1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The Parametric Functions of a Bezier Curve

  1. Jan 1, 2012 #1
    1. The problem statement, all variables and given/known data
    Hello. I'm currently doing some work with bezier curves and have come across a certain format, which, from what I can tell, is called the parametric form of a bezier curve. I've run several searches and can't seem to find anything that explains how to obtain this form. The usual notation I see it written in is as follows:

    x(t)= x(t)/w(t), y(t)=y(t)/w(y)

    So basically, my question is, given I have all the control points of a cubic bezier curve, how do I find the parametric function (assuming that's what the notation above is called)? I've been trying to solve this myself for a while, and feel I won't get much further without help. If someone could explain this or post a link to something that does, I'd be more than grateful.

    2. Relevant equations
    The polynomial functions I currently have:

    x(t) = axt^3 + bxt^2 + cxt + x0

    y(t) = ayt^3 + byt^2 + cyt + y0

    The Bernstein basis functions of a cubic curve:

    t^3

    3t^2(1 - t)

    3t(1-t)^2

    (1-t)^3

    3. The attempt at a solution
    As I've said, I've run several searches. From what I can gather, this is called the parametric form of a bezier curve. The x(t) and y(t) functions may be the same as the polynomial functions I have, but I doubt that. I think the third function, w(t), is a "weight function" of the bezier curve. If this is correct, I guess it works as the "magnetic attraction" of bezier control points, so maybe it relates to the Bernstein basis functions somehow? But as I've said, I can barely find anything explaining these functions and most of this is guess work.
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted



Similar Discussions: The Parametric Functions of a Bezier Curve
  1. Parametric curve (Replies: 3)

  2. Parametrize this curve (Replies: 14)

  3. Parametrizing a curve (Replies: 3)

Loading...