Curve intersections软件

Fast computation of intersections and self-intersections of curves using vectorization.

软件应用简介

While a few other functions already exist in FEX that compute the intersection points of curves, this short piece of code was written with speed being the highest priority. No loops are used throughout, taking full advantage of MATLAB’s vectorization capabilities

I welcome any comments, suggestions, bug reports etc.

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INTERX Intersection of curves

P = INTERX(L1,L2) returns the intersection points of two curves L1

and L2. The curves L1,L2 can be either closed or open and are described

by two-row-matrices, where each row contains its x- and y- coordinates.

The intersection of groups of curves (e.g. contour lines, multiply

connected regions etc) can also be computed by separating them with a

column of NaNs as for example

L = [x11 x12 x13 … NaN x21 x22 x23 …;

y11 y12 y13 … NaN y21 y22 y23 …]

P has the same structure as L1 and L2, and its rows correspond to the

x- and y- coordinates of the intersection points of L1 and L2. If no

intersections are found, the returned P is empty.

P = INTERX(L1) returns the self-intersection points of L1. To keep

the code simple, the points at which the curve is tangent to itself are

not included. P = INTERX(L1,L1) returns all the points of the curve

together with any self-intersection points.

Example:

t = linspace(0,2*pi);

r1 = sin(4*t)+2; x1 = r1.*cos(t); y1 = r1.*sin(t);

r2 = sin(8*t)+2; x2 = r2.*cos(t); y2 = r2.*sin(t);

P = InterX([x1;y1],[x2;y2]);

plot(x1,y1,x2,y2,P(1,:),P(2,:),’ro’)