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
KBOY
September 15, 2018
Technology
1
730
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
100
iOS15から使えるScreenTimeAPIをFlutterアプリで動かす
fujikawakei
0
130
FlutterエンジニアがFlutterFlowを使ってみた感想
fujikawakei
0
140
Flutterと課金
fujikawakei
0
140
【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
580
ARCore-Kotlin-Sampler作ってきました
fujikawakei
0
250
ARKitのための3D算数
fujikawakei
3
4.6k
ARKitでお絵かきする方法2選
fujikawakei
0
1.8k
assertion を積極的に使って 役立った話
fujikawakei
0
2k
Other Decks in Technology
See All in Technology
プロダクトエンジニアリング組織への歩み、その現在地 / Our journey to becoming a product engineering organization
hiro_torii
0
130
Fabric + Databricks 2025.6 の最新情報ピックアップ
ryomaru0825
1
140
Windows 11 で AWS Documentation MCP Server 接続実践/practical-aws-documentation-mcp-server-connection-on-windows-11
emiki
0
970
2年でここまで成長!AWSで育てたAI Slack botの軌跡
iwamot
PRO
4
710
Node-RED × MCP 勉強会 vol.1
1ftseabass
PRO
0
140
セキュリティの民主化は何故必要なのか_AWS WAF 運用の 10 の苦悩から学ぶ
yoh
1
160
Liquid Glass革新とSwiftUI/UIKit進化
fumiyasac0921
0
210
AWS テクニカルサポートとエンドカスタマーの中間地点から見えるより良いサポートの活用方法
kazzpapa3
2
550
【5分でわかる】セーフィー エンジニア向け会社紹介
safie_recruit
0
26k
ひとり情シスなCTOがLLMと始めるオペレーション最適化 / CTO's LLM-Powered Ops
yamitzky
0
440
rubygem開発で鍛える設計力
joker1007
2
200
25分で解説する「最小権限の原則」を実現するための AWS「ポリシー」大全 / 20250625-aws-summit-aws-policy
opelab
9
1.1k
Featured
See All Featured
Making Projects Easy
brettharned
116
6.3k
StorybookのUI Testing Handbookを読んだ
zakiyama
30
5.8k
Understanding Cognitive Biases in Performance Measurement
bluesmoon
29
1.8k
CoffeeScript is Beautiful & I Never Want to Write Plain JavaScript Again
sstephenson
161
15k
Being A Developer After 40
akosma
90
590k
No one is an island. Learnings from fostering a developers community.
thoeni
21
3.3k
The Success of Rails: Ensuring Growth for the Next 100 Years
eileencodes
45
7.4k
Site-Speed That Sticks
csswizardry
10
660
Become a Pro
speakerdeck
PRO
28
5.4k
Bootstrapping a Software Product
garrettdimon
PRO
307
110k
Automating Front-end Workflow
addyosmani
1370
200k
Docker and Python
trallard
44
3.4k
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