Basic 3D Math for ARKit

Transcript

1. Basic 3D Mathematics for ARKit Kei Fujikawa 2018.9.15@Tokyo iOS Meetup
2. Who?
3. Who?
4. Why is ے೑?
5.           Spajam 2nd Prized Best Body Japan Held ے೑.swift Showing in Article Smooth-sailing?
6. Not so easy.
7. A bunch of ے೑
8. ے೑
   4FOHPLV
   1FSJPE
9. AR!
10. Question!
11.           Spajam 2nd Prized Best Body Japan Held ے೑.swift Showing in Article
12. I have to ride on this big wave.
13. So,
14. I joined AR startup this January
15. Graffity Inc.
16. Apps we’re making
17. I studied ARKit for so much time
18. Not so easy.
19. Let’s think about this example.
20. Place an airplane at the 30cm in front of screen’s touched point.
22. Looks way too easy
23. Getting x,y from touch gesture and Z is 0.3?
24. Finally
26. It does not show
27. Ideal
29. Real
31. Not so easy
32. So,
33. I studied 3D programming.
34. Books I read for study IUUQTBN[OUP.4V.F( IUUQTBN[OUP1,'Z5
35. So,
36. Today I will explain 3D Programming clearly.
37. Basic 3D Mathematics for ARKit Kei Fujikawa 2018.9.15@Tokyo iOS Meetup
38. Today’s goal
39. Place an airplane at the 30cm in front of screen’s touched point.
41. We will study •Coordinate systems •Method for coordinate transformation
42. Coordinate system for ARKit
43. Coordinates World Object Camera Screen Drawn by iPad Pro
44. World Coordinate system The biggest coordinates In your iPhone
45. Object Coordinate system Airplane’s own coordinate
46. Camera coordinate system ΧϝϥͷϩʔΧϧ࠲ඪ
47. Camera
48. Screen
49. Screen
50. Coordinates World Object Camera Screen Drawn by iPad Pro
51. Let’s check the Goal
52. Place an airplane at the 30cm in front of screen’s touched point.
53. 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
54. ᶃPlace at 30cm in front of camera Minus 30cm
56. ᶄConvert to World
57. Convert from a coordinate to a coordinate
58. ᶄ’Convert to screen
59. World <-> Screen
60. ᶅGet x,y from tap gesture
61. ᶆPlace in the world
62. Screen <-> World
63. At 30cm Tapped position Convert Convert
64. Calculate at easy coordinate system
65. By the way
66. You can do it all in the screen coordinate
67. 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
68. Removabl
69. It looks easier!!
70. Yes
71. You can code shorter
73. But
74. 
75. In fact
76. This 0.996 is Same with 0.3m in camera coordinate
77. What is 0.996?
78. Review for coordinate system
79. 0.0 1.0 Screen’s z 0.001m 1000m Camera’s z
80. Screen’s Z
81. https://developer.apple.com/documentation/scenekit/scnscenerenderer/1522631-unprojectpoint Z is 0.0~1.0
82. Camera’s Z?
86. debug
88. Z is 0.01~1000
89. Let’s change zNear.
91. 0.0 1.0 Screen’s z 0.001m 1000m Camera’s z
92. Screen’s z vs Camera’s z
93. http://www.alecjacobson.com/weblog/?p=3835 -0.001 -1000 0.996 screenZ = f(n + cameraZ)/((f − n)cameraZ) -0.3 screenZ cameraZ
94. 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...
95. Way too hassle
96. Removable?
97. Must
98. So,
99. Understanding Coordinate’s system And..
101. Make sense?
102. Let’s study more?
103. Make a airplane Bigger or Rotation
104. Scale
105. Rotate by SCNVector4 Axis Degree
106. Rotate by Euler angle
107. Rotate by Euler angle x
108. Rotate by Euler angle Y
109. Rotate by Euler angle Z
110. x Y Z
111. That’s it
112. One more thing.
113. Making ARKit 2.0 repository
114. End