Homework curves

Homework curves - e Find tangent vectors in Q(0 and Q(1(10...

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The Development of Graphics in Technology Department of Computer Graphics Technology Purdue University Homework Curves 1) Having control points P 0 =[A,B], P 1 =[C,D], P 2 =[E,F], and P 3 =[G,H] where the numbers ABCDEFGH are taken from your birthdate in the following way AB/CD/EFGH. E.g., 11/08/1999 gives points [1,1], [0,8], [1,9], [9,9] a. Sketch the Bezier cubic defined by the control points (5 pts) b. Express equation of Bezier cubic using these four control points (10 pts) c. Calculate tangent in Q(0.5) (10 pts) d. Find points Q(1/3) and Q(2/3) using geometrical representation of de Casteljau algorithm. (10 pts)
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Unformatted text preview: e. Find tangent vectors in Q(0) and Q(1) (10 pts) 2) Having control points P =[0,0], P 1 =[0,0] and tangent vectors in them , P’ =(0,1), and P’ 1 =( ‐ 1,0) a. Sketch Hermite cubic defined by the points and vectors (5 pts) b. Express equation of Hermite cubic (10 pts) c. Find a segment of Hermite cubic that C 1 interpolates the input curve from the endpoint and passes through the point P=[1,1]. Is the problem well ‐ defined? (10 pts) d. Find tangent to the curve in point Q(0.5) (10 pts) e. How would you express the same curve as Bezier cubic?...
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