Normalteil
Normalteil is a term used in vector calculus and physics to denote the normal component of a vector relative to a given surface or submanifold. For a surface with unit normal vector n at a point, the normalteil of a vector v is v_n = (v · n) n, and the scalar normal component is v · n. The remaining component is the tangential component v_t = v - v_n. This decomposition is unique when n is defined. The normal direction is perpendicular to the surface.
In differential geometry, the concept extends to vectors in the tangent space and the normal bundle; the
Computation: if the surface normal is n, then compute the dot product to obtain the scalar projection
Applications: evaluating fluxes across surfaces, stress analysis where forces act normal to a boundary, boundary conditions
Limitations: the concept requires a well-defined normal; at edges or corners or non-smooth surfaces the normal
Etymology: German "Normal" meaning perpendicular, "Teil" meaning part or component.