CSE 167 Lecture 11: L11 2/12/19

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Problem 1 - consider a uniform quadratic b-spline. Consider a segment w/ control points (1,0) (1,1) and (0,1) in that order. B = p0 + 6/8 p1 + p2 = (p0 + 6p1 + p2) / 8. Notice: curve is not touching any of the points. Knot vector: -2, -1, 0, 1, 2, 3. Any point on the curve is designated by uuu. Therefore the leftmost endpoint (a) = 000. A = (p0 + 4p1 + p2) / 6. B = (p0 + 23p1 + 23p2 + p3) / 48 = (0, 11/12) Idea: just find the approximation for a quadrant (positive one), and mirror that for the other 3 quadrants because we can assume they"re symmetrical! B = (p0 + 2p1 + p2) / 4. Actual midpoint? (45 degree angle) = (1/sqrt(2), 1/sqrt(2)) Non-uniform bspline = bezier 0 0 1 1. Q0 = 2p0 - q1 = 2p0 - p1.

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