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# lecture16 - CSE472 Computer Graphics Curves III Don't we...

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1 CSE472 Computer Graphics Curves III Don’t we have all we need? Spline Curves NURBS

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2 CSE472 Computer Graphics Interpolating Curves An interpolating curve will hit certain points on the curve. Bezier curves hit the end points What if we have a lot of segments?
3 CSE472 Computer Graphics What’s bad about that? Specifying points on the curve (surface) is often difficult We like to specify end points, but not other points What we would really like:

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4 CSE472 Computer Graphics What else do we want? We want local control A control point effects a limited range of the curve We want more control points Why only 4?
5 CSE472 Computer Graphics Some ideas Remember that a Bézier curve can be defined as: This uses a function b k (u) that controls the influence of the points. = = 3 0 ) ( ) ( k k k p u b u p

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6 CSE472 Computer Graphics The Bézier Blending Polynomials -0.2 0 0.2 0.4 0.6 0.8 1 1.2 0 0.08 0.16 0.24 0.32 0.4 0.48 0.56 0.64 0.72 0.8 0.88 0.96 (1-u)^3 3u(1-u)^2 3u^2(1-u) u^3 = = 3 0 ) ( ) ( k k k p u b u p
7 CSE472 Computer Graphics Can we extend this? Suppose we have 5 points? Can we create a blending function of some kind?

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8 CSE472 Computer Graphics One (dumb) idea… 0 0.2 0.4 0.6 0.8 1 1.2 0 0.070.140.210.280.350.420.490.560.63 0.7 0.770.840.910.98 p0 p1 p2 p3 p4 What would this draw?
9 CSE472 Computer Graphics Can we do better? What do we want?

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lecture16 - CSE472 Computer Graphics Curves III Don't we...

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