# What is MATLAB convention for the direction of normal vector of a triangulated mesh?

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### Answers (1)

Soumya Saxena
on 27 Jan 2017

Edited: Soumya Saxena
on 27 Jan 2017

The orientation of the normal is implicitly defined by the ordering of the vertices in a triangle. For all triangulations generated in MATLAB via DELAUNAY, delaunayTriangulation, CONVHULL, BOUNDARY, alphaShape, etc., the ordering follows the right-hand rule. For example, when you view the triangular facets on a convex hull boundary, the vertices are ordered in a counter-clockwise manner and the normal is in the outward direction with respect to the hull. In terms of the right-hand rule, your four fingers curl around in the orientation of the triangle and your thumb indicates the direction of the triangle normal.

The normal vector is obtained from the cross-product of two edges of the triangle.

Please consider the following example:

[x, y, z] = meshgrid(0:1);

x = x(:);

y = y(:);

z = z(:);

tri = convhull(x,y,z);

tr = triangulation(tri, x, y, z);

figure('Color', 'white')

trisurf(tr,'faceColor','cyan')

axis equal;

fn = faceNormal(tr);

P = incenter(tr);

hold on;

quiver3(P(:,1),P(:,2),P(:,3),fn(:,1),fn(:,2),fn(:,3),0.5, 'color','r');

hold off;

% Now flip the ordering of the vertices and the normals will point

% in the opposite direction. We can do this by exchanging any two

% colums of the triangles matrix.

tri = [tri(:,1), tri(:,3), tri(:,2)];

figure('Color', 'white')

tr = triangulation(tri, x, y, z);

trisurf(tr,'faceColor','cyan', 'FaceAlpha',0.5)

axis equal;

fn = faceNormal(tr);

P = incenter(tr);

hold on;

quiver3(P(:,1),P(:,2),P(:,3),fn(:,1),fn(:,2),fn(:,3),0.5, 'color','r');

hold off;

##### 1 Comment

Patrick Lv
on 29 Apr 2019

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