Accelerating MATLAB Performance

283Implicit Parallelization (Vectorization and Indexing)

%...Transpose and prepare for output

i=i'; dx2=dx2'; dy2=dy2'; S2 = S2';

L = dy2(j).*dx1(i) - dy1(i).*dx2(j);

i=i(L~=0); j=j(L~=0); L=L(L~=0); %...Avoid divisions by 0

%...Solve system of eqs to get the common points

P = unique([dx2(j).*S1(i) - dx1(i).*S2(j),...

dy2(j).*S1(i) - dy1(i).*S2(j)]./[L L],'rows')';

function u = D(x,y)

u = bsxfun(,1:end-1),y).*bsxfun(,2:end),y);

end

The usage, as shown in the utility’s help section, is as follows:

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);