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# a1 - CPSC 314 Assignment 1 due Tuesday 2pm Worth 9 of your...

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CPSC 314 Assignment 1 due: Tuesday, October 12, 2010, 2pm Worth 9% of your final grade. Answer the questions in the spaces provided on the question sheets. If you run out of room for an answer, continue on the back of the page. Name: Student Number: Question 1 / 10 Question 2 / 3 Question 3 / 5 Question 4 / 4 Question 5 / 5 Question 6 / 30 TOTAL / 57 1

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CPSC 314 Assignment 1 September 2010 1. Composing Transformations (a) (4 points) Express point P and vector V in F w and F obj . (b) (2 points) Give the 4 × 4 transformation matrix M that should be used to draw the house, i.e., that takes a point in known object coordinates and transforms it to world coordinates. Assume that z remains unaltered, i.e., z w = z obj . Verify that you get the correct answer for point P . (c) (2 points) Given M = Translate ( a, b, 0) Rotate ( z, θ 1 ) Scale ( c, c, c ), provide the val- ues of a, b, c, and θ 1 that would implement the given transformation. (d) (2 points) Given M = Rotate ( z, θ 2 ) Translate ( d, e, 0) Scale ( f, f, f ), provide the val- ues of d, e, f, and θ 2 that would implement the given transformation. Page 2 of 8
CPSC 314 Assignment 1 September 2010 2. (3 points) Determine the viewing transformation, M view , that takes points from WCS (world coordinates) to VCS (viewing or camera coordinates) for the following camera parameters: P eye = ( - 40 , - 10 , - 10) , P ref = (0 , - 10 , - 10) , V up = (0 , 0 , 1). Do not bother with numerically inverting any matrices. 3. (a) (2 points) Draw a scene graph for the scene below. Label each of the edges in the scene graph with a unique name, M n , to represent the transformation matrix that takes points from the child frame to the parent frame. Assume that there is hand geometry that is associated with each of F L 3 and F R 3 , and that the camera and body are positioned with respect to the world frame. (b) (1 point) Give the transformation that would be used when drawing the right fore- arm, i.e., to transform points in F R 2 to F cam .

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a1 - CPSC 314 Assignment 1 due Tuesday 2pm Worth 9 of your...

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