Index: ../trunk-jpl/src/m/geometry/GetAreas.py
===================================================================
--- ../trunk-jpl/src/m/geometry/GetAreas.py	(revision 0)
+++ ../trunk-jpl/src/m/geometry/GetAreas.py	(revision 13472)
@@ -0,0 +1,52 @@
+import numpy
+
+def GetAreas(index,x,y,z=numpy.array([])):
+	"""
+	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.mesh.elements,md.mesh.x,md.mesh.y);
+	      volumes=GetAreas(md.mesh.elements,md.mesh.x,md.mesh.y,md.z);
+	"""
+
+	#get number of elements and number of nodes
+	nels=numpy.size(index,axis=0)
+	nods=numpy.size(x)
+
+	#some checks
+	if numpy.size(y)!=nods or (z and numpy.size(z)!=nods):
+		raise TypeError("GetAreas error message: x,y and z do not have the same length.")
+	if numpy.max(index)>nods:
+		raise TypeError("GetAreas error message: index should not have values above %d." % nods)
+	if (not z and numpy.size(index,axis=1)!=3):
+		raise TypeError("GetAreas error message: index should have 3 columns for 2d meshes.")
+	if (z and numpy.size(index,axis=1)!=6):
+		raise TypeError("GetAreas error message: index should have 6 columns for 3d meshes.")
+
+	#initialization
+	areas=numpy.zeros(nels)
+	x1=x[index[:,0].astype(int)-1]
+	x2=x[index[:,1].astype(int)-1]
+	x3=x[index[:,2].astype(int)-1]
+	y1=y[index[:,0].astype(int)-1]
+	y2=y[index[:,1].astype(int)-1]
+	y3=y[index[:,2].astype(int)-1]
+
+	#compute the volume of each element
+	if not z:
+		#compute the surface of the triangle
+		areas=(0.5*((x2-x1)*(y3-y1)-(y2-y1)*(x3-x1)))
+	else:
+		#V=area(triangle)*1/3(z1+z2+z3)
+		thickness=numpy.mean(z[index[:,3:6].astype(int)-1])-numpy.mean(z[index[:,0:3].astype(int)-1])
+		areas=(0.5*((x2-x1)*(y3-y1)-(y2-y1)*(x3-x1)))*thickness
+
+	return areas
+
Index: ../trunk-jpl/src/m/mesh/GetNodalFunctionsCoeff.py
===================================================================
--- ../trunk-jpl/src/m/mesh/GetNodalFunctionsCoeff.py	(revision 0)
+++ ../trunk-jpl/src/m/mesh/GetNodalFunctionsCoeff.py	(revision 13472)
@@ -0,0 +1,58 @@
+import numpy
+
+def 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.mesh.elements,md.mesh.x,md.mesh.y);
+	"""
+
+	#make columns out of x and y
+	x=x.rshape(-1)
+	y=y.rshape(-1)
+
+	#get nels and nods
+	nels=numpy.size(index,axis=0)
+	nods=numpy.size(x)
+
+	#some checks
+	if numpy.size(y)!=nods:
+		raise TypeError("GetNodalFunctionsCoeff error message: x and y do not have the same length.")
+	if numpy.max(index)>nods:
+		raise TypeError("GetNodalFunctionsCoeff error message: index should not have values above %d." % nods)
+	if numpy.size(index,axis=1)!=3:
+		raise TypeError("GetNodalFunctionsCoeff error message: only 2d meshes supported. index should have 3 columns.")
+
+	#initialize output
+	alpha=numpy.zeros((nels,3))
+	beta=numpy.zeros((nels,3))
+
+	#compute nodal functions coefficients N(x,y)=alpha x + beta y +gamma
+	x1=x[index[:,0].astype(int)-1]
+	x2=x[index[:,1].astype(int)-1]
+	x3=x[index[:,2].astype(int)-1]
+	y1=y[index[:,0].astype(int)-1]
+	y2=y[index[:,1].astype(int)-1]
+	y3=y[index[:,2].astype(int)-1]
+	invdet=1./(x1*(y2-y3)-x2*(y1-y3)+x3*(y1-y2))
+
+	#get alpha and beta
+	alpha=numpy.hstack((invdet*(y2-y3),invdet*(y3-y1),invdet*(y1-y2)))
+	beta =numpy.hstack((invdet*(x3-x2),invdet*(x1-x3),invdet*(x2-x1)))
+
+	#get gamma if requested
+	gamma=numpy.zeros((nels,3))
+	gamma=numpy.hstack((invdet*(x2*y3-x3*y2),invdet*(y1*x3-y3*x1),invdet*(x1*y2-x2*y1)))
+
+	return alpha,beta,gamma
+