How can I calculate the area bounded by a large number of intersecting lines displayed on a graph?

[David Harrowfield]

Can I adapt 'particle (or blob) analysis' to a graph, or would I be better off saving my graph as an image and using IMAQ VI's to do particle analysis on the image?

[VIGuy]

Almost wish they some sort of a whiteboard feature on this forum. 'Cause this would be easiest to explain with some dynamic pictures.

Any way, to calculate the area "shared" by two or more functions you subtract the areas. Piecewise: calculate the area of fuction 1 by integrating over range of intersection, calculate the area of fuction 2 by integrating over range of intersection, subtract Area 1 from Area 2 and take the absolute value.

If more than 2 functions, start with the two functions with the greatest area of overlap, and work towards the smallest.

This is assuming continuous polynomial functions comprise the intersections and you know the points of intersection. If they are simple linear functions you might be able to do some geometric additions (a
dd up all the trapizoidal/triangle areas formed by consecutive points of intersection).

This is the robust works-for-most-cases solution, your particular instance may provide short cuts, but no details were given that might provide clues to those short cuts.

Good luck.

[David Harrowfield]

Hi, thanks for your comments. I did think of this at first, but the number of lines and intersection points makes this approach very complicated. If I had my whiteboard, I would draw say 40 pairs of parallel lines, where each pair consists of the tangents at a given angle to either side of an object of arbitrary cross-section. The reason I'm doing this is to graph the information I get from a laser micrometer when an object is rotated in its field of view - overall diameter for a series of angles. Specifically, I want to calculate the object's cross-sectional area (non-destructively) and the only way I can think of doing this is to plot the tangential lines and find the enclosed area.

[VIGuy]

Sounds extremely cool.

Do you have a VI or a screen shot that shows a "typical" cross-section you wish to measure and the data that generated that cross-section? Do you know the points of intersection? Is there ever a chance that a sigle object will display a cross section that appears as two or more "islands"?