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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 varargout = transformPoint3d(pts, transfo, varargin)
%TRANSFORMPOINT3D Transform a point with a 3D affine transform.
%
% PT2 = transformPoint3d(PT1, TRANS);
% PT2 = transformPoint3d(X1, Y1, Z1, TRANS);
% where PT1 has the form [xp yp zp], and TRANS is a 3-by-3, 3-by-4, or
% 4-by-4 matrix, returns the point transformed according to the affine
% transform specified by TRANS.
%
% The function accepts transforms given using the following formats:
% [a b c] , [a b c j] , or [a b c j]
% [d e f] [d e f k] [d e f k]
% [g h i] [g h i l] [g h i l]
% [0 0 0 1]
%
% PT2 = transformPoint3d(PT1, TRANS)
% also work when PT1 is a N-by-3-by-M-by-P-by-ETC array of double. In
% this case, PT2 has the same size as PT1.
%
% PT2 = transformPoint3d(X1, Y1, Z1, TRANS);
% also work when X1, Y1 and Z1 are 3 arrays with the same size. In this
% case, PT2 will be a 1-by-3 cell containing {X Y Z} outputs of size(X1).
%
% [X2, Y2, Z2] = transformPoint3d(...);
% returns the result in 3 different arrays the same size as the input.
% This form can be useful when used with functions like meshgrid or warp.
%
% MESH2 = transformPoint3d(MESH, TRANS)
% transforms the field 'vertices' of the struct MESH and returns the same
% struct with the transformed vertices.
% (It is recommended to use the function 'transformMesh', within the
% "meshes3d" module).
%
% See also
% points3d, transforms3d, transformMesh, createTranslation3d
% createRotationOx, createRotationOy, createRotationOz, createScaling
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2005-02-10
% Copyright 2005-2023 INRA - TPV URPOI - BIA IMASTE
%% Parse input arguments
% Check special case: if first argument is a struct with a field named
% 'vertices', then the output will be the same struct, but with the
% transformed vertices.
if nargin == 2 && isstruct(pts) && isfield(pts, 'vertices')
mesh = pts;
mesh.vertices = transformPoint3d(mesh.vertices, transfo);
varargout = {mesh};
return;
end
% Parse x, y, and z coordinates of input points from input arguments
if nargin == 2
% Point coordinates are given in a single N-by-3-by-M-by-etc argument.
% Preallocate x, y, and z to size N-by-1-by-M-by-etc, then fill them in
dim = size(pts);
dim(2) = 1;
[x, y, z] = deal(zeros(dim, class(pts)));
x(:) = pts(:,1,:);
y(:) = pts(:,2,:);
z(:) = pts(:,3,:);
elseif nargin == 4
% Point coordinates are given in 3 different arrays
x = pts;
y = transfo;
z = varargin{1};
transfo = varargin{2};
dim = size(x);
else
error('MatGeom:geom3d:WrongInputArgumentNumber', ...
'Requires number of input arguments to be either 2 or 4');
end
%% Process transformation matrix
% extract the linear and the translation parts of the matrix
linear = transfo(1:3, 1:3)';
trans = [0 0 0];
if size(transfo, 2) > 3
trans = transfo(1:3, 4)';
end
%% Main processing
% convert coordinates
try
% vectorial processing, if there is enough memory.
% same as:
% res = (transfo * [x(:) y(:) z(:) ones(NP, 1)]')';
res = bsxfun(@plus, [x(:) y(:) z(:)] * linear, trans);
% Back-fill x,y,z with new result (saves calling costly reshape())
x(:) = res(:,1);
y(:) = res(:,2);
z(:) = res(:,3);
catch ME
disp(ME.message)
% process each point one by one, writing in existing array
NP = numel(x);
for i = 1:NP
res = [x(i) y(i) z(i)] * linear + trans;
x(i) = res(1);
y(i) = res(2);
z(i) = res(3);
end
end
% process output arguments
if nargout <= 1
% results are stored in a unique array
if length(dim) > 2 && dim(2) > 1
warning('geom3d:shapeMismatch',...
'Shape mismatch: Non-vector xyz input should have multiple x,y,z output arguments. Cell {x,y,z} returned instead.')
varargout{1} = {x,y,z};
else
varargout{1} = [x y z];
end
elseif nargout == 3
% results are returned in three array with same size.
varargout = {x, y, z};
end
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