Basic 3D Math for ARKit

Transcript

1. Basic
   3D Mathematics
   for ARKit
   Kei Fujikawa
   2018.9.15@Tokyo iOS Meetup
   

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2. Who?
   

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3. Who?
   

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4. Why is ے೑?
   

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5. 
   
   
   
   
   
   Spajam 2nd Prized
   Best Body Japan
   Held ے೑.swift
   Showing in Article
   Smooth-sailing?
   

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6. Not so easy.
   

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7. A bunch of ے೑
   

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8. ے೑
   4FOHPLV1FSJPE
   

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9. AR!
   

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10. Question!
    

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11. 
    
    
    
    
    
    Spajam 2nd Prized
    Best Body Japan
    Held ے೑.swift
    Showing in Article
    

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12. I have to ride
    on this big wave.
    

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13. So,
    

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14. I joined AR startup
    this January
    

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15. Graffity Inc.
    

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16. Apps we’re making
    

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17. I studied ARKit
    for so much time
    

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18. Not so easy.
    

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19. Let’s think about
    this example.
    

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20. Place an airplane
    at the 30cm
    in front of screen’s
    touched point.
    

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22. Looks way too easy
    

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

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24. Finally
    

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26. It does not show
    

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27. Ideal
    

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29. Real
    

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31. Not so easy
    

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32. So,
    

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33. I studied
    3D programming.
    

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34. Books I read for study
    IUUQTBN[OUP.4V.F( IUUQTBN[OUP1,'Z5
    

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35. So,
    

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36. Today
    I will explain
    3D Programming
    clearly.
    

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37. Basic
    3D Mathematics
    for ARKit
    Kei Fujikawa
    2018.9.15@Tokyo iOS Meetup
    

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38. Today’s goal
    

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39. Place an airplane
    at the 30cm
    in front of screen’s
    touched point.
    

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41. We will study
    •Coordinate systems
    •Method for coordinate
    transformation
    

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42. Coordinate system
    for ARKit
    

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43. Coordinates
    World
    Object
    Camera
    Screen
    Drawn by iPad Pro
    

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44. World Coordinate system
    The biggest coordinates
    In your iPhone
    

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45. Object Coordinate system
    Airplane’s own
    coordinate
    

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46. Camera coordinate system
    ΧϝϥͷϩʔΧϧ࠲ඪ
    

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47. Camera
    

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48. Screen
    

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49. Screen
    

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50. Coordinates
    World
    Object
    Camera
    Screen
    Drawn by iPad Pro
    

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51. Let’s check the Goal
    

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52. Place an airplane
    at the 30cm
    in front of screen’s
    touched point.
    

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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
    

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54. ᶃPlace at 30cm
    in front of camera
    Minus
    30cm
    

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56. ᶄConvert to World
    

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57. Convert from
    a coordinate
    to
    a coordinate
    

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58. ᶄ’Convert to screen
    

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59. World Screen
    

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60. ᶅGet x,y from tap gesture
    

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61. ᶆPlace in the world
    

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62. Screen World
    

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63. At 30cm
    Tapped
    position
    Convert
    Convert
    

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64. Calculate at
    easy coordinate system
    

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65. By the way
    

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66. You can do it all
    in the screen coordinate
    

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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
    

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68. Removabl
    

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69. It looks easier!!
    

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70. Yes
    

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71. You can code shorter
    

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73. But
    

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74. 
    

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75. In fact
    

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76. This 0.996 is
    Same with 0.3m in
    camera coordinate
    

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77. What is 0.996?
    

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78. Review for
    coordinate system
    

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79. 0.0
    1.0
    Screen’s
    z
    0.001m
    1000m
    Camera’s
    z
    

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80. Screen’s Z
    

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81. https://developer.apple.com/documentation/scenekit/scnscenerenderer/1522631-unprojectpoint
    Z is 0.0~1.0
    

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82. Camera’s Z?
    

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86. debug
    

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88. Z is 0.01~1000
    

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89. Let’s change zNear.
    

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91. 0.0
    1.0
    Screen’s
    z
    0.001m
    1000m
    Camera’s
    z
    

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92. Screen’s z
    vs
    Camera’s z
    

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93. http://www.alecjacobson.com/weblog/?p=3835
    -0.001
    -1000
    0.996
    screenZ = f(n + cameraZ)/((f − n)cameraZ)
    -0.3
    screenZ
    cameraZ
    

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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...
    

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95. Way too hassle
    
    

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96. Removable?
    

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97. Must
    

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98. So,
    

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99. Understanding
    Coordinate’s system
    And..
    

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101. Make sense?
     

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102. Let’s study more?
     

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103. Make a airplane
     Bigger or Rotation
     

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104. Scale
     

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105. Rotate by SCNVector4
     Axis
     Degree
     

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106. Rotate by Euler angle
     

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107. Rotate by Euler angle
     x
     

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108. Rotate by Euler angle
     Y
     

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109. Rotate by Euler angle
     Z
     

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110. x Y Z
     

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111. That’s it
     

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112. One more thing.
     

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113. Making
     ARKit 2.0 repository
     

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114. End
     

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