Finding intersecting points in the Lissajous scan pattern

Hi.

I'm trying to find the intersecting points in the Lissajous scan pattern.

For

x = A * sin(2*pi*f1*t)

y = B * sin(2*pi*f2*t+pi/2)

drawing the Lissajous scan pattern itself was not that difficult,

but I had a lot of trouble finding out the intersecting points.

Does anyone have any experience with this problem?

[Dyuman Joshi]

Any updates, @창현 지? Did you try the FEX submisisons I linked?

[창현 지]

Thank you for the comments and ideas.

We did get some good results using your last suggestion, but we are still in the process of resolving the following issues.

1. Intersections are marked in unwanted regions for relatively low frequencies
2. Code takes up too much time for frequencies in the kHz range

Thanks.

Answer 1

[Dyuman Joshi]

There are several options available in FEX -

https://in.mathworks.com/matlabcentral/fileexchange/11837-fast-and-robust-curve-intersections

https://in.mathworks.com/matlabcentral/fileexchange/22441-curve-intersections?s_tid=srchtitle

You could also go through this forum and find different approaches for finding intersections of 2 curves (mostly utilizing interp1), as this type of question has been asked many times.

[DGM]

In this question, we're trying to find the points where a single parametric curve intersects itself. That doesn't seem as simple as the typical request.

[Dyuman Joshi]

(If I understood your point clearly, @DGM) The 2nd FEX submission can be used for finding self-intersections points as well.

Another option is - https://in.mathworks.com/matlabcentral/fileexchange/13351-fast-and-robust-self-intersections?s_tid=srchtitle