Does curve fitting toolbox support 3D points?

Hi, I am beginning to use curve fitting toolbox. I read the document about the functions, however I find the functions are defined to fit 2D points. Currently I have to fit one curve for a 3D data set. I don't find any example code that fits 3D points. Many users need to fit 3D data set. Can anyone give me some advice or link to show how to use curve fitting toolbox for 3D points.

Regards Jogging

[Matt J]

Do you mean that you're fitting a function whose output takes values in R^3 or whose input? takes values in R^3? Do you have and could you use the Optimization Toolbox? LSQCURVEFIT can handle problems in arbitrary dimension.

[Liwei]

Given input is 3D points, I hope to use one spline to represent the 3d points.

[Matt J]

Then your input is not 3D. Your output space is 3D [x(t), y(t), z(t)] while your input is the 1D parameter, t. You are trying to fit a space curve in 3D.

Answer 1

[Sean de Wolski]

lsqcurvefit in the Optimization Toolbox or NonLinearModel.fit in the Statistics Toolbox.

[Liwei]

Thanks. Why does curve fitting toolbox have not such interface or example? It may help a lot if people try to use curve fitting for 3D points. Such question have been posted on the forum for several times.

Now I try to use the function from curve fitting toolbox and I will look into the the functions you mentioned later.

I have one question and hope to give some help.

It seems that curve fitting toolbox tries to fit a simple curve y(x),not a parametrized curve [x(t), y(t)]. Am I right?

From one post http://www.mathworks.com/matlabcentral/answers/1717-3d-line-approximation-spline. The post contains such code

t = cumsum([0;sqrt(diff(x(:)).^2 + diff(y(:)).^2 + diff(z(:)).^2)]);
sx = spline(t,x);
sy = spline(t,y);
sz = spline(t,z);

I don't understand that three components are functions of the distance between points.

Regards

Jogging

[Matt J]

It may help a lot if people try to use curve fitting for 3D points.

Fitting a 3D spline [x(t), y(t), z(t)] is the same as doing 1D spline fits separately to x(t), y(t), and z(t). It doesn't require any new functionality. Also, as noted at the link you posted, there are already many tools for doing this kind of fitting freely available on the File Exchange, so there is less reason for MathWorks to try to sell their own.

I don't understand that three components are functions of the distance between points.

You want the curve [x(t),y(t),z(t)] to be traversed as t increases from 0 to something. The above is just one possible way of defining a range for the parameter t.

[Liwei]

Thanks, Matt. Your clarification helps me understand spline curve.

I have several questions about the relation of knots and control points.

1. Is there any requirement about the number of knots and number of control points?

2. How are the knots obtained from control points? Is there any way to get the parameter t corresponding to one control points? From the link http://www.mathworks.com/help/curvefit/aptknt.html What does tau mean? Does it mean control points or knows points?

Answer 2

[Marc]

Maybe I am not getting it but the current curve fitting tool allows for x, y and z data so there is 3D fitting support in the curve fitting toolbox.

[Liwei]

If the three components are fitting separately, do they need the same knot sequence? If so, why?

[VIGNESH BALAJI]

@Marc the current curve fitting toolbox allows either giving x,y (2D as input) or [x,y] and z meaning a surface. It does not allow to fit a 2d curve in 3d space. If there are any tools like that please let me know