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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 [min_width, min_angle] = minimumCaliperDiameter(points)
%MINIMUMCALIPERDIAMETER Minimum caliper diameter of a set of points.
%
% WIDTH = minimumCaliperDiameter(POINTS)
% Computes the minimum width of a set of points. As polygons and
% polylines are represented as point lists, this function works also for
% polygons and polylines.
%
% [WIDTH THETA] = minimumCaliperDiameter(POINTS)
% Also returns the direction of minimum width. The direction corresponds
% to the horizontal angle of the edge that minimizes the width. THETA is
% given in radians, between 0 and PI.
%
%
% Example
% % Compute minimal caliper diameter, and check coords of rotated points
% % have expected extent
% points = randn(30, 2);
% [width theta] = minimumCaliperDiameter(points);
% points2 = transformPoint(points, createRotation(-theta));
% diff = max(points2) - min(points2);
% abs(width - diff(2)) < 1e-10
% ans =
% 1
%
% References
% Algorithms use rotating caliper. Implementation was based on that of
% Wikipedia:
% http://en.wikipedia.org/wiki/Rotating_calipers
%
% See also
% polygons2d, convexHull, orientedBox
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2011-04-08, using Matlab 7.9.0.529 (R2009b)
% Copyright 2011-2023 INRA - Cepia Software Platform
% first, compute convex hull of the polygon
inds = convhull(points(:,1), points(:,2));
hull = points(inds, :);
% if first and last points are the same, remove the last one
if inds(1) == inds(end)
hull = hull(1:end-1, :);
end
% number of hull vertices
nV = size(hull, 1);
% default values
rotated_angle = 0;
min_width = inf;
min_angle = 0;
% avoid degenerated cases
if nV < 3
return;
end
[tmp, p_a] = min(hull(:, 2)); %#ok<ASGLU>
[tmp, p_b] = max(hull(:, 2)); %#ok<ASGLU>
caliper_a = [ 1 0]; % Caliper A points along the positive x-axis
caliper_b = [-1 0]; % Caliper B points along the negative x-axis
while rotated_angle < pi
% compute the direction vectors corresponding to each edge
ind_a2 = mod(p_a, nV) + 1;
vector_a = hull(ind_a2, :) - hull(p_a, :);
ind_b2 = mod(p_b, nV) + 1;
vector_b = hull(ind_b2, :) - hull(p_b, :);
% Determine the angle between each caliper and the next adjacent edge
% in the polygon
angle_a = vectorAngle(caliper_a, vector_a);
angle_b = vectorAngle(caliper_b, vector_b);
% Determine the smallest of these angles
minAngle = min(angle_a, angle_b);
% Rotate the calipers by the smallest angle
caliper_a = rotateVector(caliper_a, minAngle);
caliper_b = rotateVector(caliper_b, minAngle);
rotated_angle = rotated_angle + minAngle;
% compute current width, and update opposite vertex
if angle_a < angle_b
line = createLine(hull(p_a, :), hull(ind_a2, :));
width = distancePointLine(hull(p_b, :), line);
p_a = mod(p_a, nV) + 1;
else
line = createLine(hull(p_b, :), hull(ind_b2, :));
width = distancePointLine(hull(p_a, :), line);
p_b = mod(p_b, nV) + 1;
end
% update minimum width and corresponding angle if needed
if width < min_width
min_width = width;
min_angle = rotated_angle;
end
end
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