polygon_z_normal, polygon_z_normal_f - Finds the Z component of the normal vector to three vertices. Allegro game programming library.
fixed polygon_z_normal(const V3D *v1, const V3D *v2, const V3D *v3);
float polygon_z_normal_f(const V3D_f *v1, const V3D_f *v2, const V3D_f *v3);
Finds the Z component of the normal vector to the specified three vertices (which must be part of a convex polygon). This is used mainly in back-face culling. The back-faces of closed polyhedra are never visible to the viewer, therefore they never need to be drawn. This can cull on average half the polygons from a scene. If the normal is negative the polygon can safely be culled. If it is zero, the polygon is perpendicular to the screen.
However, this method of culling back-faces must only be used once the X and Y coordinates have been projected into screen space using persp_project() (or if an orthographic (isometric) projection is being used). Note that this function will fail if the three vertices are co-linear (they lie on the same line) in 3D space.