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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 = intersectLineSphere(line, sphere, varargin)
%INTERSECTLINESPHERE Return intersection points between a line and a sphere.
%
% PTS = intersectLineSphere(LINE, SPHERE);
% Returns the two points which are the intersection of the given line and
% sphere.
% LINE : [x0 y0 z0 dx dy dz]
% SPHERE : [xc yc zc R]
% PTS : [x1 y1 z1 ; x2 y2 z2]
% If there is no intersection between the line and the sphere, return a
% 2-by-3 array containing only NaN.
%
% Example
% % draw the intersection between a sphere and a collection of parallel
% % lines
% sphere = [50.12 50.23 50.34 40];
% [x, y] = meshgrid(10:10:90, 10:10:90);
% n = numel(x);
% lines = [x(:) y(:) zeros(n,1) zeros(n,2) ones(n,1)];
% figure; hold on; axis equal;
% axis([0 100 0 100 0 100]); view(3);
% drawSphere(sphere);
% drawLine3d(lines);
% pts = intersectLineSphere(lines, sphere);
% drawPoint3d(pts, 'rx');
%
% % apply rotation on set of lines to check with non vertical lines
% rot = eulerAnglesToRotation3d(20, 30, 10);
% rot2 = recenterTransform3d(rot, [50 50 50]);
% lines2 = transformLine3d(lines, rot2);
% figure; hold on; axis equal;
% axis([0 100 0 100 0 100]); view(3);
% drawSphere(sphere);
% drawLine3d(lines2);
% pts2 = intersectLineSphere(lines2, sphere);
% drawPoint3d(pts, 'rx');
%
% See also
% spheres, circles3d, intersectPlaneSphere
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2005-02-18
% Copyright 2005-2023 INRA - TPV URPOI - BIA IMASTE
%% Process input arguments
% check if user-defined tolerance is given
tol = 1e-14;
if ~isempty(varargin)
tol = varargin{1};
end
% difference between centers
dc = bsxfun(@minus, line(:, 1:3), sphere(:, 1:3));
% equation coefficients
a = sum(line(:, 4:6) .* line(:, 4:6), 2);
b = 2 * sum(bsxfun(@times, dc, line(:, 4:6)), 2);
c = sum(dc.*dc, 2) - sphere(:,4).*sphere(:,4);
% solve equation
delta = b.*b - 4*a.*c;
% initialize empty results
points = NaN * ones(2 * size(delta, 1), 3);
%% process couples with two intersection points
% process couples with two intersection points
inds = find(delta > tol);
if ~isempty(inds)
% delta positive: find two roots of second order equation
u1 = (-b(inds) -sqrt(delta(inds))) / 2 ./ a(inds);
u2 = (-b(inds) +sqrt(delta(inds))) / 2 ./ a(inds);
% convert into 3D coordinate
points(inds, :) = line(inds, 1:3) + bsxfun(@times, u1, line(inds, 4:6));
points(inds+length(delta),:) = line(inds, 1:3) + bsxfun(@times, u2, line(inds, 4:6));
end
%% process couples with one intersection point
% proces couples with two intersection points
inds = find(abs(delta) < tol);
if ~isempty(inds)
% delta around zero: find unique root, and convert to 3D coord.
u = -b(inds) / 2 ./ a(inds);
% convert into 3D coordinate
pts = line(inds, 1:3) + bsxfun(@times, u, line(inds, 4:6));
points(inds, :) = pts;
points(inds+length(delta),:) = pts;
end
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