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set8 - $ Set 8 Parametric Curves Kyle A Gallivan Department...

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a39 a38 a36 a37 Set 8: Parametric Curves Kyle A. Gallivan Department of Mathematics Florida State University Foundations of Computational Math 2 Spring 2011 1
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a39 a38 a36 a37 Parametric Curves Consider a curve in R 2 . Parametric form ( x ( t ) , y ( t )) for t 0 t t n and t R . Implies an ordering to the points. The interval can be adjusted to yield any length or rate of motion. Used in phase plane representation of behavior of a dynamical system. May have sample points of an underlying system. May have points in a plane from a graphics application. Order can be chosen and imposed on the parameter. Want a smooth curve to indicate the shape of the point collection. 2
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a39 a38 a36 a37 Parametric Curves A circle can be parameterized as (sin ωt, cos ωt ) Frequency ω can be set to dictate the velocity around the circle as a function of t . Suppose you had points on the circle ( x i , y i ) , 0 i n Could draw the curve with simple linear connections piecewise Lagrange of any degree splines of any degree 3
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