Welcome back to
Computer Graphics course
 Please raise your hand if you are new to this course.
You need course ID.
Write your name on the registration list.
 We use “course ID” for grading.
Remember it for future references.
Computer Graphics
1st
quarter, 2015
Nara Institute of Science and Technology
 Please check the syllabus.
 Sorry, but this course is not archived.
 We require you to enroll edX CS184.1x
 You can access course material on the web.
(but limited)
April 16, 2015
(Recap)
Grading
(Recap)
Course style
 Assignments : 75%
 @class
 Surveys during the course
 Uniform grading independent from the responses.
 Graphics programming
 Participating Discussions during the class : 25%
 Asking questions about computer graphics
 “question” is more important than answer.
 Answering the question
 Welcome to answer the question!
 Bring your own device! Participate actively!
 We will take surveys for check your understandings
 You can do assignment during the class
 You can also audit edX course while you wait others
 Please bring earphone/headphone if you have
 @home
 Audit edX course
 You can download video/transcript if you want.
 Please tell me your ID when you ask/answer.
Feedback to survey
Follow up
- Please tell us if you have concerns
about flipped classroom.
 ヘビーそう。
This course seems tough…
 課題には早く取り掛かってください．そうすれば必要な支援が受けら
れます．
Start early!! We can support you if you start early.
 授業内で課題が終わらなかった場合，持ち帰ることは可能か？
If I could not finish homework, can I do it at home?
questions/comments in the previous survey
 可能です，まずは早く始めてください．課題の提出期日は，課されて
から2週間後に提出期限になるようにします．必要があれば翌週授業中
に支援を受けてください．
Yes, you can, but Start early!! Each assignment will be due two
weeks after it is out. Please ask us next week if you need supports.
1
Start early!!!
Feedback to survey
- Please tell us if you have concerns
about flipped classroom.
 英語が苦手なので自習の進度が授業に間に合わないのではな
いかという不安があります。
I’m concerned that I cannot catch up with the course
to audit the online lecture because of English skills.
 慣れないスタイルなので正しく活用できるかは心配です。
I’m concerned because I’m not familiar with the style.
 こんな形の授業を受けたことないので、まず、うけて見ます。
I’m not familiar with the “flipped classroom.”
https://courses.edx.org/courses/BerkeleyX/CS_184.1x/3T2014/courseware/Unit_3/Homework_3/
 オンライン教材は再生が何度もでき，英語の書き起こし文もあり
ますので，英語講義を対面授業でただ聞くだけよりも多くの面で
有利です．英語の勉強にもなりますので頑張ってください．
By using online course material, you can repeat the movie
and read the transcripts.
It must be easier than to audit face-to-face lecture.
Feedback to survey
Feedback to survey
- Please tell us if you have concerns
about flipped classroom.
- Please tell us in your own words if you
expect/feel/think/doubt something about this
course.
 情報系出身でないのでコンピュータグラフィックスについて基礎
的な部分もわかってないし、英語なのが不安
I’m concerned that I do not know much about computer
graphics. I’m not confident in my English skills as well.
 I‘m concerned about following up the course since
my background in CG is not very strong. I hope the
complexity of the course will raise really gradually so
that it’s easier to follow.
CGについてあまり詳しくないので付いていけるか不安で
す．難易度が徐々に上がるようにしてください．
 英語がわからないというより、他分野出身なので日本語でも用語
がわからない。
I’m not familiar with technical terms even if it is in Japanese.
 もちろん，初学者を対象とした講義内容としますので，心配いりませ
ん．
日本語の質問も歓迎します．分からなければ遠慮なく聞いてください．
Do not worry, this course targets beginners.
Do not hesitate to ask me anything in Japanese.
I will pay efforts to translate it into English.
 Do not worry, this course targets beginners.
Do not hesitate to ask me anything.
初学者を対象としていますので心配ありません．
分からなければ遠慮なく聞いてください．
Feedback to survey
Feedback to survey
- Please tell us in your own words if you
expect/feel/think/doubt something about this course.
- Please tell us in your own words if you
expect/feel/think/doubt something about this course.
 laptopが重くて持って来れないのですが、必要ならがん
ばって持ってきます。
My laptop is so heavy…Do I need to bring it?
 it seems interesting. i want to learn how to use
OpenGL properly.
 持ってくるのはassignmentの次の週，支援が必要な時だけで
結構です．支援が必要なければ，そのあいだ（授業中に）
Online courseの次の単元を（Smartphoneなどで）聴講して
もらって構いません．
You can bring your laptop only when you need support
to finish the assignment. If you do not need any support,
you can audit next lecture in edX while waiting for others
during this class.
 After watching SIGGRAPH's video, I think CG is very
cool and interesting research field.
 SIGGRAPHに非常に興味をもちました。初めて勉強する分
野なので、非常に楽しみです。
 楽しみにしています
 I hope you enjoy this CG course!
2
Today’s topics
Questions?
 Check your understanding
 Computer Graphics Pipeline
 Course overview
 basic math: Vector/Matrix calculation
 Demonstration of homework0
 Preview for next topics
Please tell us your ID & name
before asking/answering.
 Geometrical transforms
 Next homework
 Homework support
 Homework0
Check!
Take a short test from
Questions?
http://goo.gl/cBLqSm
Please tell us your ID & name
before asking/answering.
Today’s topics
Pipeline
 Check your understanding
 Make a scene as INPUT
 Computer Graphics Pipeline
 Course overview
 basic math: Vector/Matrix calculation
 Demonstration of homework0
 Preview for next topics
 Geometrical transforms
 Next homework
 Homework support
 Homework0
 Modeling
 Describe objects in a scene
 Shape / material (color)
 Animation
 Describe temporal changes of objects
 motion
 Synthesize an image as OUTPUT
 Rendering
 Compute light transport
3
(Recap)
What is Computer Graphics?
3D Computer Graphics
 Outputs visual representation via computation
 Main target of this course:
For example,
 Static:
 How to describe 3D scene as INPUT
 How to compute 2D image as OUTPUT
Pictures / Objects
 Other representations
 Dynamic: Movies
 2D scene -> 2D
 Output devices
 Printer
Display
(static)
(dynamic: varying with time)
 3D scene -> 3D printer
 2D / 3D
(spatially)
 3D scene -> 3D display
 Sometimes require “Rasterize” (ラスタライズ)
 “3D display” mostly use a set of 2D images
 ND scene -> 2D : “Visualization” (可視化) research field
How to represent
INPUT/OUTPUT?
Many output devices use
raster description
raster
vector
raster
(x1,y1)
(x2,y2)
(x3,y3)
(x1,y1) - (x2,y2) - (x3,y3)
f (x,y) = color
f (x,y) = color
http://www.canon.com/v-square/movie.html
http://www.eizoglobal.com/products/flexscan/ev3237/index.html
Some devices use vector
description
vector
Questions?
(x1,y1)
Please tell us your ID & name
before asking/answering.
(x2,y2)
(x3,y3)
(x1,y1) - (x2,y2) - (x3,y3)
http://fablabkitakagaya.org/
4
Discuss pros and cons of raster
and vector representation?
ラスタ・ベクタ表現の
利点・欠点はなんでしょう？
A 3D scene is
usually described by vector
A set of polygon
(many tetragons)
Sphere
Find neighborhood to discuss
Take 5 min.
How about raster
as an INPUT?
In 3DCG, we need conversion
from vector to raster
CT Scan
Digital camera
raster
vector
(x1,y1)
(x2,y2)
http://vector-conversions.com/vectorizing/raster_vs_vector.html
doi>10.1145/1028523.1028571
Rasterization
ラスタライズ
Trace
トレース
raster
vector
(x3,y3)
vector
raster
(x1,y1)
(x2,y2)
(x3,y3)
http://tv.adobe.com/watch/visual-design-cs6/new-image-trace/
How to do that?
5
Curves
http://en.wikipedia.org/wiki/B%C3%A9zier_curve
http://en.wikipedia.org/wiki/B-spline
B-Spline curve
Bézier curve
Questions?
Please tell us your ID & name
before asking/answering.
Today’s topics
Today’s topics
 Check your understanding
 Check your understanding
 Computer Graphics Pipeline
 Computer Graphics Pipeline
 Course overview
 Course overview
 basic math: Vector/Matrix calculation
 basic math: Vector/Matrix calculation
 Demonstration of homework0
 Demonstration of homework0
 Preview for next topics
 Preview for next topics
 Geometrical transforms
 Geometrical transforms
 Next homework
 Homework support
 Homework support
 Homework0
 Homework0
Recap
Recap: dual matrix
𝑗𝑥
𝑖𝑥
 Given two column vector 𝒊 = 𝑖𝑦 and 𝒋 = 𝑗𝑦 ,
𝑖𝑧
𝑗𝑧
express dot product as matrix multiplication.
𝑗𝑥
𝑖𝑥
 Given two column vector 𝒊 = 𝑖𝑦 and 𝒋 = 𝑗𝑦 ,
𝑖𝑧
𝑗𝑧
express cross product as matrix multiplication.
𝒊 ⋅ 𝒋 = 𝒋⊤ 𝒊 = 𝑗𝑥
𝑗𝑦
𝑗𝑧
𝑖𝑥
𝑖𝑦
𝑖𝑧
𝑖×𝑗 =
0
𝑖𝑧
−𝑖𝑦
−𝑖𝑧
0
𝑖𝑥
𝑖𝑦
−𝑖𝑥
0
𝑗𝑥
𝑗𝑦
𝑗𝑧
Dual matrix
6
Recap:
other important ideas
 Identity (単位行列)
 Inverse
Questions?
(逆行列)
 Transpose
(転置)
 Non-commutative
(非可換)
Please tell us your ID & name
before asking/answering.
Today’s topics
 Check your understanding
 Computer Graphics Pipeline
Homework0
demonstration
 Course overview
 basic math: Vector/Matrix calculation
 Demonstration of homework0
 Preview for next topics
 Geometrical transforms
 Next homework
 Homework support
 Homework0
Today’s topics
 Check your understanding
 Computer Graphics Pipeline
Homework 1
demonstration
 Course overview
 basic math: Vector/Matrix calculation
 Demonstration of homework0
 Preview for next topics
 Geometrical transforms
 Next homework
 Homework support
 Homework0
7
Geometric transform
Questions?
vector
 Transform the objects
in the scene
(x1,y1)
 for animation
 with respect to the
camera position/direction
 Project the scene (3D)
onto the image plane (2D)
of the camera
(x2,y2)
Please tell us your ID & name
before asking/answering.
(x3,y3)
(x1,y1) - (x2,y2) - (x3,y3)
Today’s topics
Homework
 Check your understanding
 Unit 1
 Computer Graphics Pipeline
 Course overview
 basic math: Vector/Matrix calculation
 Demonstration of homework0
 Preview for next topics
 Geometrical transforms
 Lecture 3: Transforms 1
 Homework 0
due April 23, 2015.
 Three movie clips,
about 35 min.
 Lecture 4: Transforms 2
 Only first movie clips,
about 20 min.
 Print out the results,
submit it in next class.
 Include in one page
 Your name
 Student No.
 course ID
 Next homework
 screenshot1.png
 Homework support
 screenshot2.png
 Homework0
Today’s topics
Questions?
 Check your understanding
 Computer Graphics Pipeline
 Course overview
 basic math: Vector/Matrix calculation
 Demonstration of homework0
 Preview for next topics
Please tell us your ID & name
before asking/answering.
 Geometrical transforms
 Next homework
 Homework support
 Homework0
8
Homework 0 support
 Raise your hand for assistance.
 If you have no problem,
you can audit next lecture (do homework) now.
 Please use earphone/headphone
 Unit 1 - Lecture 3 and 4
9