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70 CS488/688 Introduction to Computer Graphics making the same angle with n as l does but on the reflected side. Give an equation for unit vector r in terms of the vectors above. n l r v x 59. What effect does the Phong lighting term (k s (⃗r · ⃗v) p ) attempt to model? What effect does varying p have? 60. What is a matrix stack and how is it used in computer graphics? 61. Suppose we have a 1280x1024 raster display, with a single window/viewport that covers the entire display, with pixel 0,0 in the upper left hand corner as illustrated below. In the picture, give a reasonable sketch indicating how normalized device coordinates would map on to this display. Further, give the NDC coordinates of at least two points in the picture. 0,0 1279,1023 62. The Lambertian lighting term approximates the amount of light coming in from a light in direction ˆl, reflecting off a matte surface at a point with normal ˆn, and reflecting in direction ˆv. The Lambertian lighting term is I o = k d I i (ˆl · ˆn), where k d is an RGB triple describing the material properties of the surface, and I i is an RGB triple of intensities of the light coming into the surface, and I o is the intensity of light leaving in direction ˆv. Why doesn’t the outgoing direction ˆv of the light enter into this equation? 63. Why do you have to clip to the near plane before doing perspective projection (or at least, before doing the normalization step)? 64. Draw a picture of a set of simple polygons that the Painter’s algorithm can not render without splitting the polygons.
CS488/688 Introduction to Computer Graphics 71 65. In class, we studied the Liang-Barsky clipping algorithm for lines (i.e., the one for lines, not the one for polygons). Typically this algorithm is used to clip lines to an axis aligned, rectangular window. Can the Liang-Barsky algorithm be used to clip lines to the following, non-rectangular window? If so, note any additional difficulties in implementation (as compared to implementing it for axis aligned, rectangular windows), and if not, justify your answer. 66. Can the Liang-Barsky algorithm be used to clip lines to the following, non-rectangular window? If so, note any additional difficulties in implementation (as compared to implementing it for axis aligned, rectangular windows), and if not, justify your answer. 67. What is the difference between Gouraud shading and Phong shading? 68. Demonstrate, using algebra or a picture, that order matters when composing transformations. 69. Suppose we have the standard, orthonormal World Frame F w = {ŵ 1 , ŵ 2 , ŵ 3 , O w } and a Viewing Frame F v = {ˆv 1 , ˆv 2 , ˆv 3 , O v } where v 1 = w 2 v 2 = −w 3 v 3 = w 1 O v = O w + w 1 Give the change of basis matrix to take coordinates relative to F v and returns coordinates relative to F w . 70. In volume rendering, you can either render from “front to back” or from “back to front.” What are the advantages each method?
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