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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 obox = orientedBox(points)
%ORIENTEDBOX Minimum-width oriented bounding box of a set of points.
%
% OBOX = orientedBox(PTS)
% Computes the oriented bounding box of a set of points. Oriented box is
% defined by a center, two dimensions (the length and the width), and the
% orientation of the length axis. Orientation is counted in degrees,
% counter-clockwise.
%
% Example
% % Draw oriented bounding box of an ellipse
% elli = [30 40 40 20 30];
% pts = ellipseToPolygon(elli, 120);
% obox = orientedBox(pts);
% figure; hold on;
% drawEllipse(elli);
% drawOrientedBox(obox, 'm');
%
% See also
% drawOrientedBox, orientedBoxToPolygon
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2012-03-29, using Matlab 7.9.0.529 (R2009b)
% Copyright 2012-2023 INRA - Cepia Software Platform
%% initialisations
% 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
% compute convex hull centroid, that corresponds to approximate
% location of rectangle center
center = mean(hull, 1);
hull = bsxfun(@minus, hull, center);
% number of hull vertices
nV = size(hull, 1);
% default values
rotatedAngle = 0;
minWidth = inf;
minAngle = 0;
% avoid degenerated cases
if nV < 3
return;
end
% indices of vertices in extreme y directions
[tmp, indA] = min(hull(:, 2)); %#ok<ASGLU>
[tmp, indB] = max(hull(:, 2)); %#ok<ASGLU>
caliperA = [ 1 0]; % Caliper A points along the positive x-axis
caliperB = [-1 0]; % Caliper B points along the negative x-axis
%% Find the direction with minimum width (rotating caliper algorithm)
while rotatedAngle < pi
% compute the direction vectors corresponding to each edge
indA2 = mod(indA, nV) + 1;
vectorA = hull(indA2, :) - hull(indA, :);
indB2 = mod(indB, nV) + 1;
vectorB = hull(indB2, :) - hull(indB, :);
% Determine the angle between each caliper and the next adjacent edge
% in the polygon
angleA = vectorAngle(caliperA, vectorA);
angleB = vectorAngle(caliperB, vectorB);
% Determine the smallest of these angles
angleIncrement = min(angleA, angleB);
% Rotate the calipers by the smallest angle
caliperA = rotateVector(caliperA, angleIncrement);
caliperB = rotateVector(caliperB, angleIncrement);
rotatedAngle = rotatedAngle + angleIncrement;
% compute current width, and update opposite vertex
if angleA < angleB
line = createLine(hull(indA, :), hull(indA2, :));
width = distancePointLine(hull(indB, :), line);
indA = mod(indA, nV) + 1;
else
line = createLine(hull(indB, :), hull(indB2, :));
width = distancePointLine(hull(indA, :), line);
indB = mod(indB, nV) + 1;
end
% update minimum width and corresponding angle if needed
if width < minWidth
minWidth = width;
minAngle = rotatedAngle;
end
end
%% Compute box dimensions
% orientation of the main axis
theta = rad2deg(minAngle);
% pre-compute trigonometric functions
cot = cos(minAngle);
sit = sin(minAngle);
% elongation in direction of rectangle length
x = hull(:,1);
y = hull(:,2);
x2 = x * cot + y * sit;
y2 = - x * sit + y * cot;
% compute extension along main directions
xmin = min(x2); xmax = max(x2);
ymin = min(y2); ymax = max(y2);
% position of the center with respect to the centroid compute before
dl = (xmax + xmin)/2;
dw = (ymax + ymin)/2;
% change coordinate from rectangle to user-space
dx = dl * cot - dw * sit;
dy = dl * sit + dw * cot;
% coordinates of oriented box center
center = center + [dx dy];
% size of the rectangle
rectLength = xmax - xmin;
rectWidth = ymax - ymin;
% concatenate rectangle data
obox = [center rectLength rectWidth theta];
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