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36 CS488/688 Introduction to Computer Graphics 14.12 Forced perspective [Last Used: Winter 2011 Final A classic “forced perspective” trick in photography is to have two friends Nero and Farley pose for the camera, with Farley standing much farther away than Nero. Nero then holds her hand up in such a way that in the resulting photograph she appears to be holding a tiny statue of Farley in her upturned palm. The photograph on the right gives an example. Assume that the ground is perfectly level, and that the photographer, Nero and Farley stand in a straight line. The photographer holds the camera at height h C above the ground. Nero’s body (including her hand) is at distance d N from the photographer (measure d along the ground). Her hand is at height h N above the ground. Photo by Shane Huang (a) Assuming that you are given h C , d N and h N , find an expression for d F , the distance required between Farley and the camera in order to ensure that his feet rest precisely in Nero’s hand. (You may wish to draw a diagram of this scene as viewed from the side.) (b) Assume that Nero and Farley are of identical heights. At what height h N must Nero hold her hand so that in the photograph, Farley appears to be exactly 1/10 as tall as Nero? 15 Shading and Lighting 15.1 Diffuse and Specular Last Used: Fall 2011 Final In the 2D figure below, we have the eye located on the left, a plane (line) along the bottom, and a point light source towards the right; the light is twice as far from the plane/line as the eye is from the plane/line. The marked and labeled locations on the plane/line indicate the closest point of the eye and the light to the plane/line. For the purposes of this question, the dot at the front of the eye is used as the eye point, and (for the first two parts) the intensity of the light does NOT attenuate with distance.
CS488/688 Introduction to Computer Graphics 37 Light Eye Eye Light 1. Assume the plane/line only has a diffuse material component. Mark with a ’D’ on the figure where the plane/line will appear brightest to the viewer. 2. Assume instead that the plane/line only has a specular material component. Mark with an ’S’ on the figure where the plane/line will appear brightest to the viewer. 3. Suppose now the light has r 2 attenuation. How will the location of the brightest point change if the plane/line only has a diffuse material component? 4. Again suppose the light has r 2 attenuation. How will the location of the brightest point change if the plane/line only has a specular material component? 15.2 Phong Lighting and Gouraud Shading [Last Used: Spring 1992 Final] Answer the following parts, giving details and/or reasons for all answers. (a) The shading intensity at any given point on a surface is, in general, comprised of three contributions, each of which corresponds to a distinct physical phenomenon. List all three, stating how they are computed in terms of the appropriate vectors (which you should define). In particular, what is the formula for the “reflection vector”? (b) How is any interior pixel of a triangle, indicated below by P , to be coloured according to the Gouraud method? In which spaces (object, world, perspective, or screen) could one compute the normals? In which spaces could one compute the shades? In which spaces should the normals not be computed? In which spaces should the shades not be computed? What information must the pixel-filling algorithm have in order to assign pixel shades to the edges and interior of the screen projection of a polygon? (c) Answer all of the questions in part (b) for the Phong method of assigning pixel colours.
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