Recap

• Display lists and multiple transformations: pytw/demos/modeling/Fence.py
• Teddy bear and coordinate frames
• 
• Nested frames: pytw/demos/modeling/Mobile.py

New Material

• Matrix representation of affine transformations:
  • The Current Transformation Matrix (CTM)
  • Associativity and non-commutativity of matrix multiplication
  • matrix for scaling
  • matrix for rotation
  • matrix for translation and the need for homogeneous coordinates
  • OpenGL matrices, points and vectors are 4D.
• pinhole cameras
  • Pinhole camera:
    
  • Pinhole camera with object and its projection:
    
  • Pinhole camera showing similar triangles:
    
  • Synthetic camera moves the image plane in front to elimate negatives:
    
• What is the height of the projected tree?
• Perspective: projections shrink with distance
• Example: With the standard camera and the image plane at z=-3, find the projection of (7,8,-9).
• why doesn't the world look upside down?
• perspective matrices
• perspective division
• orthogonal projection
• gluPerspective, glOrtho, glFrustum
• placing the camera
• the VPN, VRP, VUP frame
• gluLookAt

Tutors

Some OpenGL wizards (not me) have built a tutor for playing with these camera APIs. It is in:

$TWHOMEDIR/tutors/

Demos

All of these demos are in tw/demos/camera:

• Frustum.py shows what a Frustum looks like. This one has a pretty wide FOVY.
• Perspective.py shows the same wire cube using two different cameras.
• BarnViews.py shows the barn from different viewpoints (VRP) and even with a random FOVY (use the "G" callback).
• CityView.py shows the effects of FOVY and near/far. Use + and - to adjust FOVY, and use N/N and F/f to adjust near/far. Try viewing from the side (the X axis), too.
• Viewports.py shows the same object with the same camera (a square frustum) rendered in three different viewports.
• FrustumModes.py shows the same object but with a camera where the frustum is determined by the shape of the window and the desired presentation (l=letterbox, c=clipping or d=distortion).
• Click.py shows the idea of unprojection and how to do it.

Exercise

We'll work through the following together:

• Set up a camera to view the twSolidBarn from some position, say in front.
• First, figure out the function calls we'll need and the arguments:

  glMatrixMode(GL_PROJECTION);
  glLoadIdentity();
  gluPerspective(fovy, aspect_ratio, near, far);
  glMatrixMode(GL_MODELVIEW);
  glLoadIdentity();
  gluLookAt(eyex, eyey, eyez, atx, aty, atz, upx, upy, upz);
  

• Copy the Barn demo
• Replace twCamera() with what we have above.
• Compile, cross fingers and run it.

Forced Perspective

We'll look at the DVD for LotR:The Fellowship of the Ring, where they explain how forced perspective works and other camera tricks that they used. (The segment takes about 10 minutes.)

twCamera

If we have time, we can talk about how the twCamera setup works.

Written by Scott D. Anderson
scott.anderson@acm.org

This work is licensed under a Creative Commons License.