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Minkowski sums are used in motion planning of an object among obstacles. They are used for the computation of the configuration space, which is the set of all admissible positions of the object. In the simple model of translational motion of an object in the plane, where the position of an object may be uniquely specified by the position of a ...
Thus in order to compute the linking number of the diagram corresponding to v it suffices to count the signed number of times the Gauss map covers v. Since v is a regular value, this is precisely the degree of the Gauss map (i.e. the signed number of times that the image of Γ covers the sphere). Isotopy invariance of the linking number is ...
The object complement is bold in the following examples: She painted the barn red. – Adjective as object complement; Here, painted is an attributive ditransitive verb. The direct object is the barn. The object complement construction allows for the combination of the sentences She painted the barn and The barn was painted red. He considers ...
The complement of an edgeless graph is a complete graph and vice versa. Any induced subgraph of the complement graph of a graph G is the complement of the corresponding induced subgraph in G. An independent set in a graph is a clique in the complement graph and vice versa. This is a special case of the previous two properties, as an independent ...
In mathematics, the knot complement of a tame knot K is the space where the knot is not. If a knot is embedded in the 3-sphere , then the complement is the 3-sphere minus the space near the knot. To make this precise, suppose that K is a knot in a three-manifold M (most often, M is the 3-sphere ).
In set theory, the complement of a set A, often denoted by (or A′), [1] is the set of elements not in A. [ 2 ] When all elements in the universe , i.e. all elements under consideration, are considered to be members of a given set U , the absolute complement of A is the set of elements in U that are not in A .
Informally, it is called the perp, short for perpendicular complement. It is a subspace of . Example. Let = (, , ) be the vector ...
If is a vector subspace of a real or complex vector space then there always exists another vector subspace of , called an algebraic complement of in , such that is the algebraic direct sum of and (which happens if and only if the addition map is a vector space isomorphism). In contrast to algebraic direct sums, the existence of such a ...