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Homework
Texture Mapping and Ray Tracing
Due Thursday, November 8 by the end of class
(Grade out of 100 points)
Question #1 - Texture Mapping: (30 points) Assume that you are given the following texture: And you want to map it onto two triangles arranged as follows: For each of the following questions, I will give you the rendered image that is desired. Please give the (u,v) texture coordinates for each of the 4 triangle vertices that would result in that image. (7.5 pts each) (a) (b) (c) (d)
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Question #2 - Ray-Object Intersections: (30 points) For each part, solve for the ray-intersection equation with the following geometric shape. (In the form t = f(x, y, z)) (a) Infinite planes in the xz-plane (b) Rectangles in the xz-plane (defined by (x 1 , y 1 ): lower left corner, (x 2 , y 2 ): upper right corner) (c) Circular discs in the xz-plane (defined by (x 1 , y 1 ): center, r: radius) Question #3 - Generating Rays: (30 points) Build the camera matrix for a camera located at (4, 3, 0) looking at the origin (0, 0, 0). Its field of view is 60°, the resolution of the final image is 800x600. The up vector is the positive y- axis, (0, 1, 0). Question #3 - Refracting Rays: (20 points) Assume that you have one object in your scene: a unit sphere made of glass (refractive index n=1.5), located at the origin. The sphere is surrounded by air (n = 1). Consider a single ray incident on the sphere, originating from (3, 3, 3) and directed toward the origin (0, 0, 0). Using Snell’s law (from the October 23 slides), compute: (a) the new ray inside the sphere (point and vector) (10 pts), and (b) the ray that exits the sphere (point and vector) (10 pts)
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