Upgrade to Pro
— share decks privately, control downloads, hide ads and more …
Speaker Deck
Features
Speaker Deck
PRO
Sign in
Sign up for free
Search
Search
Basic 3D Math for ARKit
Search
Sponsored
·
Ship Features Fearlessly
Turn features on and off without deploys. Used by thousands of Ruby developers.
→
KBOY
September 15, 2018
Technology
1
790
Basic 3D Math for ARKit
KBOY
September 15, 2018
Tweet
Share
More Decks by KBOY
See All by KBOY
How to make Stripe and RevenueCat coexist in an app
fujikawakei
0
150
iOS15から使えるScreenTimeAPIをFlutterアプリで動かす
fujikawakei
0
150
FlutterエンジニアがFlutterFlowを使ってみた感想
fujikawakei
0
160
Flutterと課金
fujikawakei
0
160
【スタートアップ開発者必見】firebaseとalgoliaとstripeで1人で本格的なiOSアプリを作る方法
fujikawakei
2
620
ARCore-Kotlin-Sampler作ってきました
fujikawakei
0
290
ARKitのための3D算数
fujikawakei
3
5k
ARKitでお絵かきする方法2選
fujikawakei
0
2k
assertion を積極的に使って 役立った話
fujikawakei
0
2.1k
Other Decks in Technology
See All in Technology
使って学ぼう MCP (と GitHub Codespaces)
tsubakimoto_s
1
220
Agent Skills 入門
puku0x
0
910
AIで「ふとした疑問」を即座に検証する 〜定量で圧倒するN1理解〜
kakehashi
PRO
3
730
大規模な組織におけるAI Agent活用の促進と課題
lycorptech_jp
PRO
4
5.5k
Snowflakeデータ基盤で挑むAI活用 〜4年間のDataOpsの基礎をもとに〜
kaz3284
1
130
1 年間の育休から時短勤務で復帰した私が、 AI を駆使して立ち上がりを早めた話
lycorptech_jp
PRO
0
150
バイブコーディングで作ったものを紹介
tatsuya1970
0
180
「技術的にできません」を越えて価値を生み出せ──研究開発チームをPMが率いて生み出した価値創出
hiro93n
1
320
LINEヤフーにおけるAI駆動開発組織のプロデュース施策
lycorptech_jp
PRO
0
140
Three-Legged OAuth in AgentCore Gateway
hironobuiga
2
190
Claude Codeと駆け抜ける 情報収集と実践録
sontixyou
1
890
Getting started with Google Antigravity
meteatamel
0
360
Featured
See All Featured
Winning Ecommerce Organic Search in an AI Era - #searchnstuff2025
aleyda
1
1.9k
[SF Ruby Conf 2025] Rails X
palkan
2
790
Bioeconomy Workshop: Dr. Julius Ecuru, Opportunities for a Bioeconomy in West Africa
akademiya2063
PRO
1
65
Hiding What from Whom? A Critical Review of the History of Programming languages for Music
tomoyanonymous
2
460
What Being in a Rock Band Can Teach Us About Real World SEO
427marketing
0
180
How To Stay Up To Date on Web Technology
chriscoyier
791
250k
Site-Speed That Sticks
csswizardry
13
1.1k
Design in an AI World
tapps
0
160
YesSQL, Process and Tooling at Scale
rocio
174
15k
The untapped power of vector embeddings
frankvandijk
2
1.6k
The Pragmatic Product Professional
lauravandoore
37
7.2k
How People are Using Generative and Agentic AI to Supercharge Their Products, Projects, Services and Value Streams Today
helenjbeal
1
130
Transcript
Basic 3D Mathematics for ARKit Kei Fujikawa 2018.9.15@Tokyo iOS Meetup
Who?
Who?
Why is ے?
Spajam 2nd Prized Best Body Japan Held ے.swift Showing in Article Smooth-sailing?
Not so easy.
A bunch of ے
ے 4FOHPLV1FSJPE
AR!
Question!
Spajam 2nd Prized Best Body Japan Held ے.swift Showing in Article
I have to ride on this big wave.
So,
I joined AR startup this January
Graffity Inc.
Apps we’re making
I studied ARKit for so much time
Not so easy.
Let’s think about this example.
Place an airplane at the 30cm in front of screen’s
touched point.
None
Looks way too easy
Getting x,y from touch gesture and Z is 0.3?
Finally
None
It does not show
Ideal
None
Real
None
Not so easy
So,
I studied 3D programming.
Books I read for study IUUQTBN[OUP.4V.F( IUUQTBN[OUP1,'Z5
So,
Today I will explain 3D Programming clearly.
Basic 3D Mathematics for ARKit Kei Fujikawa 2018.9.15@Tokyo iOS Meetup
Today’s goal
Place an airplane at the 30cm in front of screen’s
touched point.
None
We will study •Coordinate systems •Method for coordinate transformation
Coordinate system for ARKit
Coordinates World Object Camera Screen Drawn by iPad Pro
World Coordinate system The biggest coordinates In your iPhone
Object Coordinate system Airplane’s own coordinate
Camera coordinate system ΧϝϥͷϩʔΧϧ࠲ඪ
Camera
Screen
Screen
Coordinates World Object Camera Screen Drawn by iPad Pro
Let’s check the Goal
Place an airplane at the 30cm in front of screen’s
touched point.
30cm Get x,y from tap gesture Place the object In
the world. Place at 30cm In front of camera Convert to world ᶃ ᶄ ᶅ Convert to Screen ᶆ ᶄ’ Convert to screen
ᶃPlace at 30cm in front of camera Minus 30cm
None
ᶄConvert to World
Convert from a coordinate to a coordinate
ᶄ’Convert to screen
World <-> Screen
ᶅGet x,y from tap gesture
ᶆPlace in the world
Screen <-> World
At 30cm Tapped position Convert Convert
Calculate at easy coordinate system
By the way
You can do it all in the screen coordinate
30cm Get x,y from tap gesture Place the object In
the world. Place at 30cm In front of camera Convert to world ᶃ ᶄ ᶅ Convert to Screen ᶆ ᶄ’ Convert to screen Removable
Removabl
It looks easier!!
Yes
You can code shorter
None
But
In fact
This 0.996 is Same with 0.3m in camera coordinate
What is 0.996?
Review for coordinate system
0.0 1.0 Screen’s z 0.001m 1000m Camera’s z
Screen’s Z
https://developer.apple.com/documentation/scenekit/scnscenerenderer/1522631-unprojectpoint Z is 0.0~1.0
Camera’s Z?
None
None
None
debug
None
Z is 0.01~1000
Let’s change zNear.
None
0.0 1.0 Screen’s z 0.001m 1000m Camera’s z
Screen’s z vs Camera’s z
http://www.alecjacobson.com/weblog/?p=3835 -0.001 -1000 0.996 screenZ = f(n + cameraZ)/((f −
n)cameraZ) -0.3 screenZ cameraZ
screenZ = f(n + cameraZ)/((f − n)cameraZ) screenZ = 1000(0.001
+ (−0.3))/((1000 − 0.002)(−0.3)) f = 1000 n = 0.001 cameraZ = − 0.3 screenZ = 0.9966...
Way too hassle
Removable?
Must
So,
Understanding Coordinate’s system And..
None
Make sense?
Let’s study more?
Make a airplane Bigger or Rotation
Scale
Rotate by SCNVector4 Axis Degree
Rotate by Euler angle
Rotate by Euler angle x
Rotate by Euler angle Y
Rotate by Euler angle Z
x Y Z
That’s it
One more thing.
Making ARKit 2.0 repository
End