surfplane

 plane=surfplane(node,face)

 plane equation coefficients for each face in a surface

 author: Qianqian Fang, <q.fang at neu.edu>

 input:
   node: a list of node coordinates (nn x 3)
   face: a surface mesh triangle list (ne x 3)

 output:
   plane: a (ne x 4) array, in each row, it has [a b c d]
        to denote the plane equation as "a*x+b*y+c*z+d=0"

 -- this function is part of iso2mesh toolbox (http://iso2mesh.sf.net)

0001 function plane=surfplane(node,face)
0002 %
0003 % plane=surfplane(node,face)
0004 %
0005 % plane equation coefficients for each face in a surface
0006 %
0007 % author: Qianqian Fang, <q.fang at neu.edu>
0008 %
0009 % input:
0010 %   node: a list of node coordinates (nn x 3)
0011 %   face: a surface mesh triangle list (ne x 3)
0012 %
0013 % output:
0014 %   plane: a (ne x 4) array, in each row, it has [a b c d]
0015 %        to denote the plane equation as "a*x+b*y+c*z+d=0"
0016 %
0017 % -- this function is part of iso2mesh toolbox (http://iso2mesh.sf.net)
0018 %
0019 
0020 AB=node(face(:,2),1:3)-node(face(:,1),1:3);
0021 AC=node(face(:,3),1:3)-node(face(:,1),1:3);
0022 
0023 N=cross(AB',AC')';
0024 d=-dot(N',node(face(:,1),1:3)')';
0025 plane=[N,d];