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PARALLEL SURFACE (OR OFFSET) OF A SURFACE

For an initial surface (S) with current point , a parallel is a set (S_{0}) of points ._{a} |

Two surfaces are said to be *parallel* if any normal to one is normal to the other; it can be proved that, then, the distance between two points with common normal is a constant, called parallelism constant. Do not mistake this notion for the notion of *translated surface*.

Like for planes, the parallelism relation of surfaces is an equivalence relation.

The parallel surfaces of a surface (S_{0}) are the surfaces (S* _{a}*), parallel of index

The union of (S* _{a}*) and (S

The singular points of the parallel surfaces describe the focal of the base surface????

A similar notion is that of level surface of the function "distance (of a point in space) to the surface". These level surfaces are composed of portions of parallel surfaces and portions of spheres, and one of their interests is that they constitute a partition of space, contrary to the parallel surfaces.

Opposite, animation obtained by the succession of various parallel surfaces of a Moebius strip. The parallel surface of index a is identical to that of index -a, contrary to the parallel surfaces of a normal strip.... Moreover, this surface has the feature of being strictly parallel to itself. |

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© Robert FERRÉOL 2017