Lecture21-Curves-I

# Lecture21-Curves-I - Curve 2 Curve Continuity C2 continuity...

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CS 455 – Computer Graphics Curves

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Parametric Function Complexity We need functions that give us enough flexibility to represent interesting surfaces We want to keep the complexity reasonable We will work primarily with 3rd order (cubic) polynomials § lower degree does not give us enough flexibility § higher degree or more complex functions require too much computation § can get curves such as:
Curve Formulation

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Curve Continuity Often times we want to join multiple curves together The continuity is measured by how smoothly they join C0 continuity refers to curves that join at their endpoints Curve 1 Curve 2
Curve Continuity Typically we will want curves that join with more smoothness than just C0 continuity C1 continuity refers to curves that join at their endpoints, and also have first derivatives equal at the join point Curve 1

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Unformatted text preview: Curve 2 Curve Continuity C2 continuity gives us common joint points, and 1st and 2nd derivatives equal at the joint point. Two curves that join at the endpoint and have the nth derivatives equal at that point are called Cn continuous. For most applications, we want to join curves with either C1 or C2 continuity. Why Cubic Curves? Get upto C2 continuity. Need more non-0 derrivatives to get more continuity. Minimal curviness when fitting a set of points. Specifying position and derivative at beginning and end is nice. Numerical computation issues are well-behaved enough Artist Friendly Controls We want the same expressive power we see in powerpoint curves You specify endpoints and tangents, math does the rest Curves Curves Now for quadratic curves. Cubics...
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## Lecture21-Curves-I - Curve 2 Curve Continuity C2 continuity...

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