/usr/share/octave/packages/msh-1.0.10/msh3m_geometrical_properties.m is in octave-msh 1.0.10-1.
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##
## This file is part of:
## MSH - Meshing Software Package for Octave
##
## MSH is free software; you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 2 of the License, or
## (at your option) any later version.
##
## MSH is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
## GNU General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with MSH; If not, see <http://www.gnu.org/licenses/>.
##
## author: Carlo de Falco <cdf _AT_ users.sourceforge.net>
## author: Massimiliano Culpo <culpo _AT_ users.sourceforge.net>
## -*- texinfo -*-
## @deftypefn {Function File} {[@var{varargout}]} = @
## msh3m_geometrical_properties(@var{mesh},[@var{string1},@var{string2},...])
##
##
## Compute @var{mesh} geometrical properties identified by input strings.
##
## Valid properties are:
## @itemize @bullet
## @item @code{"bar"}: return a matrix with size 3 times the number of mesh
## elements containing the center of mass coordinates.
## @item @code{"wjacdet"}: return the weigthed Jacobian determinant used
## for the numerical integration with trapezoidal rule over an element.
## @item @code{"shg"}: return a matrix of size 3 times the number of
## elements matrix containing the gradient of P1 shape functions.
## @item @code{"shp"}: return a matrix containing the the value of P1 shape
## functions.
## @item @code{"area"}: return a row vector containing the volume of each
## element.
## @end itemize
##
## The output will contain the geometrical properties requested in the
## input in the same order specified in the function call.
##
## If an unexpected string is given as input, an empty vector is
## returned in output.
##
## @seealso{msh2m_topological_properties, msh2m_geometrical_properties}
## @end deftypefn
function [varargout] = msh3m_geometrical_properties (imesh,varargin)
## Check input
if (nargin < 2) # Number of input parameters
error ("msh3m_geometrical_properties: wrong number of input parameters.");
elseif (! (isstruct (imesh) && isfield (imesh,"p") &&
isfield (imesh,"t") && isfield (imesh,"e")))
error ("msh3m_geometrical_properties: first input is not a valid mesh structure.");
elseif (! iscellstr (varargin))
error ("msh3m_geometrical_properties: only string value admitted for properties.");
endif
## Compute properties
## Extract tetrahedra node coordinates
x1 = imesh.p(1,imesh.t(1,:));
y1 = imesh.p(2,imesh.t(1,:));
z1 = imesh.p(3,imesh.t(1,:));
x2 = imesh.p(1,imesh.t(2,:));
y2 = imesh.p(2,imesh.t(2,:));
z2 = imesh.p(3,imesh.t(2,:));
x3 = imesh.p(1,imesh.t(3,:));
y3 = imesh.p(2,imesh.t(3,:));
z3 = imesh.p(3,imesh.t(3,:));
x4 = imesh.p(1,imesh.t(4,:));
y4 = imesh.p(2,imesh.t(4,:));
z4 = imesh.p(3,imesh.t(4,:));
nelem = columns(imesh.t); # Number of elements in the mesh
for nn = 1:length (varargin)
request = varargin{nn};
switch request
case "bar" # Center of mass coordinates
if isfield (imesh,"bar")
varargout{nn} = imesh.bar;
else
b = zeros (3, nelem);
b(1,:) = ( x1 + x2 + x3 + x4 )/4;
b(2,:) = ( y1 + y2 + y3 + y4 )/4;
b(3,:) = ( z1 + z2 + z3 + z4 )/4;
varargout{nn} = b;
clear b;
endif
case "wjacdet" # Weighted Jacobian determinant
if isfield (imesh,"wjacdet")
varargout{nn} = imesh.wjacdet;
else
b = wjacdet (x1,y1,z1,...
x2,y2,z2,...
x3,y3,z3,...
x4,y4,z4);
varargout{nn} = b;
clear b
endif
case "area" # Element area
if isfield (imesh,"area")
varargout{nn} = imesh.area;
else
tmp = wjacdet (x1,y1,z1,...
x2,y2,z2,...
x3,y3,z3,...
x4,y4,z4);
b = sum (tmp,1);
varargout{nn} = b;
clear b;
endif
case "shg" # Gradient of shape functions
if isfield (imesh,"shg")
varargout{nn} = imesh.shg;
else
b = shg (x1,y1,z1,...
x2,y2,z2,...
x3,y3,z3,...
x4,y4,z4);
varargout{nn} = b;
clear b
endif
case "shp" # Value of shape functions
if isfield (imesh,"shp")
varargout{nn} = imesh.shp;
else
varargout{nn} = eye (4);
endif
otherwise
warning ("msh3m_geometrical_properties: unexpected value in property string. Empty vector passed as output.")
varargout{nn} = [];
endswitch
endfor
endfunction
function [b] = wjacdet(x1,y1,z1,x2,y2,z2,x3,y3,z3,x4,y4,z4)
## Compute weighted yacobian determinant
weight = [1/4 1/4 1/4 1/4]';
Nb2 = y1.*(z3-z4) + y3.*(z4-z1) + y4.*(z1-z3);
Nb3 = y1.*(z4-z2) + y2.*(z1-z4) + y4.*(z2-z1);
Nb4 = y1.*(z2-z3) + y2.*(z3-z1) + y3.*(z1-z2);
## Determinant of the Jacobian of the
## transformation from the base tetrahedron
## to the tetrahedron K
detJ = (x2-x1).*Nb2 +(x3-x1).*Nb3 +(x4-x1).*Nb4;
## Volume of the reference tetrahedron
Kkvolume = 1/6;
b(:,:) = Kkvolume * weight * detJ;
endfunction
function [b] = shg(x1,y1,z1,x2,y2,z2,x3,y3,z3,x4,y4,z4)
## Compute gradient of shape functions
Nb2 = y1.*(z3-z4) + y3.*(z4-z1) + y4.*(z1-z3);
Nb3 = y1.*(z4-z2) + y2.*(z1-z4) + y4.*(z2-z1);
Nb4 = y1.*(z2-z3) + y2.*(z3-z1) + y3.*(z1-z2);
## Determinant of the Jacobian of the
## transformation from the base tetrahedron
## to the tetrahedron K
detJ = (x2-x1).*Nb2 +(x3-x1).*Nb3 +(x4-x1).*Nb4;
## Shape function gradients follow
## First index represents space direction
## Second index represents the shape function
## Third index represents the tetrahedron number
b(1,1,:) = (y2.*(z4-z3) + y3.*(z2-z4) + y4.*(z3-z2))./ detJ;
b(2,1,:) = (x2.*(z3-z4) + x3.*(z4-z2) + x4.*(z2-z3))./ detJ;
b(3,1,:) = (x2.*(y4-y3) + x3.*(y2-y4) + x4.*(y3-y2))./ detJ;
b(1,2,:) = ( Nb2 ) ./ detJ;
b(2,2,:) = (x1.*(z4-z3) + x3.*(z1-z4) + x4.*(z3-z1)) ./ detJ;
b(3,2,:) = (x1.*(y3-y4) + x3.*(y4-y1) + x4.*(y1-y3)) ./ detJ;
b(1,3,:) = ( Nb3 ) ./ detJ;
b(2,3,:) = (x1.*(z2-z4) + x2.*(z4-z1) + x4.*(z1-z2)) ./ detJ;
b(3,3,:) = (x1.*(y4-y2) + x2.*(y1-y4) + x4.*(y2-y1)) ./ detJ;
b(1,4,:) = ( Nb4) ./ detJ;
b(2,4,:) = (x1.*(z3-z2) + x2.*(z1-z3) + x3.*(z2-z1)) ./ detJ;
b(3,4,:) = (x1.*(y2-y3) + x2.*(y3-y1) + x3.*(y1-y2)) ./ detJ;
endfunction
%!shared mesh,wjacdet,shg,shp
% x = y = z = linspace(0,1,2);
% [mesh] = msh3m_structured_mesh(x,y,z,1,1:6)
% [wjacdet] = msh3m_geometrical_properties(mesh,"wjacdet")
% [shg] = msh3m_geometrical_properties(mesh,"shg")
% [shp] = msh3m_geometrical_properties(mesh,"shp")
%!test
% assert(columns(mesh.t),columns(wjacdet))
%!test
% assert(size(shg),[3 4 6])
%!test
% assert(shp,eye(4))
%!test
% fail(msh3m_geometrical_properties(mesh,"samanafattababbudoiu"),"warning","Unexpected value in passed string. Empty vector passed as output.")
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