# 4 then t4 t t5 and the control points that affect the

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Unformatted text preview: lt; t5, and the control points that affect the final position are P4, P3, P2, P1 Example • Assume we have a cubic B-spline whose knot vector is {0, 0, 0, 0, 0.25, 0.5, 0.75, 1, 1, 1, 1} • Let’s compute a point at t = 0.4 • Then, t4 &lt; t &lt; t5, and the control points that affect the final position are P4, P3, P2, P1 What if you want to edit some details? • You might want to add some high resolution details at a particular area while keeping the rest the same Knot insertion • We can do this by knot Insertion – increase the resolution for some area • New knots and control points can be added without changing the shape of the curve • Both the knots and control points are going to increase Knot insertion • For a curve of degree f, we remove f-1 points and add f points • i.e., for a cubic B-spline, remove 2 points and add 3 points Knot insertion • If the new knot t is inserted into the span [tj, tj+1), the new control points can be computed by where Qi is the new control p...
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