determine a point curve

i have a vector with the x points, and another with the y points.

could anyone help me with the matlab code for the following objective: determine the ‘’first’’ intersection point in order to obtain only (the data points of ) the closed curve(inside red).

this intersection point is not necessarily a x,y point from my data, but belongs to the its line. Also, the intersections can be located at the left of the closed curve (as in this figure) or at the right.

So my objective is just to know the ‘’first’’ intersection point.

Thank you very very much.

[Walter Roberson]

Please read the guide to tags and retag this question; see http://www.mathworks.co.uk/matlabcentral/answers/43073-a-guide-to-tags

Answer 1

[Image Analyst]

Are you starting with the RGB image of some cartoon someone drew by hand? Or do you have actual numerical data for the lines/curves? I also don't know what this means: " intersection point is not necessarily a x,y point from my data, but belongs to the its line" What is an "its" line? How do you define "first" intersection point when there is substantial overlap of two curves?

[joo]

no, no. it is all numerical data. i meant that i want the 'first intersection' between the two lines (it can be a point that it is not in my sampled data). am i clear? i sent you the excel file. thank you!

[joo]

if you could just tell me how to do it just in this case it would be perfect! thank you very much!

[Image Analyst]

Sorry I don't have any code for that all ready to go, plus my email doesn't take attachments and I never look at it. I'd have to write custom code and you can do that just as well as I can (well, almost).

[joo]

i have been searching, i think the correct term for what i need is self intersection of the line itself. thank you very much.

[Image Analyst]

Did you see my response to this thread: http://www.mathworks.com/matlabcentral/answers/43969#answer_53975

[joo]

no... but i think the code is not appropriate since what i have is a closed curve and a polygon is all about straight lines. am i wrong? i am trying for days, but I find very strange the inexistence of code to this simple problem: self intersection of the line itself. Maybe I am missing some good word.

Again thank you very very much for your help and kindness.

[Image Analyst]

I don't see any difference between a closed curve and a polygon. Your "closed curve" is made up of an ordered set of (x,y) coordinates isn't it? So why can't those be considered as endpoints of a straight line segment? So you could do the brute force case of seeing if any adjacent pairs of vertices (i.e. a single line segment) crosses any other line segment in the list of coordinates. You'll easily find web sites that explain exactly how to do that like: http://bloggingmath.wordpress.com/2009/05/29/line-segment-intersection/, http://ptspts.blogspot.com/2010/06/how-to-determine-if-two-line-segments.html, http://mathforum.org/kb/thread.jspa?forumID=226&threadID=1312304&messageID=4142617, etc.

[joo]

ok. i made it! thank you very much!