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## Copyright (C) 2024 David Legland
## All rights reserved.
##
## Redistribution and use in source and binary forms, with or without
## modification, are permitted provided that the following conditions are met:
##
## 1 Redistributions of source code must retain the above copyright notice,
## this list of conditions and the following disclaimer.
## 2 Redistributions in binary form must reproduce the above copyright
## notice, this list of conditions and the following disclaimer in the
## documentation and/or other materials provided with the distribution.
##
## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS''
## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR
## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
##
## The views and conclusions contained in the software and documentation are
## those of the authors and should not be interpreted as representing official
## policies, either expressed or implied, of the copyright holders.
function edges = crackPattern(box, points, alpha, varargin)
%CRACKPATTERN Create a (bounded) crack pattern tessellation.
%
% E = crackPattern(BOX, POINTS, ALPHA)
% create a crack propagation pattern wit following parameters :
% - pattern is bounded by area BOX given by [xmin xmax ymin ymax].
% - each crack originates from points given in POINTS
% - direction of each crack is given by array ALPHA
% - a crack stop when it reaches another already created crack.
% - all cracks stop when they reach the border of the frame, given by box
% (a serie of 4 points).
% The result is a collection of edges, in the form [x1 y1 x2 y2].
%
% E = crackPattern(BOX, POINTS, ALPHA, SPEED)
% Also specify speed of propagation of each crack.
%
%
% See the result with :
% figure;
% drawEdge(E);
%
% See also
% drawEdge
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2004-05-25
% Copyright 2004-2023 INRA - TPV URPOI - BIA IMASTE
if ~isempty(varargin)
speed = varargin{1};
else
speed = ones(size(points, 1), 1);
end
% Compute line equations for each initial crack.
% The two 'Inf' at the end correspond to the position of the limit.
% If an intersection point is found with another line, but whose position
% is after this value, this means that another crack stopped it before it
% reach the intersection point.
% There is one 'end position' for each side of the crack.
lines = [points speed.*cos(alpha) speed.*sin(alpha) Inf*ones(size(points, 1), 2)];
% initialize lines for borders, but assign a very high speed, to be sure
% borders will stop all cracks.
dx = (box([2 3 4 1],1)-box([1 2 3 4],1))*max(speed)*5;
dy = (box([2 3 4 1],2)-box([1 2 3 4],2))*max(speed)*5;
% add borders to the lines set
lines = [lines ; createLine(box, dx, dy) Inf*ones(4,2)];
edges = zeros(0, 4);
while true
modif = 0;
% try to update each line
for i=1:size(points, 1)
% compute intersections with all other lines
pi = intersectLines(lines(i,:), lines);
% compute position of all intersection points on the current line
pos = linePosition(pi, lines(i,:));
% consider points to the right (positive position), and sort them
indr = find(pos>=0 & pos~=Inf);
[posr, indr2] = sort(pos(indr));
% look for the closest intersection to the right
for i2=1:length(indr2)
% index of intersected line
il = indr(indr2(i2));
% position of point relative to intersected line
pos2 = linePosition(pi(il, :), lines(il, :));
% depending on the sign of position, tests if the line2 can
% stop the current line, or if it was stopped before
if pos2>0
if pos2<abs(posr(i2)) && pos2<lines(il, 5)
if lines(i, 5) ~= posr(i2)
edges(i, 3:4) = pi(il,:);
lines(i, 5) = posr(i2);
modif = 1;
end
break;
end
else
if abs(pos2)<abs(posr(i2)) && abs(pos2)<lines(il, 6)
if lines(i, 5) ~= posr(i2)
edges(i, 3:4) = pi(il,:);
lines(i, 5) = posr(i2);
modif = 1;
end
break;
end
end
end % end processing of right points of the line
% consider points to the left (negative position), and sort them
indl = find(pos<=0 && pos~=Inf);
[posl, indl2] = sort(abs(pos(indl)));
% look for the closest intersection to the right
for i2 = 1:length(indl2)
% index of intersected line
il = indl(indl2(i2));
% position of point relative to intersected line
pos2 = linePosition(pi(il, :), lines(il, :));
% depending on the sign of position, tests if the line2 can
% stop the current line, or if it was stopped before
if pos2>0
if pos2<abs(posl(i2)) && pos2<lines(il, 5)
if lines(i, 6) ~= abs(posl(i2))
edges(i, 1:2) = pi(il, :);
lines(i, 6) = abs(posl(i2));
modif = 1;
end
break;
end
else
if abs(pos2)<abs(posl(i2)) && abs(pos2)<lines(il, 6)
if lines(i, 6) ~= abs(posl(i2))
edges(i, 1:2) = pi(il, :);
lines(i, 6) = abs(posl(i2));
modif = 1;
end
break;
end
end
end % end processing of left points of the line
end % end processing of all lines
% break the infinite loop if no more modification was made
if ~modif
break;
end
end
% add edges of the surronding box.
edges = [edges ; box(1,:) box(2,:) ; box(2,:) box(3,:); ...
box(3,:) box(4,:) ; box(4,:) box(1,:) ];
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