Index: /issm/trunk/src/m/utils/Mesh/GetAreas.m
===================================================================
--- /issm/trunk/src/m/utils/Mesh/GetAreas.m	(revision 1235)
+++ /issm/trunk/src/m/utils/Mesh/GetAreas.m	(revision 1235)
@@ -0,0 +1,50 @@
+function areas=GetAreas(index,x,y,varargin)
+%GETAREAS - compute areas or volumes of elements
+%
+%   compute areas of triangular elements or volumes 
+%   of pentahedrons
+%
+%   Usage:
+%      areas  =GetAreas(index,x,y);
+%      volumes=GetAreas(index,x,y,z);
+%
+%   Examples:
+%      areas  =GetAreas(md.elements,md.x,md.y);
+%      volumes=GetAreas(md.elements,md.x,md.y,md.z);
+
+%get number of elements and number of nodes
+nels=size(index,1);
+nods=length(x);
+
+%some checks
+if nargout~=1 | (nargin~=3 & nargin~=4),
+	help GetAreas
+	error('GetAreas error message: bad usage')
+end
+if ((length(y)~=nods) | (nargin==4 & length(z)~=nods)),
+	error('GetAreas error message: x,y and z do not have the same length')
+end
+if max(index(:))>nods,
+	error(['GetAreas error message: index should not have values above ' num2str(nods) ])
+end
+if (nargin==3 & size(index,2)~=3),
+	error('GetAreas error message: index should have 3 columns for 2d meshes.')
+end
+if (nargin==4 & size(index,2)~=6),
+	error('GetAreas error message: index should have 6 columns for 3d meshes.')
+end
+
+%initialization
+areas=zeros(nels,1);
+x1=x(index(:,1)); x2=x(index(:,2)); x3=x(index(:,3));
+y1=y(index(:,1)); y2=y(index(:,2)); y3=y(index(:,3));
+
+%compute the volume of each element
+if nargin==3,
+	%compute the surface of the triangle
+	areas=abs(0.5*((x2-x1).*(y3-y1)-(y2-y1).*(x3-x1)));
+else
+	%V=area(triangle)*1/3(z1+z2+z3)
+	thickness=mean(z(index(:,4:6)))-mean(z(index(:,1:3)));
+	areas=abs(0.5*((x2-x1).*(y3-y1)-(y2-y1).*(x3-x1)))*thickness;
+end
Index: /issm/trunk/src/m/utils/Mesh/GetNodalFunctionsCoeff.m
===================================================================
--- /issm/trunk/src/m/utils/Mesh/GetNodalFunctionsCoeff.m	(revision 1235)
+++ /issm/trunk/src/m/utils/Mesh/GetNodalFunctionsCoeff.m	(revision 1235)
@@ -0,0 +1,56 @@
+function [alpha beta varargout]=GetNodalFunctionsCoeff(index,x,y)
+%GETNODELFUNCTIONSCOEFF - compute nodal functions coefficients
+%
+%   Compute the coefficients alpha beta and optionaly gamma of
+%   2d triangular elements. For each element, the nodal function
+%   is defined as:
+%   N(x,y)=sum(i=1:3) alpha_i * x + beta_i * y + gamma_i
+%
+%   Usage:
+%      [alpha beta]=GetNodalFunctionsCoeff(index,x,y);
+%      [alpha beta gamma]=GetNodalFunctionsCoeff(index,x,y);
+%
+%   Example:
+%      [alpha beta gamma]=GetNodalFunctionsCoeff(md.elements,md.x,md.y);
+
+%make columns out of x and y
+x=x(:); y=y(:);
+
+%get nels and nods
+nels=size(index,1);
+nods=length(x);
+
+%some checks
+if nargin~=3 | (nargout~=2 & nargout~=3),
+	help GetNodalFunctionsCoeff
+	error('GetNodalFunctionsCoeff error message: bad usage')
+end
+if length(y)~=nods,
+	error('GetNodalFunctionsCoeff error message: x and y do not have the same length')
+end
+if max(index(:))>nods,
+	error(['GetNodalFunctionsCoeff error message: index should not have values above ' num2str(nods) ])
+end
+if size(index,2)~=3,
+	error('GetNodalFunctionsCoeff error message: only 2d meshes supported. index should have 3 columns.')
+end
+
+%initialize output
+alpha=zeros(nels,3);
+beta=zeros(nels,3);
+
+%compute nodal functions coefficients N(x,y)=alpha x + beta y +gamma
+x1=x(index(:,1)); x2=x(index(:,2)); x3=x(index(:,3));
+y1=y(index(:,1)); y2=y(index(:,2)); y3=y(index(:,3));
+invdet=1./(x1.*(y2-y3)-x2.*(y1-y3)+x3.*(y1-y2));
+
+%get alpha and beta
+alpha=[invdet.*(y2-y3) invdet.*(y3-y1) invdet.*(y1-y2)];
+beta =[invdet.*(x3-x2) invdet.*(x1-x3) invdet.*(x2-x1)];
+
+%get gamma if requested
+if nargout==3,
+	gamma=zeros(nels,3);
+	gamma=[invdet.*(x2.*y3-x3.*y2) invdet.*(y1.*x3-y3.*x1) invdet.*(x1.*y2-x2.*y1)];
+	varargout{1}=gamma;
+end