Past Midterm and Exam Questions (PDF) - Student.cs.uwaterloo.ca ...

More documents

Recommendations

Info

32 CS488/688 Introduction to Computer Graphics Now suppose we perform a uniform scale of 2.0 about the view point (e.g., about the point (.5, .5, 2)). Describe how the picture above will change. You may assume there are no clipping planes and that nothing else changes (e.g., we use the same perspective transformation). You may label the drawing above if it will help your description, and you may also sketch a picture below if you find that helpful (but you must still give a verbal description of any changes to the picture). 14.7 Perspective Projection [Last Used: Fall 2002 Midterm] A point p = [x y z 1] t is transformed by multiplying by the matrix product P V M, where M represents the modeling transformation, V represents the world-to-view change of basis, and P is the following OpenGL perspective transformation matrix ⎡ ⎤ cot(θ/2) aspect 0 0 0 ⎢ ⎥ P = ⎢ ⎣ 0 cot(θ/2) 0 0 0 0 − f+n f−n 0 0 −1 0 −2fn f−n where ’aspect’ is the ratio of the width to height of our viewport. The resulting matrix product yields ⎡ ⎤ A B P V Mp = ⎢ ⎥ ⎣ C ⎦ D 1. What must be done after computing P V Mp to complete the perspective transformation? Be specific (i.e., show the final result in terms of A, B, C, and D). 2. After completing part (a), what coordinate system is your result in? Describe the coordinate system in words, stating anything you know about the range of the coordinates. 3. Suppose our viewport is 200 pixels high. How must we further adjust the coordinates to map to this viewport? For simplicity, assume the lower left corner of the viewport has device coordinates (0,0) and that x increases to the right and y increases upward. 4. Suppose we transform our model by a transformation represented by a matrix T m relative to modeling coordinates. Show how to modify P V M to get a new transformation representing the composition of the new transformation with the old transformation. ⎥ , ⎦
CS488/688 Introduction to Computer Graphics 33 5. Suppose we transform our model by a transformation represented by a matrix T w relative to world coordinates. Show how to modify P V M to get the new transformation representing the composition of the new transformation with the old transformation. 14.8 Perspective transformation of line segments [Last Used: Fall 2009 Final] Suppose you have three line segments that project onto the screen as in the following diagram: Now suppose we look at an orthographic projection of these line segments from a side view in the direction indicated by the arrow in the above diagram (with the arrow being parallel to the projection plane). Circle the figures below that could possibly be a view of this orthographic projection of the line segments appearing in the above perspective projection, and cross out those that can not be a view of this orthographic projection of the line segments. Notes: in each of the figures below, the viewing parameters used in the figure above are indicated by E, the eye point, and ⃗v, the view direction. Also note that the height of the line segment representing the projection plane is equal to the height of the window in the picture above.
Page 1 and 2: CS488/688 Sample Exam Questions Uni
Page 3 and 4: CS488/688 Introduction to Computer
Page 31: CS488/688 Introduction to Computer
Page 77: CS488/688 Introduction to Computer

Past Midterm and Exam Questions (PDF) - Student.cs.uwaterloo.ca ...

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?