local interpolation

Discussion in 'Software' started by redcoopers, Aug 12, 2004.

  1. redcoopers
    Joined: Dec 2003
    Posts: 55
    Likes: 2, Points: 0, Legacy Rep: 40
    Location: Pensacola, FL

    redcoopers Member

    Hi all,

    Well, this may be more directed towards people such as Andrew Mason or people with experience with computational geometry:

    I need to find a bivariate interpolation of scattered data (but on a very local nature to each point in question). What I really need is a set of points (r=very close to each point; and theta= 0, 90, 180, 270). Algorithms such as a Monte Carlo method will not work, so I am leaning to a radial weighted method combined with an angular lagrange polynomial.

    I've thought of using radial NURBS curves, but this seems computationally expensive since I need only a few radial points for each set of curves. Furthermore, I can't seem to set knots how I would need... For each radial curve I would be interpolating for, I would need the origin point be set absolutely, (ie, delta_ij = kronecker delta), but the end point would not necessarily need to have this condition. As an example for 5 control points of order 3, if I wanted up to C2 continuity at the origin, but didn't care about the rest of my points, why wouldn't a knot vector such as [0,0,0,1/5,2/5,3/5,4/5,1] work? Maybe my recursion algorithm is flawed, but I always get a closed curve, but not an open curve...

    In any case, I think I need a least squares fit of order=n>=2 for a set of radial data. Does anyone have experience with weighted least squares methods or NURBS methods of fitting data?

    -Jon
     
  2. Andrew Mason
    Joined: Mar 2003
    Posts: 397
    Likes: 18, Points: 18, Legacy Rep: 206
    Location: Perth, Western Australia

    Andrew Mason Senior Member

    Red

    Actually we have been doing a lot of work with Neural Networks for data fitting, if you have access to the Maxsurf Academic site have a look at the paper "Artificial Neural Networks for Hull Resistance Prediction. COMPIT 2004" on the Maxsurf Academic Technical Papers page.

    The NN program I recommend is NeuroIntelligence by Alyuda, www.Alyuda.com. They have a 30 day demo version that can handle 1000 data points, full working program is about $400.

    Andrew
     
  3. redcoopers
    Joined: Dec 2003
    Posts: 55
    Likes: 2, Points: 0, Legacy Rep: 40
    Location: Pensacola, FL

    redcoopers Member

    Thanks for the link.

    I'm actually looking for a linear method (ie, z2 = K z1) where K is my interpolation matrix.

    I think I developed somthing which may work, however. For a univariate case, I would simply use lagrange polynomials of a limited degree centered around each point.

    Moving to a bivariate case, now I interpolate in the x and y directions for each point. I use weighted Bernstein polynomials where the weight depends on how close each point is to the axis. I evaluate a few parametric points, and put these into a lagrange polynomial to finally complete the interpolation.

    It works better than anything else I've tried and is rather robust. This works only because I do not want a global interpolation - only very locally near each point.

    You have some rather good papers on your site. Using genetic algorithms to fit a drawing is impressive, but seems like overkill... Does the algorithm manipulate the control net for a NURBS surface, or does it develop its own surface?

    -Jon
     
Forum posts represent the experience, opinion, and view of individual users. Boat Design Net does not necessarily endorse nor share the view of each individual post.
When making potentially dangerous or financial decisions, always employ and consult appropriate professionals. Your circumstances or experience may be different.