Solve Lagrange Interpolation Problem with Pen Position Detection

In summary, the conversation is about a problem with a digitizer that uses a Lagrange algorithm to determine the pen position. The issue is that when the pen is in the middle of two antennae, the energy values are similar and the highest point of the curve remains the same, causing slow movement. The person is wondering if it is possible to introduce a factor to narrow the curve at the highest point. One suggestion is to use splines instead of Lagrange, as they allow for more control over the curve.
  • #1
Nihi
2
0
Hi all

I am facing a problem and I hope that you can give me a hand. Here I describe the situation

I am working on a digitizer that can detect the pen position by measuring the antennae energy that are placed in a grid fashion. To get the x coordinate of the pen I measure the energy of three antennae where the pen is supposed to be and then I interpolate this 3 energy-value with Lagrange algorithm.
Finally I determine the pen coordinate by finding the highest f(x) of the curve using a loop.

With Lagrange method it approximates pretty well the actual relationship position-energy but it's not linear.

So here is the problem: when the pen is in the middle of two antennae I get 2 similar energy value whereas the 3rd is lower then these latter, so the highest point of the curve remains about the same when I move the pen around the middle position of 2 antennae. The result is that when the pen crosses these middle points it moves slowly because there is not much changes in the curve which is limited by these 2 similar energy-value.

Is it possible to introduce a factor that changes the curve making it more narrow at the highest point? it's just a thought, I appreciate any solution.

Xcoordinate_Table_M.jpg


In the picture you can see the measurement and the coordinate calculated through Lagrange algorithm. I hope that someone can help me. Thank you!
 
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  • #2
Hey Nihi.

Have you ever heard of splines before?
 
  • #3
chiro said:
Hey Nihi.

Have you ever heard of splines before?

Thank you Chiro.
Yes I had. I want to remain with Lagrange and see if I can improve the current result but I will try Spline to see if get better.
 
  • #4
Lagrange just fits the curve without any sort of information on how it changes (even though they still interpolate between the points).

Splines and more complex structures (like NURBS) allow fine-grained control on what happens outside of the interpolation points.

It's a lot more complex but it gives you those extra options in what happens to the curve.
 

1. What is the Lagrange Interpolation Problem?

The Lagrange Interpolation Problem is a mathematical method used to find a polynomial function that fits a given set of data points. It is often used in areas such as signal processing, control systems, and computer graphics.

2. How does Lagrange Interpolation work?

Lagrange Interpolation works by constructing a polynomial function that passes through all the given data points. This is achieved by using a system of equations called Lagrange polynomials, which are based on the coordinates of the data points.

3. What is the role of Pen Position Detection in solving the Lagrange Interpolation Problem?

Pen Position Detection is used to accurately record the position of the pen as it moves across a surface. This data is then used as input for the Lagrange Interpolation Problem, allowing for a more precise and accurate polynomial function to be constructed.

4. What are the applications of solving the Lagrange Interpolation Problem with Pen Position Detection?

This method has various applications, including handwriting recognition, computer-aided design, and motion capture. It is also commonly used in graphics tablets and touchscreens, where the pen position is detected and translated into digital input.

5. Are there any limitations to using Lagrange Interpolation with Pen Position Detection?

Like any mathematical method, Lagrange Interpolation has its limitations. It can be sensitive to outliers in the data, and the accuracy of the polynomial function depends on the number of data points. Additionally, Pen Position Detection may be affected by external factors such as noise or uneven surfaces.

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