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.
21. None

22. Looks way too easy

23. Getting x,y from touch gesture and Z is 0.3?

24. Finally

25. None

26. It does not show

27. Ideal

28. None

29. Real

30. None

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.
40. None

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

55. None

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

72. None

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?

83. None
84. None
85. None

86. debug

87. None

88. Z is 0.01~1000

89. Let’s change zNear.

90. None

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..

100. None

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