ME325_HW6

ME325_HW6 - functions 3 If we want to use a B-spline to...

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ME325, Homework 6 1. Finish reading Chapter 6 of Lee. 2. A matrix of control points for a cubic Bezier curve are given by : P = ± ² ² ² ² ³ ´ µ µ µ µ 1 1 0 1 3 0 3 4 0 5 4 0 a) Sketch the curve. b) Compute the two new control point matrices obtained by splitting the above Bezier curve at t=0.25. 2. Starting with the B-Spline basis functions. Show that if we use the knot vector T={0,0,0,1,1,1} and using k=3 (quadratic) that the B-Spline curve is identical to the Bezier curve. Hint: Compute number of control points, work out math for basis
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Unformatted text preview: functions. 3. If we want to use a B-spline to interpolate (or fit) data we need to be able to evaluate the values of the N i,k (u i ) given a value of u i . Suppose we are using a second degree (quadratic) B-spline and have chosen a knot vector T={0,0,0,1/3,2/3,1,1,1} (assume the spline is non-periodic). How many control points can we use in this spline? Compute the non-zero function values of N i,k (u i ) at u=.50....
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