`faceNormal`

Unit normal vector of each triangle of a triangulated surface.

Category: Mathematics > Computational Geometry

Syntax

N = faceNormal(TR)

Normals for all triangles.

N = faceNormal(TR, T)

Normals only for the triangles with indices in T.

Description

The normal of a triangle is perpendicular to its plane. Its direction follows the right-hand rule on the vertex order in the connectivity list: curling the fingers from the first vertex to the second to the third, the thumb points along the normal. A planar 2-D mesh with counterclockwise triangles therefore has all normals equal to [0 0 1].

Reversing the vertex order of a triangle flips its normal.

Input arguments

TR: A triangulation of triangles in 2-D or 3-D space.
T: Optional column vector of triangle indices.

Output arguments

N: Matrix with one unit vector per triangle, three columns.

Example

Normals of a tetrahedron's faces

P = [0 0 0; 1 0 0; 0 1 0; 0 0 1];
T = [1 3 2; 1 2 4; 1 4 3; 2 3 4];
tr = triangulation(T, P);
N = faceNormal(tr)

Output

N = 4×3

         0         0   -1.0000
         0   -1.0000         0
   -1.0000         0         0
    0.5774    0.5774    0.5774

faceNormal