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Written Assignment #1 Math for Computer Graphics 15-462 Computer Graphics, Fall 2004 DUE: Thursday, September 9, just before class The work must be your own. Please use any resources available to you (the book, the web, etc.), but write up the answers in your own words, explaining all of the steps. Also please cite any external references you use (other than the textbook) to come up with your answers. 1. Shirley 2.9. Given the non-parallel 3D vectors a and b, compute a right-handed orthonormal basis such that u is parallel to a, and c is normal to the planes defined by a and b. 2. Shirley 2.11. What is a parametric form for the axis-aligned 2D ellipse? 3. Shirley 2.12. What is the implicit equation of the plane through 3D points (1,0,0), (0,1,0), and (0,0,1)? What is the parametric equation? What is the normal vector to this plane? 4. Shirley 2.13. Given four 2D points a0, a1, b0, and b1, design a robust procedure to determine whether the line segments a0a1 and b0b1 intersect. [Note: you do not need to write C code, just carefully outline the steps in the algorithm. ‘Robust’ means that your algorithm should work for all possible values of a0, a1, b0, and b1, and that you should avoid problems such as dividing by zero. Do not worry about situations where points are NAN or infinity.] 5. Given 3D points (0,0,0), (3,0,0), and (1,1,0), derive the expression for the barycentric coordinates for any point p in the z=0 plane. Test several points to make sure your solution is correct.