Help with understanding homework
Good morning,
I have a problem with understanding my homework. I have to write a program that computes a circumference of a parametric curve(it is really not important what curve it is), firstly by computing N points of the curve and comuting distances between them, to do this, I have to write a function ApproximateCircumference(Write real function ApproximateCircumference of integer parameter N, that computes circumference of polygon with N sides with vertexes equal to parameter t=(N-1)*2pi/N, t is the parameter in the parametric curve). Easy one.
The second task is, to write a function that computes lagrangean polynomial(interpolation) of k-1th order from k points. Also easy.
But the last task is, to write a function BetterCircumference that computes the circumference by extrapolates ApproximateCircumference(N/2^(k-1)) as function of x=1/N^2 in point x=0 where N would be equal to infinity.
I don't know how, I don't know what the third task means, I suppose I should use the Lagrangean polynomial, but how? What does that x=1/N^2 mean? N is constant, it is number of points/sides of a polygon in the first task...
Please, help.
Thank you
P.S. please excuse me for my english.
I have a problem with understanding my homework. I have to write a program that computes a circumference of a parametric curve(it is really not important what curve it is), firstly by computing N points of the curve and comuting distances between them, to do this, I have to write a function ApproximateCircumference(Write real function ApproximateCircumference of integer parameter N, that computes circumference of polygon with N sides with vertexes equal to parameter t=(N-1)*2pi/N, t is the parameter in the parametric curve). Easy one.
The second task is, to write a function that computes lagrangean polynomial(interpolation) of k-1th order from k points. Also easy.
But the last task is, to write a function BetterCircumference that computes the circumference by extrapolates ApproximateCircumference(N/2^(k-1)) as function of x=1/N^2 in point x=0 where N would be equal to infinity.
I don't know how, I don't know what the third task means, I suppose I should use the Lagrangean polynomial, but how? What does that x=1/N^2 mean? N is constant, it is number of points/sides of a polygon in the first task...
Please, help.
Thank you
P.S. please excuse me for my english.
> circumference of a parametric curve
> circumference of polygon
Please define those
> What does that x=1/N^2 mean?
I don't know, ¿what's `x'?
> circumference of polygon
Please define those
> What does that x=1/N^2 mean?
I don't know, ¿what's `x'?
http://www.wolframalpha.com/input/?i=x%3Dsin%28t%29-sin%286t%29%2F2%3B+y%3Dcos%28t%29%2Bcos%286t%29%2F4
This is the curve. t is the parameter.
http://en.wikipedia.org/wiki/Parametric_equation
This is what "parametric" means.
You approximate this as a polygon with N vertexes/sides, each vertex is an intersection of the approximating polygon with the curve.
I don't know what x is. Certainly not the x in the parametric (equation of) curve.
This is the curve. t is the parameter.
http://en.wikipedia.org/wiki/Parametric_equation
This is what "parametric" means.
You approximate this as a polygon with N vertexes/sides, each vertex is an intersection of the approximating polygon with the curve.
I don't know what x is. Certainly not the x in the parametric (equation of) curve.
Last edited on
I was asking for circumference.
As you say `circumference' of a polygon (instead of `perimeter') it makes me think that you would put arcs between the points.
After a second reading it seems:
_ Compute arc length with the polygonal approximation.
_ Change the number of points.
Now you've got a function s(N),
a) interpolate with a polynomial.
b) Instead of a polynomial, use a rational approximation. (¿?)
As you say `circumference' of a polygon (instead of `perimeter') it makes me think that you would put arcs between the points.
After a second reading it seems:
_ Compute arc length with the polygonal approximation.
_ Change the number of points.
Now you've got a function s(N),
a) interpolate with a polynomial.
b) Instead of a polynomial, use a rational approximation. (¿?)
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