Sentence examples for combination of vertices from inspiring English sources

In order to be able to deform the interface (mathcal {C}), a point p belonging to Ω1 or Ω2 is expressed as an affine combination of vertices v1,…2,v,v N of a cage.

Let (mathcal{A}=A_{1}cdots A_{n+1}) be an n-simplex in (mathbb {R}^{n}), and let (A=sum_{i=1}^{n+1}alpha_{i}A_{i}) be a convex combination of the vertices (A_{i}).

Let (mathcal{A}=A_{1}cdots A_{n+1}) be an n-simplex in (mathbb {R}^{n}), and let (A=sum_{i=1}^{n+1}alpha_{i}A_{i}) be a convex combination of the vertices (A_{i}) with coefficients (alpha _{i}) satisfying (alpha_{i}>0).

Let (mathcal{A}=A_{1}cdots A_{n+1}) be an n-simplex in (mathbb {R}^{n}), let (A=sum_{i=1}^{n+1}alpha_{i}A_{i}) be a convex combination of the vertices (A_{i}) with coefficients (alpha _{i}) satisfying (0

The point A can be uniquely represented as the convex combination of the vertices (A_{i}) by means of A=sum_{i=1}^{n+1} alpha_{i}A_{i}, (5) where we have the coefficients alpha_{i}=frac{operatorname{vol}(mathcal{A}_{i})}{operatorname{vol}(mathcal{A})}.

The position of an accession relative to these vertices encodes the admixture proportion of that accession in the sense that it can be uniquely expressed as a convex combination of the vertices of that simplex.

F ij ≥ 0. Collectively, the constraints ensure that each point be expressed exactly as a unique convex combination of the vertices.

The new method first computes all combinations of eight vertices whose connectivity in T matches the connectivity of a hexahedron.

In the present paper, a new approach to the problem, which builds on the fact that points in the polytope can be represented as convex combinations of the vertices of that polytope, is introduced.

First, all combinations of eight/six/five vertices whose connectivity in T matches the connectivity of a hexahedron/prism/pyramid are computed.

With an increase in the number of bonds and atoms, the search space also increases due to the combination of edges and vertices.