$30 off During Our Annual Pro Sale. View Details »
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
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
140
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
150
Flutterと課金
fujikawakei
0
150
【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
610
ARCore-Kotlin-Sampler作ってきました
fujikawakei
0
290
ARKitのための3D算数
fujikawakei
3
4.9k
ARKitでお絵かきする方法2選
fujikawakei
0
1.9k
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
M&Aで拡大し続けるGENDAのデータ活用を促すためのDatabricks権限管理 / AEON TECH HUB #22
genda
0
240
MySQLのSpatial(GIS)機能をもっと充実させたい ~ MyNA望年会2025LT
sakaik
0
120
日本Rubyの会: これまでとこれから
snoozer05
PRO
6
240
AWSに革命を起こすかもしれない新サービス・アップデートについてのお話
yama3133
0
510
2025年のデザインシステムとAI 活用を振り返る
leveragestech
0
250
普段使ってるClaude Skillsの紹介(by Notebooklm)
zerebom
8
2.2k
[Neurogica] 採用ポジション/ Recruitment Position
neurogica
1
130
Amazon Connect アップデート! AIエージェントにMCPツールを設定してみた!
ysuzuki
0
140
たまに起きる外部サービスの障害に備えたり備えなかったりする話
egmc
0
410
Oracle Database@Google Cloud:サービス概要のご紹介
oracle4engineer
PRO
1
770
AI with TiDD
shiraji
1
290
Next.js 16の新機能 Cache Components について
sutetotanuki
0
190
Featured
See All Featured
個人開発の失敗を避けるイケてる考え方 / tips for indie hackers
panda_program
122
21k
The B2B funnel & how to create a winning content strategy
katarinadahlin
PRO
0
190
Intergalactic Javascript Robots from Outer Space
tanoku
273
27k
Visual Storytelling: How to be a Superhuman Communicator
reverentgeek
2
400
コードの90%をAIが書く世界で何が待っているのか / What awaits us in a world where 90% of the code is written by AI
rkaga
57
40k
<Decoding/> the Language of Devs - We Love SEO 2024
nikkihalliwell
0
100
How to build an LLM SEO readiness audit: a practical framework
nmsamuel
1
580
Producing Creativity
orderedlist
PRO
348
40k
Winning Ecommerce Organic Search in an AI Era - #searchnstuff2025
aleyda
0
1.8k
The browser strikes back
jonoalderson
0
120
XXLCSS - How to scale CSS and keep your sanity
sugarenia
249
1.3M
Design of three-dimensional binary manipulators for pick-and-place task avoiding obstacles (IECON2024)
konakalab
0
320
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