Curve interpolation problem

Hello, I have a project in the university to make a video of a car moving by a road defined by the user with the ginput() function. I can make this.. but the curve that the car is moving needs to be smoothed. So I tryed the 'basic fitting' tools and some more functions but the moving line is almost a closed curve... so I can`t make a smooth curve based on the poinst of the user input.

Can some one help me?! Here is an example of a user defined curve:

XX=[100.0000 167.3203 359.0253 410.6382 585.7535 716.6290 712.9424 476.9977 364.5553 185.7535 100.9608 86.2143];

YY=[150.0000 59.9470 107.8733 242.4355 100.5000 235.0622 441.5138 423.0806 529.9931 533.6797 364.0945 170.5461];

plot(XX,YY,'b-');

Answer 1

[Teja Muppirala]

Maybe something like this?

XX=[100.0000 167.3203 359.0253 410.6382 585.7535 716.6290 712.9424 476.9977 364.5553 185.7535 100.9608 86.2143];

YY=[150.0000 59.9470 107.8733 242.4355 100.5000 235.0622 441.5138 423.0806 529.9931 533.6797 364.0945 170.5461];

plot(XX,YY,'b');

f = 10;

XXf = interpft(XX,numel(XX)*f);
YYf = interpft(YY,numel(YY)*f);

hold all;
plot(XXf(1:end-f+1),YYf(1:end-f+1),'r');

[vasil enchev]

Perfect! Thank you all!

Answer 2

[the cyclist]

The basic fitting tools are mostly designed to fit one function y=f(x) to all the data. But that is not what you are trying to do, so it is not surprise to me that those were not the right tools.

I think the hard part of this problem is hidden inside the simple phrase "needs to be smoothed". You will need to be much more explicit about what that means. Must the curve go through the points specified, or just near them? Must there be no kinks? Is it OK to have your curve go VERY far away from the points, in an effort to keep things smooth?

Answer 3

[vasil enchev]

Well the used words in the project are: "There is bonification in smoothing the curve.". Sinse my car is mooving by this curve it would seem unnatural to move by such way. So I suppose that i really doesn't need interpolation, but a way to smooth my curve and make it less edgy.

This is a picture example:

<http://vasile.free.bg/cgi-php/net2ftp/index.php?ftpserver=188.40.80.188&ftpserverport=21&username=vasile.free.bg&language=en&skin=blue&ftpmode=automatic&passivemode=no&sslconnect=no&viewmode=list&sort=&sortorder=&state=view&state2=image&directory=%2F&entry=road.jpg>

user name: vasile.free.bg

password: 123456

[John D'Errico]

So then YES, you do need interpolation, and not smoothing. Interpolation is a process wherein the points themselves are not changed, but a smooth curve drawn between them. Smoothing allows the points themselves to be moved.

[John D'Errico]

The interpolant can be a smooth one. It need not be a linear, connect the dots interpolant.

Answer 4

[vasil enchev]

I see. So interpolation it is. Can someone give me an example, because I tried all I could think of. The main problem I see here is that my curve is almost closed. So "basic fitting" tools does some function passing thrue all the points but between the point there is so much noise. Unless my driver is drunk I don`t think this could work.

Answer 5

[John D'Errico]

Use a tool designed to fit a general space curve. My interparc is such a tool.

If you can't use a tool from the file exchange, but must write it yourself since this is a homework project, then you will need to do some writing.

A problem that you MAY find, is if you allow the interpolant to be a general smooth curve instead of piecewise linear segments, then you must constrain that curve to not pass through the walls of the coarse it appears to follow. Given that the splines ANY such tool must be based on are notorious for ringing, this may be an issue. Therefore, I would strongly recommend the 'pchip' method in interparc, as it is less susceptible to problems in this respect.

[vasil enchev]

Useful information too! Thank you.