open soon (instructor needs to adjust weight of the score later).
• The assignments might not be graded soon.

Slides

• [1] Introduction

• [2] C++ programming

• [3] Git+GitHub

• [4] Digital Image

• [5] Rasterization in 2D

• [6] Barycentric Coordinates

• [7] Parametric Curve

• [8] Polynominal Root finding

• [9] Coordinate Transformation

• [10] 2D Homogeneous Transformation

• [11] 3D Homogeneous Transformation

• [12] 3D Rasterization

• [13] Graphics Pipeline

• [14] Shading

• [15] Subpixel Effect

• [16] Implicit Modeling

• [17]Ray Casting

• [18]Monte Carlo Integration

• [19]Ray Triangle Collision

• [20]Character deformation

• [21] Jacobian&Hessian

• [22] Optimization

• [23] Mesh laplacian

• [24] Sparse linear system

• [25] Fluid simulation

Reading Material

• Introduction to Computer Graphics by Cem Yuksel](https://www.youtube.com/watch?v=vLSphLtKQ0o&list=PLplnkTzzqsZTfYh4UbhLGpI5kGd5oW_Hh)
• Scratchpixel 2.0
• Awesome Computer Graphics (GitHub)
• Skinning: Real-time Shape Deformation SIGGRAPH 2014 Course
• Physics-based Animation2023S (Another course by the instructor)
• Physics-based Animation2021S (Another course by the instructor)
• Applied Computer Graphics 2022S (The same course two years ago)