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
740
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
110
iOS15から使えるScreenTimeAPIをFlutterアプリで動かす
fujikawakei
0
140
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
590
ARCore-Kotlin-Sampler作ってきました
fujikawakei
0
270
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
1.9k
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
Cloud WANの基礎から応用~少しだけDeep Dive~
masakiokuda
3
100
大規模イベントに向けた ABEMA アーキテクチャの遍歴 ~ Platform Strategy 詳細解説 ~
nagapad
0
230
Claude Codeは仕様駆動の夢を見ない
gotalab555
23
6.6k
Foundation Model × VisionKit で実現するローカル OCR
sansantech
PRO
1
370
【新卒研修資料】数理最適化 / Mathematical Optimization
brainpadpr
27
13k
形式手法特論:位相空間としての並行プログラミング #kernelvm / Kernel VM Study Tokyo 18th
ytaka23
3
1.3k
いかにして命令の入れ替わりについて心配するのをやめ、メモリモデルを愛するようになったか(改)
nullpo_head
7
2.6k
専門分化が進む分業下でもユーザーが本当に欲しかったものを追求するプロダクトマネジメント/Focus on real user needs despite deep specialization and division of labor
moriyuya
1
1.3k
はじめての転職講座/The Guide of First Career Change
kwappa
4
3.7k
全員が手を動かす組織へ - 生成AIが変えるTVerの開発現場 / everyone-codes-genai-transforms-tver-development
tohae
0
180
Findy Freelance 利用シーン別AI活用例
ness
0
500
20250807 Applied Engineer Open House
sakana_ai
PRO
2
390
Featured
See All Featured
XXLCSS - How to scale CSS and keep your sanity
sugarenia
248
1.3M
GitHub's CSS Performance
jonrohan
1031
460k
How to Think Like a Performance Engineer
csswizardry
25
1.8k
Save Time (by Creating Custom Rails Generators)
garrettdimon
PRO
32
1.3k
Performance Is Good for Brains [We Love Speed 2024]
tammyeverts
10
1k
A better future with KSS
kneath
239
17k
A designer walks into a library…
pauljervisheath
207
24k
The Language of Interfaces
destraynor
158
25k
Fight the Zombie Pattern Library - RWD Summit 2016
marcelosomers
234
17k
Designing for Performance
lara
610
69k
Fireside Chat
paigeccino
38
3.6k
Building Better People: How to give real-time feedback that sticks.
wjessup
367
19k
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