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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 poly2 = clipPolygonByPlane3d(poly, plane, varargin)
%CLIPPOLYGONBYPLANE3D clip a 3d polygon by a plane.
%
% POLY2 = clipPolygonByPlane3d(POLY, PLANE)
% The 3d polygon POLY is clipped by the PLANE. The result POLY2:
% - Represents the part of the polygon below the plane if the plane
% intersects the polygon.
% - Is the same as POLY if the polygon is below the plane and the plane
% does not intersect the polygon.
% - Is an empty 3d polygon [0x3] if the polygon is above the plane and
% the plane does not intersect the polygon.
%
% Example
% % 2d poly
% pol = [6 7 6 6 5 4 3 2 2 1 2 2 6 ...
% NaN 3 3 4 5 5 3 NaN 4 5 5;
% 4 4 5 6 6 7 6 6 4 2 2 2 1 ...
% NaN 4 5 5 4 4 3 NaN 3 2 3]';
% % Transform into 3d polygon
% phi=-360+720*rand;
% theta=-360+720*rand;
% psi=-360+720*rand;
% pol3d = transformPolygon3d(pol,eulerAnglesToRotation3d(phi, theta, psi));
% plane = [polygonCentroid3d(pol3d) rand(1,6)];
% % Clip polygon
% pol3d2 = clipPolygonByPlane3d(pol3d, plane);
% % Draw results
% figure; hold on; axis equal; view(3)
% drawPolygon3d(pol3d, 'linewidth', 2, 'color', 'y');
% drawPlane3d(plane)
% drawPolygon3d(pol3d2, 'linewidth', 2, 'color', 'b');
% drawArrow3d(polygonCentroid3d(pol3d), ...
% normalizeVector3d(planeNormal(plane))*3,'g')
%
% See also
% poygons3d, intersectLinePolygon3d
% ------
% Author: David Legland, oqilipo
% E-mail: david.legland@inrae.fr
% Created: 2005-08-02
% Copyright 2005-2023 INRA - TPV URPOI - BIA IMASTE
parser = inputParser;
addRequired(parser, 'poly', @isPolygon3d)
addRequired(parser, 'plane', @isPlane)
addOptional(parser,'tolerance',1e-14, ...
@(x) validateattributes(x,{'numeric'},{'scalar','>',0,'<',1}))
parse(parser, poly, plane, varargin{:});
TOL = parser.Results.tolerance;
[pol, inputFormat] = parsePolygon(poly, 'repetition');
% Check if the polygon's plane is the same as the clipping plane
[~, dist] = planePosition(unique(pol,'rows'), plane);
if all(dist<TOL)
poly2 = poly;
warning(['The polygon''s plane is the same as the clipping plane! ' ...
'Returning the input polygon!']);
return;
end
% Check for each point of the polygon if it's above or below the plane.
below = isBelowPlane(pol, plane);
% In the case of a polygon totally over the plane, return empty array
if sum(below) == 0
poly2 = zeros(0, 3);
return;
end
% In the case of a polygon totally below the plane, return original polygon
if sum(~below) == 0
poly2 = poly;
return;
end
% Transform into 2D
basisTFM = createBasisTransform3d('global', fitPlane(pol));
poly2d = transformPoint3d(pol, basisTFM);
% Intersection line between polygon and plane
itsLine = intersectPlanes([0 0 0 1 0 0 0 1 0], ...
transformPlane3d(plane, basisTFM));
poly2dNan = parsePolygon(poly2d,'nan');
% Clip the 2d polygon by the intersection line
poly22d = clipPolygonByLine(poly2dNan(:,1:2), [itsLine(1:2) itsLine(4:5)],...
'method', 'polyshape');
% Transform the 2d polygon back to 3d
poly2 = transformPolygon3d(poly22d, inv(basisTFM));
poly2 = parsePolygon(poly2, inputFormat);
% The input format of the polygon is not clear if it only contains one
% repetition of the first and last point. It can be 'repetiton' or 'nan'.
% In this case the last point is removed.
if size(poly2, 1) - size(unique(poly2, 'rows'), 1) == 1 && ...
isequal(poly2(1,:), poly2(end,:))
poly2(end,:) = [];
end
end
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