Last Updated February 22, 2010

Projection & Viewing

  1. What is the synthetic camera? What are its components?
  2. What is the viewing transformation? Why is it needed?
  3. Derive a set of equations equation (or a matrix) for perspective projection.
  4. What is pre-warping? What is its effect on the view volume?
  5. Draw diagrams showing the difference between parallel & perspective projection
  6. Why does perspective projection give a more “realistic” view than parallel projection? Visually, how do these two projections differ?                                                                  (7 Marks)
  7. Describe the steps required to transform a vertex in model space to a point in screen space. Illustrate each step with a diagram.
  8. Given a polygon mesh describe a flexible system of viewing this polygon mesh.
  9. Describe the components and features of the Synthetic Camera.
  10. The synthetic camera model requires that point coordinates be transformed from World coordinates to Viewing coordinates. Derive a matrix to carry out this transformation.              
  11. What effect does the projection matrix have on the view volume? How is this effect useful?   
  12. Given that the centre of projection is at E(0,0,-en). Derive an equation in u, v, n for the perspective projection of a point P(pu, pv, pn) onto the u-v plane.                                           
  13. Draw three diagrams representing the View Volume; (a) before pre-warping (MsMp); (b) after pre-warping and (c) after normalisation. Clearly indicate on the diagrams to position of key components. The diagrams should be drawn in the v-n plane.                                                                         
  14. Derive a matrix to convert from world coordinates to the viewing coordinate system of the synthetic camera.
  15. Derive a matrix MTOT, which transforms a window in real world co-ordinates to a viewport in Normalised Device Co-ordinates.
  16. Given a general rectangular window defined in a 2-D world cordinate system and a general recangular viewport defined in NDC, derive a matrix which will trandsform a point in the window to a corresponding point in the viewport
  17. Prove that the view volume for a perspective projection becomes an parallelepiped when pre-warping is applied.
  18. Describe the three components of the synthetic camera viewing system. Include in your description how each component is defined.
  19. Describe the effect of normalisation on the pre-warped view volume.
  20. When viewed by a perspective projection, which of the following properties of a model will be preserved: lengths, angles, parallel lines, and straight lines?

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