Navigating in Three Dimensional Environments

1
Navigating in Three Dimensional Environments

• GROUP 5
• Eric Sedor
• Mitra Totten
• Austin Lee
• Matthew Keelan

2
Overview

• The 3D to 2D transformation
• Why is navigation useful?
• Navigation within 3 Dimensions
• The VRC as a mobile unit
• Translation of the VRC (Walking)
• Rotation of the VRC (Turning)
• Our experimentation

3
The 3D to 2D Transformation

• 3D world-coordinate
• output primitives

2D device coordinates
Transform into viewport in 2D device coordinates
for display
Clip against view volume
Project onto projection plane
Clipped world coordinates
4
Perspective Projections

• VPN This is the view plane normal, it defines
  the normal to the viewing plane in world
  coordinates.
• VUP "View Up Vector". This defines the y axis of
  the view plane in world coordinates.
• VRP "View Reference Point". This defines the
  origin of the view plane coordinate system in
  world coordinates.
• PRP "Projection Reference Point". This defines
  the place to "look from". The PRP is given in
  coordinates relative to the view coordinate
  system.
• xmin, xmax, ymin, ymax This defines the viewport
  on the VPS (View Plane coordinate system). These
  coordinates are good to use if the view is too
  small.

5
Perspective Projections (2)

• The Viewspace

6
Normalizing transformation (Nper)

• 1) Translate VRP to the origin T(-VRP)
• 2) Align VRC with World Coordinates
• Rotate VRC such that VPN becomes the Z axis, the
  u axis -gtx axis, v axis -gty axis R
• 3) Translate so that COP (PRP)  is at the origin
  T(-PRP)
• 4) Shear so that the center line of the view
  volume becomes the Z axis SHpar
• 5) Scale such that the view volume becomes
  perspective canonical view volume Sper
• NperSperSHparT(-PRP)RT(-VRP)

7
Why navigate?

• Simple projection is static and of limited use in
• Simulation
• Entertainment
• Application
• A navigable environment is the answer

8
How do you navigate in 3D?

• The VRC must be thought of as mobile, rather than
  static
• As such, a velocity must be attributed to the
  VRP. Recall that Velocity is a vector V (where
  Vspeed)
• Rotation occurs around the observer, at the PRP.

9
Walking

• Movement of a person can
• be accomplished through
• translation of the VRC
• Through the WRC.
• Walking forward requires
• calculation of a new VRP
• location inside of the WRC
• based on the desired
• direction of travel.

10
Turning

• Turning is accomplished by
• rotating the VRC inside of the
• WRC.
• Translate the VRP such that the PRP lies on the
  origins of the WRC.
• Rotate the VRP around the origin
• Rotate the VUP and the VPN by the same rotation
  matrix used on the VRP.
• Translate the VRP back such that the PRP lies
  where it began.

11
Equations

• WALKING
• VRPnew VRPold V
• TURNING
• VRPnew (-T-PRP) Rturn T-PRP VRPold
• VPNnew Rturn VPNold
• VUPnew Rturn VUPold

12
Our Program
13
References

• http//home10.inet.tele.dk/moelhave/tutors/misc/us
  rguide/usrguide.html
• http//www.cs.wisc.edu/schenney/courses/cs559-s20
  01/lectures/lecture-10-online.ppt
• http//www.ece.purdue.edu/ebertd/435/notes/435_ch
  7_part2.html