MATLAB: Intersection points of multiply lines

line

Hi,

In the last couple of days and nights I am trying to find a way to get the intersection points of 3 lines without any success since I encounter special cases (e.g., slope=0 or Inf, -Inf). Any idea how to get the intersection points that will work both on case 1 and case 2 (Visually presented in the attached image).

Thanks a lot in advance.

Best Answer

Hi!

Take a look at the great pages of Paul Bourke: http://paulbourke.net/. You can find a matlab code for the distance of two lines in 3d in section "The shortest line between two lines in 3D" on page http://paulbourke.net/geometry/pointlineplane/.

You can as well use 2d coordinates with the third entry 0. Then you just check every line against the others.

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MATLAB: Intersection between line and circle

Each circle with have either 0, 1, or 2 intersection points. Do you have the formula for each circle, meaning it's center coordinates and radius ? If seems like knowing the formulas for the lines you might be able to use fzero() to find the intersection point(s).

By the way, what toolbox is linecirc() in? I don't have it.

MATLAB: Finding intersection of two lines

If your “yellow star point” is as indicated in your diagram, there is a simple formula for finding it which doesn’t require finding J and K. Define vectors B = [x1;y1], C = [x2;y2], and define rB and rC as the respective radii of the circles with centers at B and C.

BC = B-C;
S = (B+C)/2 - (rB^2-rC^2)/(2*dot(BC,BC))*BC; % <-- yellow star point

Of course, if rB and rC are equal, then S is simply

S = (B+C)/2

which would be the midpoint between B and C.

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