intersections.m File Reference

Intersections of curves. Computes the (x,y) locations where two curves intersect. The curves can be broken with NaNs or have vertical segments. More...

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Functions
function	intersections (in x1, in y1, in x2, in y2, in robust)
	Intersections of curves. More...

Detailed Description

Intersections of curves. Computes the (x,y) locations where two curves intersect. The curves can be broken with NaNs or have vertical segments.

Example:

[X0,Y0] = intersections(X1,Y1,X2,Y2,ROBUST);

where X1 and Y1 are equal-length vectors of at least two points and represent curve 1. Similarly, X2 and Y2 represent curve 2. X0 and Y0 are column vectors containing the points at which the two curves intersect.

ROBUST (optional) set to 1 or true means to use a slight variation of the algorithm that might return duplicates of some intersection points, and then remove those duplicates. The default is true, but since the algorithm is slightly slower you can set it to false if you know that your curves don't intersect at any segment boundaries. Also, the robust version properly handles parallel and overlapping segments.

The algorithm can return two additional vectors that indicate which segment pairs contain intersections and where they are:

[X0,Y0,I,J] = intersections(X1,Y1,X2,Y2,ROBUST);

For each element of the vector I, I(k) = (segment number of (X1,Y1)) + (how far along this segment the intersection is). For example, if I(k) = 45.25 then the intersection lies a quarter of the way between the line segment connecting (X1(45),Y1(45)) and (X1(46),Y1(46)). Similarly for the vector J and the segments in (X2,Y2).

You can also get intersections of a curve with itself. Simply pass in only one curve, i.e.,

[X0,Y0] = intersections(X1,Y1,ROBUST);

where, as before, ROBUST is optional.

Version

: 1.12, 27 January 2010

Author

: Douglas M. Schwarz : dmschwarz=ieee*org, dmschwarz=urgrad*rochester*edu Real_email = regexprep(Email,{'=','*'},{'@','.'})

Definition in file intersections.m.

Function Documentation

function intersections	(	in	x1,
		in	y1,
		in	x2,
		in	y2,
		in	robust
	)

Intersections of curves.

Parameters

x1	X coordinates for curve 1
y1	Y coordinates for curve 1
x2	X coordinates for curve 2
y2	Y coordinates for curve 2
robust	Flag to enable robust mode [Default: true]

Return values

x0	X coordinates of intersections
y0	Y coordinates of intersections
iout	Indices of intersections for curve 1
jout	Indices of intersections for curve 2