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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 plane = createPlane(varargin)
%CREATEPLANE Create a plane in parametrized form.
%
% PLANE = createPlane(P1, P2, P3)
% creates a plane containing the 3 points
%
% PLANE = createPlane(PTS)
% The 3 points are packed into a single 3-by-3 array.
%
% PLANE = createPlane(P0, N);
% Creates a plane from a point P0 and a normal N to the plane. The
% parameter N is given either as a 3D vector (1-by-3 row vector), or as
% [THETA PHI], where THETA is the colatitute (angle with the vertical
% axis) and PHI is angle with Ox axis, counted counter-clockwise (both
% given in radians).
%
% PLANE = createPlane(P0, Dip, DipDir);
% Creates a plane from a point and from a dip and dip direction angles
% of the plane. Parameters Dip and DipDir angles are given as numbers.
% Dip : maximum inclination to the horizontal.
% DipDir : direction of the horizontal trace of the line of dip,
% measured clockwise from north.
%
% The created plane data has the following format:
% PLANE = [X0 Y0 Z0 DX1 DY1 DZ1 DX2 DY2 DZ2], with
% - (X0, Y0, Z0) is a point belonging to the plane
% - (DX1, DY1, DZ1) is a first direction vector
% - (DX2, DY2, DZ2) is a second direction vector
% The 2 direction vectors are normalized and orthogonal.
%
% See also
% planes3d, medianPlane
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2005-02-18
% Copyright 2005-2023 INRA - TPV URPOI - BIA IMASTE
if length(varargin) == 1
% If a single input is provided, it can be:
% * an array of three points belonging to the plane
% * a cell array -> one plane per array element is created
var = varargin{1};
if iscell(var)
plane = zeros([length(var) 9]);
for i = 1:length(var)
plane(i,:) = createPlane(var{i});
end
elseif size(var, 1) >= 3
% 3 points in a single array
p1 = var(1,:);
p2 = var(2,:);
p3 = var(3,:);
% create direction vectors
v1 = p2 - p1;
v2 = p3 - p1;
% create plane
plane = normalizePlane([p1 v1 v2]);
else
error ('MatGeom:createPlane', 'In case of single a.');
end
elseif length(varargin) == 2
% Two arguments -> correspond to plane origin and plane normal
% plane origin
p0 = varargin{1};
% second parameter is either a 3D vector or a 3D angle (2 params)
var = varargin{2};
if size(var, 2) == 2
% normal is given in spherical coordinates
n = sph2cart2([var ones(size(var, 1))]);
elseif size(var, 2) == 3
% normal is given by a 3D vector
n = normalizeVector3d(var);
else
error ('MatGeom:createPlane', 'Can not parse plane normal.');
end
% ensure same dimension for parameters
if size(p0, 1) == 1
p0 = repmat(p0, [size(n, 1) 1]);
end
if size(n, 1) == 1
n = repmat(n, [size(p0, 1) 1]);
end
% find a vector not colinear to the normal, in the direction of [1 0 0]
% first try with vector [0 0 1]
v0 = repmat([0 0 1], [size(p0, 1) 1]);
% if vectors are close to colinear, use vector [0 -1 0]
inds = vectorNorm3d(cross(n, v0, 2)) < 1e-12;
v0(inds, :) = repmat([0 -1 0], [sum(inds) 1]);
% create direction vectors
v1 = normalizeVector3d(cross(n, v0, 2));
v2 = -normalizeVector3d(cross(v1, n, 2));
% concatenate results in the array representing the plane
plane = [p0 v1 v2];
elseif length(varargin) == 3
% Three input arguments:
% * three points (as 1-by-3 or 1-by-N numeric arrays)
% * center, Dip and DipDir (?)
var1 = varargin{1};
var2 = varargin{2};
var3 = varargin{3};
if size(var1, 2) == 3 && size(var2, 2) == 3 && size(var3, 2) == 3
% input arguments are three points
p1 = var1;
p2 = var2;
p3 = var3;
% create direction vectors
v1 = p2 - p1;
v2 = p3 - p1;
plane = normalizePlane([p1 v1 v2]);
elseif size(var1, 2) == 3 && size(var2, 2) == 1 && size(var3, 2) == 1
p0 = var1;
n = [sin(var2)*sin(var3) sin(var2)*cos(var3) cos(var2)];
% find a vector not colinear to the normal
v0 = repmat([1 0 0], [size(p0, 1) 1]);
inds = vectorNorm3d(cross(n, v0, 2))<1e-14;
v0(inds, :) = repmat([0 1 0], [sum(inds) 1]);
% create direction vectors
v1 = normalizeVector3d(cross(n, v0, 2));
v2 = -normalizeVector3d(cross(v1, n, 2));
% concatenate result in the array representing the plane
plane = [p0 v1 v2];
else
error('MatGeom:createPlane', 'Wrong argument in "createPlane".');
end
else
error ('MatGeom:createPlane', 'Wrong number of input parameters.');
end
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