Stereo Computer Graphics

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Stereo Computer Graphics

• Dale D Bigham
• Naval Postgraduate School
• bigham_at_cs.nps.navy.mil

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?WHAT?

• Images created on a 3D coordinate system then
  displayed as a parallel or perspective projection
  onto a flat CRT screen
• OK, WHY?
• (show video)

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Overview

• Steroscopic
• Time Multiplexed
• Time Parallel

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Steroscopic

• Is binocular disparity.
• BUT, First
• Depth cues
• back to basics.

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What the eye does

• AccomodationPhysical change to the lens
  thickness due to tension by the ciliary muscle.
• Convergence inward rotation of the eyes to
  converge on an object.
• (show eye show)

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WALL-EYED or Free-Viewing

• Cross your eyes, but you need to be close

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What the world does

• Binocular disparity difference in the images
  projected on the left and right eye, is modeled
  in computer graphics by displaying to the eye two
  off axis centers of a perspective projection.

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WWD

• Motion Parallax By the movement of your head
  from side to side or the movement of the
  background against two objects. Your brain tells
  you which object is closer, by the relative speed
  of the objects against the background. Objects
  that are closer to you move faster.

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Mind over matter

• I dont mind so it dont matter
• -Colors, bright colored objects that are the same
  as a dark ones will appear closer.
• - Textures, closer objects have greater detail
  that blur as the object moves away.

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MOM

• Image size, We know the general size of a person,
  if we see a bowling ball that is the same size as
  the person, we surmise the bowling ball is
  closer.
• Interposition, objects in front of others are
  closer

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MOM

• Perspective, objects that are far away appear
  hazy and bluish, Blue has shorter wavelength thus
  it travel further than other colors.
• Shading, light from a light source, fades at
  greater distances making objects darker.

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How?

• Time Multiplexed
• Electro Optical
• Mechanical
• Time Parallel
• Anaglyph
• Separate image

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T P Anaglyph

• Presents left and right eye views on a single CRT
  screen by the use of filters.
• The observer wears glasses that match the filter,
  black and white color get red and green filters
  and for color red and cyan or green and magenta.
  Problem distorts the true colors of the image.

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T P Separate Image

• Right and left displays are truly on different
  displays, ie HMD, dual screen or split screen.
  Split screen often uses the partially silvered
  mirror, this uses two displays at right angles to
  each other with filters. The user wears glasses
  that are polarized so each eye gets the correct
  view.

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TM Mechanical

• Works by alternating right and left eye views on
  same CRT, must be at 120HZ so each eye gets 60HZ.
  Must be in sync with a shutter system to get
  right and left views at correct times. First used
  rotating cylinder, with correct slitsfor left and
  right eyes.

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TM Electro Optical

• -PLZT shutters(lead lanthanum zirconate titanate
  ceramic wafers) only transmitted 15 17 percent
  of light, light passes thru a front vertical
  polarizer when voltage is applied the light is
  rotated 90 degrees to pass thru a rear horizontal
  polarizer.

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TM Electro Optical (cont)

• -LCM(liquid crystal modulator)
• Active works same as PLZT except lets in twice
  as much light
• Passive The LCM is mounted to the CRT screen,
  the LCM use a circularly polarized cell that
  displays the left eye in one direction and the
  right in the other. Then the Passive glasses are
  polarized to see the correct view.

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OFF AXIS Projection

• Off axis rotates the field of view at the
  eyeball back toward the center

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ON AXIS Projection

• Slides out horizontally from center.

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OFF AXIS Projection

• Due to the rotation the field of view is greater,
  thus this method is perfered.

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ON AXIS Projection

• BUT, the on axis can be implemented in hardware
  so it has the better performance.

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THE MATH!! Viewing transformation

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THE MATH!!

• To calculate the transformation required to map
  world coordinate vertices to view coordinate
  vertices all that is required is to
• calculate the transformation required to
  transform the two coordinate systems to the same
  position and orientation.
• If we assume the simplification that the view
  direction is along the view z axis, then this
  transformation consists of the following

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THE MATH!!

• transformations
• Translate the view origin to the world
  origin
• Rotate anti-clockwise about the world y-axis
  by theta
• Rotate anti-clockwise about the world x-axis
  by phi
• With the view defined in polar coordinates, the
  calculations are as follows
• viewing vector (r, theta, phi)
• 1 0 0 -((r sin(phi))
  sin(theta))
• Translate_origin 0 1 0 -(r cos(phi))
  
• 0 0 1 -((r sin(phi))
  cos(theta))
• 0 0 0 1
  

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THE MATH!!

• Rotate_Y cos(-theta) 0 sin(-theta) 0
• 0 1 0 0
• -sin(-theta) 0 cos(-theta) 0
• 0 0 0 1
• Rotate_X 1 0
  0 0
• 0 cos(90 - phi) -sin(90 - phi)
  0
• 0 sin(90 - phi) cos(90 - phi)
  0
• 0 0
  0 1

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THE MATH!!
Viewplane located at z 0 LCoP at (-e/2, 0, -d)
RCoP at (e/2, 0 , -d) xsl (xp(d) - zpe/2)/(d
zp) ysl yp(d)/(d zp) xsr (xp(d) zpe/2)/(d
zp) ysr yp(d)/(d zp).

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ISSUES

• Interocular cross talk(Ghosting) combined
  effects of phosphor persistence and shutter leak.
• CRT refresh rate the refresh rate is at 120,
  that provides 60 to each eye, but the vertical
  resolution is divided into four sections two for
  left eye right eye being displayed and two for
  next left and right.
• Image scaling (as seen in video) there is an
  optimal view point fixed horizontal parallax,
  move away from the view and the image elongates.

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Referances

• Larry F Hodges, Georgia Institute of
  Tech,
• Stereo Computer Graphics by David F. Mcallister,
• Multimedia Laboratory Department of Computer
  Science North Carolina State University,
• Michel Capps,
• GOTO.COM

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THE Questions!