Unformatted text preview: CS480/CS680 Problem Set 2 Due in class Tuesday, April 8 at the beginning of lecture. Please prepare the answers to these questions, neatly written or typed, on separate paper. 1. (10 points) Prove the invariance property of NURBS under perspective viewing transforms. In other words, prove that applying a transform M per to the control points p k yields the same result as apply- ing M per directly to the output of the NURBS curve function P ( u ) . 2. (10 points) Are NURBS also invariant to affine transformations? Justify your answer. 3. We are given the following boundary conditions for a cubic spline section: P (0) = p k P (1) = p k +1 P 00 (0) = p k- 1 + p k +1- 2 p k P 00 (1) = p k + p k +2- 2 p k +1 In this case M geom = [ p k- 1 p k p k +1 p k +2 ] T and the boundary conditions can be written P (0) P (1) P 00 (0) P 00 (1) = 1 1 1- 2 1 1- 2 1 p k- 1 p k p k +1 p k +2...
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- Spring '08
- Manifold, Parametric equation, B-spline, pk−1 pk pk+1, pk pk+1 pk+2