Results 1 to 3 of 3

Math Help - Formula for describing a closed curve given 4 points

  1. #1
    Newbie
    Joined
    Feb 2013
    From
    Korea
    Posts
    2

    Formula for describing a closed curve given 4 points

    Hello,

    I think this falls under Trig, but maybe its something else.

    I start at (0,0), then i am given 4 points, say, (2,0) (0,1.5) (-3,0) (0,-2) I plot a point at each of those. Then i need to draw a closed curve that intersects each point. The curve should have a bezier interpolation at each vertex.

    I have written code to do this, but it also uses a closed source library to make the curve and I need to explain this mathematically and implement it myself so i can pick any point along the curve.

    Thanks for any help
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,619
    Thanks
    592

    Re: Formula for describing a closed curve given 4 points

    Hey umcadop.

    The bezier curve is not an interpolation curve: It only is gauranteed to go through the first and last points (if you are using a four point method).

    The most basic form of an interpolating curve is the one by Lagrange which just finds the simplest polynomial to go through the points.

    You can solve the Lagrange polynomial by setting up a linear system of equations and then finding the coeffecients by reducing the system (or you can use alternative formulas to do what amounts to the same thing).
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Feb 2013
    From
    Korea
    Posts
    2

    Re: Formula for describing a closed curve given 4 points

    thanks for the help chiro,

    I have been looking at lagrange and i dont see any way of giving it ordered pairs, so i dont see how it can create a closed curve as it seems to progress along the X axis. Am I missing something?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Closed Curve Integral
    Posted in the Calculus Forum
    Replies: 5
    Last Post: January 12th 2012, 09:27 AM
  2. Replies: 3
    Last Post: August 24th 2011, 11:35 AM
  3. closed curve, trace
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: January 27th 2010, 07:19 PM
  4. closed curve, trace
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: January 27th 2010, 06:59 PM
  5. Integral under a closed curve
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 24th 2009, 03:07 AM

Search Tags


/mathhelpforum @mathhelpforum