Search and Interpolation

struct CellFinder{Tv, Ti}

CellFinder supports finding cells in grids.

icellfound=GFindLocal!(xref,cellfinder,p; icellstart=1,eps=1.0e-14, trybrute=true)

Find cell containing point p starting with cell number icellstart.

Returns cell number if found, zero otherwise. If trybrute==true try gFindBruteForce! before giving up. Upon return, xref contains the local (barycentric) coordinates of the point: xref[1]:xref[dim] are the coordinates along the reference edges from node 1 to nodes 2..dim+1 (i.e., the barycentric weights of nodes 2..dim+1) and xref[dim+1] is the barycentric weight of node 1. On Parallelogram2D cells xref = (ξ, η, 1-ξ) and on Parallelepiped3D cells xref = (ξ, η, ζ, 1-ξ), where (ξ,η[,ζ]) are the coordinates in the reference cell.

icellfound=gFindBruteForce!(xref,cellfinder,p; icellstart=1,eps=1.0e-14)

Find cell containing point p starting with cell number icellstart.

Returns cell number if found, zero otherwise. Upon return, xref contains the local (barycentric) coordinates of the point: xref[1]:xref[dim] are the coordinates along the reference edges from node 1 to nodes 2..dim+1 (i.e., the barycentric weights of nodes 2..dim+1) and xref[dim+1] is the barycentric weight of node 1. On Parallelogram2D cells xref = (ξ, η, 1-ξ) and on Parallelepiped3D cells xref = (ξ, η, ζ, 1-ξ), where (ξ,η[,ζ]) are the coordinates in the reference cell.

u_to=interpolate(grid_to, u_from, grid_from;eps=1.0e-14,trybrute=true)

Piecewise polynomial interpolation of function u_from on grid grid_from to grid_to; the value at each node of grid_to is reconstructed with the shape functions of the cell of grid_from the node lies in (linear on simplices, bilinear on Parallelogram2D cells, trilinear on Parallelepiped3D cells). Works for matrices with second dimension corresponding to grid nodes and for vectors.

interpolate!(u_to,grid_to, u_from, grid_from;eps=1.0e-14,trybrute=true)

Mutating form of interpolate