Surface Normals and Orientation

Surface normals and orientation help show which side of a surface is chosen as positive. A surface is orientable if one unit normal vector can be chosen consistently at every point. A thin soap film stretched across a wire loop is a familiar example. The film separates the air on one side from the air on the other, so one si...

A thin soap film stretches smoothly across a wire loop dipped into soapy water. The film separates the air on one side of the film from the air on the other. This means the surface is orientable.

At any point on this film, a unit normal vector can be assigned. Choosing one side for these arrows to point defines a positive orientation; choo...