# Fiting a surface of best fit to a set of data points

• Woland
In summary, the speaker is seeking advice on fitting a surface to a 1920x1080 grid of data points. They are considering using a least squares approach and are looking for recommendations on literature or methods. Another speaker suggests using software for the results. In the end, the speaker was able to figure it out using the usual least squares method.
Woland
Hello all,

I am trying to fit a surface to a 1920x1080 grid of evenly spaced data points. The values are supposed to be more or less uniform (its an image of a uniform white light source). So I would like to fit a plane to it (but maybe a paraboloid if it is not quiete uniform). What method should I use? A least squares approach? I can't seem to find much on google for this. Does anyone have an approach, or perhaps could recommend some literature which covers this?

Thanks!

I was able to figure it out . The usual least squares method applies to this. I fit z = Ax + By + C by creating a matrix of sums etc etc. It worked out nicely for the 3D case, same as for the 2D.

Thank you,

## 1. How do you determine the best fit for a set of data points?

The best fit for a set of data points is determined by finding a mathematical function or curve that minimizes the distance between the points and the curve. This is typically done by using a technique called regression analysis.

## 2. What is the purpose of fitting a surface of best fit to data points?

The purpose of fitting a surface of best fit to data points is to analyze and understand the relationship between the variables represented by the data points. This can help in making predictions or identifying patterns in the data.

## 3. What are some common types of best fit surfaces used in data analysis?

Some common types of best fit surfaces include linear, quadratic, exponential, and logarithmic functions. The choice of surface depends on the nature of the data and the relationship between the variables being studied.

## 4. How do you assess the accuracy of a best fit surface?

The accuracy of a best fit surface can be assessed by calculating the residual, which is the difference between the predicted values from the surface and the actual data points. A lower residual indicates a better fit.

## 5. Can a best fit surface accurately represent all data points?

No, a best fit surface is an approximation of the relationship between the variables represented by the data points. It may not accurately represent all data points, especially if the data is complex or contains outliers.

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