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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 [point, pos, isInside] = intersectLineTriangle3d(line, triangle, varargin)
%INTERSECTLINETRIANGLE3D Intersection point of a 3D line and a 3D triangle.
%
% POINT = intersectLineTriangle3d(LINE, TRI)
% Compute coordinates of the intersection point between the line LINE and
% the triangle TRI.
% LINE is a 1-by-6 row vector given as: [X0 Y0 Z0 DX DY DZ]
% TRI is given either as a row vector [X1 Y1 Z1 X2 Y2 Z2 X3 Y3 Z3], or as
% a 3-by-3 array, each row containing coordinates of one of the triangle
% vertices.
% The result is a 1-by-3 array containing coordinates of the intesection
% point, or [NaN NaN NaN] if the line and the triangle do not intersect.
%
% [POINT POS] = intersectLineTriangle3d(LINE, TRI)
% Also returns the position of the intersection point on the line, or NaN
% if the line and the supporting plane of the triangle are parallel.
%
% [POINT POS ISINSIDE] = intersectLineTriangle3d(LINE, TRI)
% Also returns a boolean value, set to true if the line and the triangle
% intersect each other. Can be used for testing validity of result.
%
% Example
% line = [1 1 0 0 0 1];
% tri = [0 0 5;5 0 0;0 5 0];
% intersectLineTriangle3d(line, tri)
% ans =
% 1 1 3
%
% See also
% points3d, lines3d, polygons3d, intersectRayPolygon3d,
% distancePointTriangle3d
%
% References
% Algorithm adapted from SoftSurfer Ray/Segment-Triangle intersection
% http://softsurfer.com/Archive/algorithm_0105/algorithm_0105.htm
%
% ------
% 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
%% Default values
% default return value
point = [NaN NaN NaN];
pos = NaN;
isInside = false;
tol = 1e-13;
if ~isempty(varargin)
tol = varargin{1};
end
%% Process inputs
% triangle edge vectors
if size(triangle, 2) > 3
% triangle is given as a 1-by-9 row vector
t0 = triangle(1:3);
u = triangle(4:6) - t0;
v = triangle(7:9) - t0;
else
% triangle is given as a 3-by-3 array
t0 = triangle(1, 1:3);
u = triangle(2, 1:3) - t0;
v = triangle(3, 1:3) - t0;
end
%% Compute intersection
% triangle normal
n = cross(u, v);
% test for degenerate case of flat triangle
if vectorNorm3d(n) < tol
return;
end
% line direction vector
dir = line(4:6);
% vector between triangle origin and line origin
w0 = line(1:3) - t0;
% compute projection of each vector on the plane normal
a = -dot(n, w0);
b = dot(n, dir);
% test case of line parallel to the triangle
if abs(b) < tol
return;
end
% compute intersection point of line with supporting plane
% If r < 0: point before ray
% If r > 1: point after edge
pos = a / b;
% coordinates of intersection point
point = line(1:3) + pos * dir;
%% test if intersection point is inside triangle
% normalize direction vectors of triangle edges
uu = dot(u, u);
uv = dot(u, v);
vv = dot(v, v);
% coordinates of vector v in triangle basis
w = point - t0;
wu = dot(w, u);
wv = dot(w, v);
% normalization constant
D = uv^2 - uu * vv;
% test first coordinate
s = (uv * wv - vv * wu) / D;
if s < 0.0 || s > 1.0
point = [NaN NaN NaN];
pos = NaN;
return;
end
% test second coordinate, and third triangle edge
t = (uv * wu - uu * wv) / D;
if t < 0.0 || (s + t) > 1.0
point = [NaN NaN NaN];
pos = NaN;
return;
end
% set the validity flag
isInside = true;
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