The final stages of Transformation

• one last trip through the pipeline for transformation
• For reference draw a positive x, y and z axis and label them.
  • State 0
  • This needs to gluLookat () called
  • T_w2m = gluLookAt(eye, center, up)
  • The frustum is 1 to 10, so the axis are outside of the frustum without this transformation.
  • Note also, that after this transformation, the positive z axis is headed out of the screen (in modeling coordinates)
  • We can move about (the eye position) with x:4-6, y: 8-2, z:1-3
• We model a unit cube centered at 0,0,0.
  • State 1
  • No transformations, except for the final model to viewing transformation are applied at this point.
  • The actual cube drawn is transformed by T_w2m
    • The cube is modeled (-.5, -.5, -.5) to (.5, .5, .5)
    • And the eye position is (0,0,2)
    • So the cube is actually drawn at (-.5, -.5, -2.5) to (.5, .5, -1.5)
• Draw some numbers on the faces of the cube,
  • State 2
  • They are drawn at the origin, but I want to center them at the origin
    • This will make them easier to move to the right place on the cube.
    • 0 is approximately 77 wide by 152 tall.
    • So I translate them by (-charWidth/2, -charHeight/2)
  • They are too tall, I want them to fit in the unit cube
    • So I need to scale them by 1/(152*1.2).
    • So I scale them by 1/largest dimension * .7
    • .7 is completely arbitrary, it looks good to me.
  • This will make it fit in the unit square.
  • I want to rotate them to align them with the face
    • By +/- 90 about y for the two sides (2,5)
    • By 180 about y for the back (6)
    • By +/- 90 about x for the top/bottom
  • Finally they need to be translated into the proper location
    • 1 on the front face, translate by (0,0, .5)
    • 6 on the back face, translate by (0,0, -.5)
  • In this case, the letters are translated, scaled, rotated, and translated from their modeling coordinates to the modeling coordinates of the die.
• I'd like to display a pair of dice, further back in the scene, showing 1 and 3.
  • The first Die
    • State 3
    • I want to do this at the origin as this is where they are modeled.
    • Otherwise, I would need to move them onto an axis then rotate.
    • The first I will rotate by -90 about the x axis.
    • This is really moving it into world coordinates.
  • It is in the wrong place
    • State 4
    • It needs translated up by 0.5,
    • And needs moved over and back
    • So the translation matrix (3, 0.5, -4)
  • The second die
    • State 5
    • Rotate by 180 about the z axis
    • Rotate by 45 about the y axis.
    • Translate by 2, 0.5, -3
• Look at the two dice.
• Turn off the axis.
• A note about the unity camera.
  • The camera documentation
  • Note, the camera is specified in world coordinate system.
  • But it has most of the properties of the openGL camera.
• One last transformation
  • After projection, items are in NDC space (-1, -1) to (1,1)
  • The openGL standard
  • The actual display window is (0,0) to (w, h)
  • specified by glViewport(0,0, w,h)
  • But remember, in X at least, we need to flip the y.
  • Can we do this?