finding intersection of two lines?

Hello

I have two points B(x1,y1) , C(x2,y2), then I calculate the corrdinate of two more points J(xdd,ydd) and k(xgg,ygg) know I want to find the coordinate of yellow star point which is the intersection of line JK and BC, How can I do it? Thanks in advance.

    xdd= x1(index1)+(DeltaX*D_CL)/D +(DeltaY/D)*sqrt(r^2-D_CL^2);
    ydd= y1(index1)+(DeltaY*D_CL)/D-(DeltaX/D)*sqrt(r^2-D_CL^2);
    xgg= x1(index1)+(DeltaX*D_CL)/D-(DeltaY/D)*sqrt(r^2-D_CL^2);
    ygg=y1(index1)+(DeltaY*D_CL)/D+(DeltaX/D)*sqrt(r^2-D_CL^2);

Answer 1

[Roger Stafford]

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.

Answer 2

[KSSV]

See this file exchange, so far this is the best one I found: https://in.mathworks.com/matlabcentral/fileexchange/22441-curve-intersections?focused=5165138&tab=function