/usr/share/octave/packages/msh-1.0.10/msh3m_geometrical_properties.m is in octave-msh 1.0.10-5.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 | ## Copyright (C) 2006,2007,2008,2009,2010 Carlo de Falco, Massimiliano Culpo
##
## 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.")
|