Thread: What's the purpose of Bezier Curves?

  1. #1
    Registered User
    Join Date
    Aug 2005
    Posts
    204

    What's the purpose of Bezier Curves?

    Why not use good old fashion interpolation to make curves?

  2. #2
    and the Hat of Guessing tabstop's Avatar
    Join Date
    Nov 2007
    Posts
    14,336
    Bezier curves is good old-fashioned interpolation.

    But the point of Bezier curves is that you can tack them together smoothly (since you are controlling the slope at the endpoints), rather than having L-shapes or V-shapes or similar abrupt, non-smooth transitions.

  3. #3
    Registered User
    Join Date
    Aug 2005
    Posts
    204
    I don't understand. What is wrong with polynomial interpolation? Does that not tack together well enough?

  4. #4
    and the Hat of Guessing tabstop's Avatar
    Join Date
    Nov 2007
    Posts
    14,336
    Polynomial interpolation doesn't tack together at all.

    Edit: Maybe I should be more specific -- the only things that will agree when you paste simple polynomial interpolation together is the value of the endpoints. Think "line graph" and you're there.

    You can do a polynomial interpolation on all the points; but polynomial interpolation is n^2 on the number of points.

    Bezier interpolation is bog-standard cubic interpolation, but instead of using four points, you use two points and two tangent values (since the tangent values agree when you paste them together, you get not only the same points, but the same direction too.
    Last edited by tabstop; 10-05-2008 at 06:22 PM.

  5. #5
    Registered User
    Join Date
    Sep 2008
    Location
    Toronto, Canada
    Posts
    1,834
    Some nice animations here: http://en.wikipedia.org/wiki/Bézier_curve

    If you wanted to connect polynomial interpolation curves smoothly (no abrupt slope changes at the endpoints), you might have to use 4th order polynomial and then extract only the central section. Then move ahead one point and do it over. Even then the resultant line isn't quite smooth.

  6. #6
    Registered User VirtualAce's Avatar
    Join Date
    Aug 2001
    Posts
    9,607
    There is work in progress to have native support for bezier curves on GPUs and in the APIs. I'm not sure where that's going since I think a complete move away from triangles is really where we need to be. Intel claims they will have CPUs that can real time ray trace within 5 years.

Popular pages Recent additions subscribe to a feed

Similar Threads

  1. Are B-splines composed of Bezier curves?
    By thetinman in forum Game Programming
    Replies: 4
    Last Post: 01-28-2009, 11:21 AM
  2. Bezier Curves where y = f(x)
    By thetinman in forum Game Programming
    Replies: 11
    Last Post: 12-27-2008, 10:21 AM
  3. Collision detection between bezier and ball.
    By CornedBee in forum Game Programming
    Replies: 1
    Last Post: 04-27-2006, 12:49 PM
  4. bezier curves
    By linuxdude in forum Game Programming
    Replies: 9
    Last Post: 12-23-2004, 02:53 AM
  5. Contest Results - May 27, 2002
    By ygfperson in forum A Brief History of Cprogramming.com
    Replies: 18
    Last Post: 06-18-2002, 01:27 PM