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24 CS488/688 Introduction to Computer Graphics Union Intersect A A−B B A−B B A T(5,4) T(1,2) S(3,6) T(4,5) S(2,2) T(5,2) S(2,6) T(4,2) S(4,6) Union T(2,2) where the circles and squares at the bottom are primitives, the T(x,y) nodes represent translations by those amounts, the S(sx,sy) nodes represent non-uniform scales by those amounts, and the A-B, Union, and Intersect nodes represent those CSG operations. In the grid below, draw the resulting scene. In this figure, we have drawn the square and circle primitives in their base locations. We have drawn them “hollow” to indicate their locations more clearly; however, you should think of them as “filled in” as shown in CSG tree above, and you should shade in the appropriate areas in your figure below. 10 Input 10.1 Virtual Input Devices [Last Used: Winter 1992 Midterm] (a) The text names six virtual graphic input primitives: locator, pick, choice, valuator, string, stroke Write a brief (one or two sentence) description of each. (b) With the exception of pick, indicate a “natural” hardware device to associate with each. (c) Abraham Maslow once said, “If the only the tool you have is a hammer, the whole world tends to look like a nail.” Suppose that the only physical input device available is a trackball, with no buttons, that responds to rotation around three axes.
CS488/688 Introduction to Computer Graphics 25 Describe what would you would do to implement each of the five virtual devices of (b) using only the trackball. The locator you implement should be a 3D locator. (You may assume that there is screen feedback provided; i.e., rolling the ball left/right moves the cursor horizontally, rolling the ball up/down moves the cursor vertically, and twisting the ball makes the cursor blink.) 11 Modeling 11.1 Tetrahedron [Last Used: Spring 2000 Final] Consider the tetrahedron whose vertices are A = (1, 1, 1), B = (0, 1, 1), C = (0, 0, 1), and D = (0, 0, 0). (a) What are the normals of the four triangles that bound the tetrahedron? (b) Assume that the eyepoint is at the point (-1,-1,-1). Which triangles (ABC, ABD, ACD, or BCD) are backfacing? (c) Assume that a light source is at the point (−∞,0,0), has intensity 10.0, and all faces of the tetrahedron have a diffuse reflectivity coefficient of 1.0. Compute the light due to diffuse reflection from all four faces of the tetrahedron. (d) Describe how to calculate vertex normals given the normals for each surface of an object. Calculate the vertex normals for the tetrahedron. 11.2 Cube Projected as Hexagon [Last Used: Winter 1992 MidTerm] A cube viewed in parallel projection along a body diagonal (corner to corner through the centre of the cube) has a hexagonal cross-section. The objective of this question is to show the sequence of transformations needed to place a cube in space so that a hexagon appears on the display. Suppose that you have viewing parameters given by:
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Past Midterm and Exam Questions (PDF) - Student.cs.uwaterloo.ca ...

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