Converting vertex normals to face normals

Question

I have a triangulated polyhedron (not necessarily convex) and the following information:

A list of the position of each vertex. A list of the vertex triples that define each face. A list of the vertex normals (Here the vertex normals are vectors from each vertex that are calculated by averaging face normals (see below) around each vertex).

I would like to calculate the list of face normals (The normalized vectors perpendicular to the plane of each face, pointing outward).

Answer 1

You can simply determines the orientation of crossed normal by dot it with one of vertex normal or average of all 3 vertices.

Here is the pseudo code:

Vec3 CalcNormalOfFace( Vec3 pPositions[3], Vec3 pNormals[3] )
{
    Vec3 p0 = pPositions[1] - pPositions[0];
    Vec3 p1 = pPositions[2] - pPositions[0];
    Vec3 faceNormal = crossProduct( p0, p1 );

    Vec3 vertexNormal = pNormals[0]; // or you can average 3 normals.
    float dot = dotProduct( faceNormal, vertexNormal );

    return ( dot < 0.0f ) ? -faceNormal : faceNormal;
}