Solve Lagrange Interpolation Problem with Pen Position Detection

  • Context: Undergrad 
  • Thread starter Thread starter Nihi
  • Start date Start date
  • Tags Tags
    Interpolation Lagrange
Click For Summary

Discussion Overview

The discussion revolves around improving the accuracy of pen position detection using a digitizer that measures antenna energy values. The focus is on the application of the Lagrange interpolation method and exploring alternatives to enhance the curve's responsiveness when the pen is positioned between two antennae.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant describes a problem with using the Lagrange interpolation method, noting that it approximates the relationship between position and energy but does not provide a linear response, particularly when the pen is between two antennae.
  • The same participant seeks a way to modify the curve to make it narrower at the highest point to improve responsiveness.
  • Another participant suggests considering splines as an alternative to Lagrange interpolation, implying they may offer better control over the curve's behavior outside of interpolation points.
  • A later reply emphasizes that while Lagrange interpolation fits the curve, it lacks information on how the curve changes, whereas splines and more complex structures like NURBS provide additional options for curve manipulation.

Areas of Agreement / Disagreement

Participants express differing views on the effectiveness of Lagrange interpolation versus splines, with some advocating for sticking with Lagrange while others suggest exploring splines for potential improvements. The discussion remains unresolved regarding the best approach to enhance the pen position detection.

Contextual Notes

The discussion highlights limitations in the Lagrange method's responsiveness to changes in pen position, particularly in scenarios with closely valued energy readings. There is an acknowledgment of the complexity involved in using splines and other advanced methods.

Nihi
Messages
2
Reaction score
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!
 
Physics news on Phys.org
Hey Nihi.

Have you ever heard of splines before?
 
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.
 
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.
 

Similar threads

Lagrange method problem: Multiple Spring-Mass System
  • · Replies 22 ·
Replies
22
Views
3K
Engineering Computer Graphics: Finding the position of a lightpen on the face of a CRT
  • · Replies 6 ·
Replies
6
Views
2K
Lagrange multipliers understanding
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad The Euler-Lagrange equation and the Beltrami identity
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Can Any Quantifiable Variable Serve as a Coordinate in Euler-Lagrange Equations?
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Question about Penning Trap
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Action in Lagrangian Mechanics
  • · Replies 5 ·
Replies
5
Views
2K
High School The mathematics of transforming images in Adobe Premiere - Part 1
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Lagrangian for pendulum
  • · Replies 11 ·
Replies
11
Views
2K
Undergrad Particle behavior in Penning trap
  • · Replies 13 ·
Replies
13
Views
2K