surface fit

[TomGutman]

What did you want to fit? What is your model for the surface?
__________________
� � � � Tom Gutman

[ptc-1368288]

No need for an Excel data sheet. Instead, use Mathcad input table. That will reduce the burden to callabs, and decide if the data are just data or data representing points on a surface. You have repeated points, therefore a surface plot can't be meshed. A bar plot is more appropriate. The data set is not representative in any way of an eventual f(x,y). The data set is just a data set. I didn't spend more effort just by the look of the data and the bar plot

jmG

[ptc-1368288]

jmG

[ptc-1214470]

I suspect the attached is what the collab is looking for...
Jim S.

[ptc-1368288]

On 2/14/2009 4:59:27 PM, Offroc wrote:
>I suspect the attached is what
>the collab is looking for...
>Jim S.
_______________________________

It looks so, I have no tried fitting such a Meshed scatter. It might be a diagonal fit is adequate ... RemToDo.

jmG

[RichardJ]

Your data has a lot of scatter, and there are a lot of functions that could fit it to within the large errors. The best option is to fit a function you know should represent the data. Here's the principle of how to do it, and also how to just fit a multidimensional polynomial.

Richard

[ptc-1368288]

Interesting Richard,

The collab didn't come back. The data set is simply a collection but it is not representative of a surface plot as a matrix of values, neither as a noisy bivariate/trivariate. Your demonstration is convincing that there is nothing to fit. Bivariate/trivariate represent quadrics. They will smooth such noisy forms collected in the bivariate/trivariate vector form, but this is not the case for the collab collection and with no more details the project is done in the sense that there is nothing to do with it.

jmG

[RichardJ]

On 2/15/2009 12:30:21 PM, jmG wrote:
> Your
>demonstration is convincing
>that there is nothing to fit.

I don't know about "nothing", but I would agree "very little".

Richard

[ptc-1368288]

On 2/15/2009 12:48:17 PM, rijackson wrote:
>On 2/15/2009 12:30:21 PM, jmG wrote:
>> Your
>>demonstration is convincing
>>that there is nothing to fit.
>
>I don't know about "nothing", but I
>would agree "very little".
>
>Richard
>_______________________

Quite right: can we say "Big little" is asymptotic to "Nothing"

A question for Watson.

In your work sheet, here is the Valery rectangular surface fit. To induce the collab what he should have as a data set for a surface fit.

jmG

[TomGutman]

Some minor corrections and emendations.
__________________
� � � � Tom Gutman

[RichardJ]

On 2/16/2009 11:35:17 AM, GR_Aero wrote:

It would be much better to post a reply in the same thread as the original question (select "Reply" or Reply/Quote at the top of a post). That's why I moved my reply here.

>thanks all so much for help.
>the data were intended to fit
>two separate surfaces, z1 and
>z2. There are 11 points for
>each surface. Can you please
>setup a program that not only
>can form a surface for
>visulization but also an
>analytical form that can be
>for future usage.

I could yes, but what sort of surface? The data has so much scatter there are any number of possible surfaces that would fit to within the errors.

If it's actual test data, what is the expected form of the equation? If you don't know the expected form, then what is the data from, and what is the intended use of the equation for the surface?

Richard

[TomGutman]

You need to be more careful about using the proper reply button for making replies. Use only the reply button in the header of the post to which you are replying (not the one at the bottom of the thread), and do not use the post button (unless you are posting about a different problem).

You have insufficient data and too much scatter to reasonably define a surface. Richard already did the bivariate quadratic for you in an earlier post. But you have only five distinct values for the independent variables. The general bivariate quadratic requires fitting six parameters. You will get a solution, but it will not be unique or meaningful.

Further, when you look at the data where you have replications, the scatter at each point is similar to the variation between points. You cannot expect much in the way of predictions based on such data, whatever the model used.
__________________
� � � � Tom Gutman

[ptc-1368288]

On 2/16/2009 2:04:11 PM, GR_Aero wrote:
...
>Expected surface would be like
>linear (z = ax+by+c) or 2th
>order polynomial
>(z=ax^2+bx^2+cxy+dx+ey+f). The
>initiative was to use up all
>of the test data as much as
>possible to generate a surface
>with minimum errors incurred
>with fitting. The analytical
>form can then be used to
>predict another z value for
>different percent, like 10%.
>Thanks in advance.
_____________________________

Again, you can fit-interpolate ... you can smooth data that are representative of a surface. Your data set is a collection that does not represent a surface, there fore what you want is out. Again, the bivariate you are showing are for "Quadrics" your data collection does not resemble quadrics as those functions are limited in number and well defined ... or your data set is totally not representative.
If you want the equivalent of the Mathcad built-in drop down "Scatter mesh", ask for it. I have no recollection such interpolation was ever done in this collab.

jmG

[TomGutman]

The last six numbers are indeed the six coefficients. But not in that order. Regress produces the coefficients in a rather weird order. Look at the quicksheet on regress to calculate the order of the coefficients.
__________________
� � � � Tom Gutman

[RichardJ]

The coefficients aren't in that order, that's all. The attached worksheet shows how to find the order.

Richard

[GR_Aero-disable]

that is great. thanks Richard and Tom for sincere assistance. Peter

[ptc-1368288]

Export as desired.

jmG

[GR_Aero-disable]

Hi Richard and Jim,

What is difference between the surface created by CreateMesh and polynomial surface formed with coeffs1 and coeffs2. I think they should be same, but the former is generated for easy viewing. Am I right? Can we view polynomial form directly? Thanks.

[RichardJ]

CreateMesh just takes a function, for example the polynomial, and creates a nested matrix of x, y, and z values for a 3D graph. So what you are looking at is the polynomial.

Richard

[ptc-1368288]

On 2/17/2009 11:33:38 AM, GR_Aero wrote:
>Hi Richard and Jim,
>
>What is difference between the
>surface created by CreateMesh
>and polynomial surface formed
>with coeffs1 and coeffs2. I
>think they should be same, but
>the former is generated for
>easy viewing. Am I right? Can
>we view polynomial form
>directly? Thanks.
______________________________

The bivariate fit is fit(u,v) as defined. This definition is for the QuickPlot and you have the bother to range both directions and you don't have an export. You can have an export from fit(u,v) by assigning to a matrix. The Createmesh is an advanced Mathcad built-in function. It creates a nested matrix of 3 planes...they are X, Y, Z

In this simple case of 3D surface, the X, Y planes are simply linear plane (just a piece of plywood in both directions). The Z plane is the "matrix valued level" corresponding to each mesh, that matrix is the same as if you would assign f(u,v) to a matrix.

The bivariate extract-export is tutored in the work sheet.

Please feel free for more.

jmG