Draw Poisson lines

 Draw Poisson lines, that is lines uniformly and isotropically
 distributed in the plane.

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 author : David Legland
 INRA - TPV URPOI - BIA IMASTE
 created the 24/06/2005

Contents

initializations
create lines
draw lines
Also draw intersection points

initializations

% clean up
clear all;
close all;

% line density
lambdaRho = .5;

% maximal distance of lines from origin
rhoMax = 150;

% number of lines
Nl = rhoMax*lambdaRho;

create lines

% use uniform distribution for \theta, and linear for \rho
theta = 2*pi*rand(Nl, 1);
rho   = rhoMax*rand(Nl, 1);

% convert to parametric representation
lines = createLine(rho, theta);

draw lines

% format output window
clf;
axis([-100 100 -100 100]);
hold on;

% draw Lines, automatically clipped
drawLine(lines);

% title
title(sprintf('poisson lines, with density %f', lambdaRho));

Also draw intersection points

% detect intersections
pts = zeros(0, 2);
for i=1:size(lines, 1)-1
    pts = [pts ; intersectLines(lines(i,:), lines(i+1:end, :))];
end

% remove cases with parallel cases (should not appear, but ...)
pts = pts(isfinite(pts(:,1)), :);

% draw points on image
hold on;
drawPoint(pts, 'ro');