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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 [points, pos, faceInds, lineInds] = intersectLineMesh3d(line, vertices, varargin)
%INTERSECTLINEMESH3D Intersection points of a 3D line with a mesh.
%
% INTERS = intersectLineMesh3d(LINE, VERTICES, FACES)
% Compute the intersection points between a 3D line and a 3D mesh defined
% by vertices and faces. The mesh data is provided as a pair of arrays,
% with VERTICES being a NV-by-3 array of vertex coordinates, and FACES
% being a NF-by-3 or NF-by-4 array of face vertex indices.
% The LINE data correspond to a 1-by-6 row vector concatenating the line
% origin and direction. LINE can also be a NL-by-6 array representing a
% collection of lines with various origins and directions.
%
% INTERS = intersectLineMesh3d(LINE, MESH)
% Provides the mesh data as a struct with the fields 'vertices' and
% 'faces'.
%
% [INTERS, POS, IFACES] = intersectLineMesh3d(...)
% Also returns the position of each intersection point on the input line,
% and the index of the intersected faces.
% If POS > 0, the point is also on the ray corresponding to the line.
%
% [INTERS, POS, IFACES, ILINES] = intersectLineMesh3d(...)
% Also returns the index of the line each intersection point belong to.
%
% Example
% [V, F] = createCube;
% line = [.2 .3 .4 1 0 0];
% pts = intersectLineMesh3d(line, V, F)
% pts =
% 1.0000 0.3000 0.4000
% 0 0.3000 0.4000
%
% See also
% meshes3d, triangulateFaces, intersectLineTriangle3d
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2011-12-20, using Matlab 7.9.0.529 (R2009b)
% Copyright 2011-2023 INRA - Cepia Software Platform
% tolerance for detecting if a point is on line or within edge bounds
tol = 1e-12;
% parsing
if ~isempty(varargin)
if isscalar(varargin{1})
tol = varargin{1};
[vertices, faces] = parseMeshData(vertices);
else
faces = varargin{1};
varargin(1) = [];
if ~isempty(varargin)
tol = varargin{1};
end
end
else
[vertices, faces] = parseMeshData(vertices);
end
% ensure the mesh has triangular faces
tri2Face = [];
if iscell(faces) || size(faces, 2) ~= 3
[faces, tri2Face] = triangulateFaces(faces);
end
% find triangle edge vectors
t0 = vertices(faces(:,1), :);
u = vertices(faces(:,2), :) - t0;
v = vertices(faces(:,3), :) - t0;
% triangle normal
n = crossProduct3d(u, v);
% direction vectors of lines and origins of lines
dv = permute(line(:,4:6), [3 2 1]);
d0 = permute(line(:,1:3), [3 2 1]);
% vector between triangle origin and line origin
w0 = d0 - t0;
a = -sum(n .* w0, 2); % negative dot product
b = sum(n .* dv, 2); % dot product
valid = abs(b) > tol & vectorNorm3d(n) > tol;
% compute intersection point of line with supporting plane
% If pos < 0: point before ray
% IF pos > |dir|: point after edge
pos = a ./ b;
% coordinates of intersection point
points = d0 + (pos .* dv);
%% test if intersection point is inside triangle
% normalize direction vectors of triangle edges
uu = dot(u, u, 2);
uv = dot(u, v, 2);
vv = dot(v, v, 2);
% coordinates of vector v in triangle basis
w = points - t0;
wu = sum(w .* u, 2);
wv = sum(w .* v, 2);
% normalization constant
D = uv.^2 - uu .* vv;
% test first coordinate
s = (uv .* wv - vv .* wu) ./ D;
ind1 = s < -tol | s > (1.0 + tol);
% test second coordinate, and third triangle edge
t = (uv .* wu - uu .* wv) ./ D;
ind2 = t < -tol | (s + t) > (1.0 + tol);
% keep only interesting points
inds = ~ind1 & ~ind2 & valid;
[faceInds, lineInds] = find(permute(inds, [1 3 2]));
% Bit of an indexing trick to get points in appropriate order
points = points(sub2ind(size(points), ...
faceInds+[0 0 0], faceInds*0+(1:3), lineInds+[0 0 0]) );
if nargout > 1
pos = pos(inds);
% convert to face indices of original mesh
if ~isempty(tri2Face)
faceInds = tri2Face(faceInds);
end
end
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