Directional scaling (of an ellipse)

In summary, The speaker is seeking help with calibrating for soft-iron distortion calibration for a magnetometer. They have a basic understanding from a publication that calibration involves scaling along the major axis of a rotated ellipse formed by readings from a 2-axis magnetometer. The speaker has done some research on using a matrix for scaling along the x and y axes, but is now looking for ways to scale along an arbitrary direction. They suggest using a non-linear programming approach to find a scaling amount that comes closest to a perfect circle, as a perfectly calibrated magnetometer would have a locus of measurements that is a perfect circle. They mention finding a technique in a paper that may be helpful and ask for pointers in the right direction. Finally, the speaker
  • #1
shimniok
2
0
Hope this is in the right forum. I apologize in advance for my ignorance and imprecise discussion as I am at a major disadvantage, lacking rich mathematical educational background enjoyed by most here.

Background is that I'm curious about calibrating for soft-iron distortion calibration for a magnetometer. If I take a number of readings from a 2-axis magnetometer, the locus of readings forms a rotated ellipse. My understanding from a Freescale publication (pdf) is that calibration involves scaling along the major axis of this ellipse. I believe the correct term is directional scaling?

I've done some reading on using a matrix for scaling along the x and y axes. I've done some extensive searching for any hint as to how one might scale along an arbitrary direction. Or are there better approaches?

Ultimately my thought is this. A theoretical, perfectly calibrated magnetometer will have a locus of measurements that is a perfect circle. So I wonder if I can use some kind of non-linear programming approach to finding a scaling amount that comes closest to a circle by summing squares of difference at each point. This idea itself may be flawed. But it seems to be at least vaguely similar to a technique written about in a paper (pdf) I found recently.

I don't necessarily need the answer spoon fed, but would greatly appreciate some pointers in the right direction so my searches will be more fruitful. Many thanks in advance.
 
Physics news on Phys.org
  • #2

1. What is directional scaling of an ellipse?

Directional scaling of an ellipse is the process of changing the size and shape of an ellipse along a specific direction or axis. It involves stretching or compressing the ellipse in one direction while keeping the other direction constant.

2. How is directional scaling different from uniform scaling?

Directional scaling and uniform scaling are two different methods of changing the size and shape of an ellipse. While directional scaling involves changing the size in a specific direction, uniform scaling changes the size of the ellipse uniformly in all directions.

3. What factors affect the directional scaling of an ellipse?

The directional scaling of an ellipse is affected by the length and position of the axis along which the scaling is performed, as well as the eccentricity of the ellipse (the ratio of the distance between the foci to the length of the major axis).

4. How is directional scaling used in real-life applications?

Directional scaling of an ellipse is commonly used in computer graphics, animations, and engineering designs. It can also be applied in fields such as architecture, where it is used to represent the scaling of buildings and structures.

5. Can directional scaling be applied to other shapes besides ellipses?

Yes, directional scaling can be applied to any shape that has an axis or direction of scaling. This includes circles, squares, rectangles, and other irregular shapes.

Similar threads

Replies
6
Views
1K
  • MATLAB, Maple, Mathematica, LaTeX
Replies
1
Views
2K
  • Linear and Abstract Algebra
Replies
6
Views
28K
Replies
7
Views
849
  • Set Theory, Logic, Probability, Statistics
Replies
7
Views
1K
Replies
1
Views
2K
Replies
2
Views
2K
Replies
2
Views
1K
Replies
3
Views
2K
  • General Math
Replies
4
Views
1K
Back
Top