SimplicialCubature (version 1.1)

CanonicalSimplex: Internal functions for defining/working with simplices.

Description

These are utility functions that are useful when defining/working with simplices in n-dimensional space.

Usage

CanonicalSimplex(n)
UnitSimplexV(n)
SimplexVolume(S)
SimplexSurfaceArea(S3)
JacobianS2Canonical(S2)

Value

Let e[j] be the j-th standard unit basis vector. CanonicalSimplex(n) gives the simplex with columns being vertices of the canonical simplex in n-dimensions: the n-dim. simplex with vertices (0,0,...,0) and e[1],...,e[n]. A vector (u[1],...,u[n]) is in the canonical simplex if 0

Examples

CanonicalSimplex(3)
UnitSimplexV(3)
SimplexVolume( CanonicalSimplex(3) ) 
SimplexSurfaceArea( UnitSimplexV(3) ) 
JacobianS2Canonical( UnitSimplexV(3) )