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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 [v2, f2, bE] = clipMeshByPlane(v, f, plane, varargin)
%CLIPMESHBYPLANE Clip a mesh by a plane.
%
% [V2, F2] = clipMeshByPlane(V, F, PLANE)
% Clip a mesh defined by the vertices V and faces F by a PLANE and return
% the part of the mesh (V2, F2) above the plane.
%
% [V2, F2, ENEW] = clipMeshByPlane(V, F, PLANE)
% Additonally returns the new boundary edges created by the clipping of
% the mesh.
%
% [...] = clipMeshByPlane(V, F, PLANE, 'part', 'below')
% Gives the part of the mesh below the plane. The options are:
% 'part','above': Mesh above the plane [default]
% 'part','below': Mesh below the plane
%
% Example
% % Create trefoil curve
% nPoints = 200; % Number of vertices of trefoil curve
% thickness = .5; % Thickness of the 3D mesh
% nCorners = 16; % Number of corners around each curve vertex
% t = linspace(0, 2*pi, nPoints + 1); % parameterisation variable
% t(end) = [];
% % Trefoil curve coordinates
% curve(:,1) = sin(t) + 2 * sin(2 * t);
% curve(:,2) = cos(t) - 2 * cos(2 * t);
% curve(:,3) = -sin(3 * t);
% % Create surrounding mesh
% [v2, f2] = curveToMesh(curve, thickness, nCorners);
% f2 = triangulateFaces(f2);
% % Clip the mesh by a plane
% plane = createPlane([0 0 0], [0.5 0.5 1]);
% [v2, f2, bE] = clipMeshByPlane(v2, f2, plane, 'part','above');
% % Display results
% figure('color','w');
% drawPolygon3d(curve, 'LineWidth', 4, 'color', 'b');
% axis equal; view(3);
% drawMesh(v2, f2, 'FaceAlpha', 0.5);
% drawPlane3d(plane)
% drawEdge3d([v2(bE(:,1),:),v2(bE(:,2),:)],'Color','g','LineWidth',4)
%
% See also
% cutMeshByPlane, intersectPlaneMesh
%
% Source
% half_space_intersect.m by Alec Jacobson:
% https://github.com/alecjacobson/gptoolbox
% ------
% Author: oqilipo
% E-mail: N/A
% Created: 2023-05-18, using Matlab 9.13.0.2080170 (R2022b) Update 1
% Copyright 2023
%% Parse input
if isstruct(v)
if nargin > 2
varargin = [plane, varargin];
end
plane = f;
f = v.faces;
v = v.vertices;
end
p = inputParser;
addRequired(p,'plane',@isPlane)
validStrings = {'above','below'};
addParameter(p,'part','above',@(x) any(validatestring(x, validStrings)))
parse(p, plane, varargin{:});
part=p.Results.part;
p = plane(1:3);
switch part
case 'above'
n = planeNormal(plane);
case 'below'
n = planeNormal(reversePlane(plane));
end
% Homogeneous coordinates
IV = sum(bsxfun(@times, [v(:,1:3) ones(size(v,1), 1)], [n(:)' -dot(p,n)]), 2);
IF = IV(f);
IF = reshape(IF, size(f));
I13 = sum(IF<0, 2) == 1;
[VV1, E13, ~, F13above, ~] = one_below(v, f(I13,:), IF(I13,:));
I31 = sum(IF>0, 2) == 1;
[VV2, E31, F31below, ~, ~] = one_below(VV1, f(I31,:), -IF(I31,:));
above = all(IF>=0, 2);
FF2 = [f(above,:); F13above; F31below];
% birth = [find(above); repmat(find(I13),2,1); find(I31)];
EE2 = [E13; E31];
% Remove duplicate vertices
bbd = norm(max(v)-min(v));
[vIdx, fIdx] = removeDuplicateVertices(VV2, FF2, 1e-14*bbd, 'IndexOutput',1);
VV3 = VV2(vIdx,:);
FF3 = fIdx(FF2);
EE3 = fIdx(EE2);
% Remove unreferenced/unindexed vertices
[vIdx, fIdx] = removeUnreferencedVertices(VV3, FF3, 'IndexOutput',1);
v2 = VV3(vIdx,:);
f2 = fIdx(FF3);
bE = fIdx(EE3);
end
function [U, E, Fbelow, Fabove, BC] = one_below(V, F, IF)
[~, J] = min(IF, [], 2);
I = sub2ind(size(F), repmat(1:size(F,1), size(F,2),1)', mod([J J+1 J+2]-1, 3)+1);
lambda = IF(I(:,2:3))./bsxfun(@minus,IF(I(:,2:3)),IF(I(:,1)));
BC = sparse( ...
repmat((1:size(F,1)*2)', 1, 2), ...
[repmat(F(I(:,1)),2,1) reshape(F(I(:,2:3)), size(F,1)*2,1)], ...
[lambda(:) 1-lambda(:)], ...
size(F,1)*2, size(V,1));
E = size(V, 1) + bsxfun(@plus, 1:size(F,1), [0;1]*size(F,1))';
U = [V; BC*V];
Fbelow = [F(I(:,1)) E];
Fabove = [F(I(:,2)) fliplr(E); F(I(:,2:3)) E(:,2)];
end
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