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program3curves

# program3curves - Program 3 Bspline Curves Foundations of...

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Program 3 Bspline Curves Foundations of Computational Math 2 Spring 2011 Example 1: no clamping or wrapping PX = [ - 1 . 5 , - 1 . 3 , - 0 . 5 , 0 . 5 , 1 . 3 , 1 . 5 , 0 . 5 , - 0 . 5] PY = [ - 1 , 0 . 0 , 1 . 0 , 1 . 0 , 0 . 0 , - 1 , - 2 , - 2] -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 Figure 1: Example 1 curve. 1

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Example 2: Example 1 with clamping of P 0 = P 1 = P 2 PX = [ - 1 . 5 , - 1 . 5 , - 1 . 5 , - 1 . 3 , - 0 . 5 , 0 . 5 , 1 . 3 , 1 . 5 , 0 . 5 , - 0 . 5] PY = [ - 1 , - 1 , - 1 , 0 . 0 , 1 . 0 , 1 . 0 , 0 . 0 , - 1 , - 2 , - 2 , ] -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 Figure 2: Example 2 curve. 2
Example 3: Example 1 with clamping of P 0 = P 1 = P 2 and clamping of P n - 2 = P n - 1 = P n PX = [ - 1 . 5 , - 1 . 5 , - 1 . 5 , - 1 . 3 , - 0 . 5 , 0 . 5 , 1 . 3 , 1 . 5 , 0 . 5 , - 0 . 5 , - 0 . 5 , - 0 . 5] PY = [ - 1 , - 1 , - 1 , 0 . 0 , 1 . 0 , 1 . 0 , 0 . 0 , - 1 , - 2 , - 2 , - 2 , - 2] -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 Figure 3: Example 3 curve. 3

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Example 4: like Fig 8.15 no clamping or wrapping PX = [ - 2 , - 1 , 0 , 0 . 5 , 0 . 25 , 0 . 75 , 1 . 5 , 1 . 3 , 0 . 75] PY = [ - 2 , - 1 , - 2 , - 1 , 0 . 5 , 1 . 5 , 1 , 0 . 4 , 0 . 8] -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 Figure 4: Example 4 curve. 4
Example 5: like Fig 8.15 Example 4 with clamping of both endpoints PX = [ - 2 , - 2 , - 2 , - 1 , 0 , 0 . 5 , 0 . 25 , 0 . 75 , 1 . 5 , 1 . 3 , 0 . 75 , 0 . 75 , 0 . 75] PY = [ - 2 , - 2 , - 2 , - 1 , - 2 , - 1 , 0 . 5 , 1 . 5 , 1 , 0 . 4 , 0 . 8 , 0 . 8 , 0 . 8] -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 Figure 5: Example 5 curve. 5

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Example 6: like Fig 8.16(a) with clamping of both endpoints to the same position. PX = [ - 2 , - 2 , - 2 , 2 , 2 , - 2 , - 2 , - 2 , - 2] PY = [ - 2 , - 2 , - 2 , - 2 , 2 , 2 , - 2 , - 2 , - 2] -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 Figure 6: Example 6 curve.

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