Compute normal vectors of 2.5D triangulation

That function compute the normal vectors of a 2.5D triangulation.

Description

It could be useful to know the normal vectors of a surface. The function provided is able to take a 2.5D unrestricted triangulation (Delaunay or not) which define a 3D surface and computes the normal vectors of each cell. It is possible to compute vectors at the center cells or at vertices.

Inputs :
           "XYZ" is the coordinate of the vertex of the triangulation (nx3 matrix).
           "TRI" is the list of triangles which contain indexes of XYZ (mx3 matrix).
           "strPosition" is the position where the normal is computed. It
           could be 'center-cells' for a computation on the center of each
           triangle or could be 'vertices' and the vectors are computed at
          vertices with respect to the neighbor cells (string).

Outputs :
           "NormalVx", "NormalVy" and "NormalVz" are the component of
          normal vectors (normalized to 1).
          "PosVx", "PosVy" and "PosVz" is the positions of each vector.
 
Note :
           if strPosition == 'center-cells', then the dimension of each
           output are mx1.
           if strPosition == 'vertices', then the dimension of each
           output are nx1.

           All cells have to be enumerated clockwise or counter-clock.

 Example :

 [X,Y,Z]=peaks(25);
 X=reshape(X,[],1);
 Y=reshape(Y,[],1);
 Z=0.4*reshape(Z,[],1);
 TRI = delaunay(X,Y);
 [NormalVx NormalVy NormalVz PosVx PosVy PosVz]=computeNormalVectorTriangulation([X Y Z],TRI,'vertices');

 quiver3(PosVx,PosVy, PosVz, NormalVx, NormalVy, NormalVz), axis equal
 hold on
 trimesh(TRI,X,Y,Z)

 David Gingras, February 2009

• MATLAB release: MATLAB 7.5 (R2007b)

[Gozde Unal]

very nice, thanks.

[Edward Bender]

Worked perfectly the first time. A+!

[ws]

n=60;
[X Y] = meshgrid(1:n, 1:n);
[X Y Z] = peaks(n);
a = delaunay(X(:),Y(:));
A = [X(a(:,1)) Y(a(:,1)) Z(a(:,1))];
B = [X(a(:,2)) Y(a(:,2)) Z(a(:,2))];
C = [X(a(:,3)) Y(a(:,3)) Z(a(:,3))];
facets.C = (A+B+C)/3;
B = B-A;
C = C-A;
M = cross(B, C, 2);
L = sqrt(sum(M.^2,2)) + 10e-20;
facets.N = M./repmat(L,1,3);
facets.S = 0.5*L;