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Curve intersection

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Curve intersection

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06 Oct 2009 (Updated )

Finds intersections of two piecewise linear plane curves.

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Description

[xs,ys] = cint(x1,y1,x2,y2) finds intersection points of the curves defined by straight lines between the length(x1) points in the plane, (x1,y1), and the length(x2) points in the plane (x2,y2).

The function essentially solves

x1(m) + t*diff(x1)(m) = x2(n) + s*diff(x2)(n);
y1(m) + t*diff(y1)(m) = y2(n) + s*diff(y2)(n);

for each combination of line segments and returns

xs = x1 + t*dx1;
ys = y1 + t*dy1;

for all t for which 0<t<1 and 0<s<1 corresponding to an intersection.

For efficiency the function uses bsxfun to construct the length(x1) x length(x2) matrices involved in the calculation.

Points shared by the two arrays (x1,y1) and (x2,y2) are also returned.

MATLAB release MATLAB 7.5 (R2007b)
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Updates
06 Oct 2009

Bug fixed: Earlier version did not return intersection points where a data point from one of the input curves was placed exactly on the line connecting two data points of the other input curve.

06 Oct 2009

Fixed bug introduced by wrong use of unique in last bug fix :-)

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