Primal to Dual Point Interpolation

[GeorgeR227]

Upon inspection of the below code, it was determined that the procedure to produce the wedge_pd_01 matrix incorporates a form of primal point to dual point interpolation, namely a bilinear interpolation with weights adjusted to favor the primal edge under consideration. This code could be hoisted out into a standalone function and generalized to produce primal to dual point interpolation in 2D.

This would, with the current d0_p0_interpolation complete a roundtrip which could be analyzed for development of errors. An implementation of dual to primal point interpolation may also be pursued by using the same principles established in the primal to dual case.

CombinatorialSpaces.jl/src/FastDEC.jl

Lines 225 to 243 in de655b3

	function wedge_pd_01_mat(sd::HasDeltaSet)
	m = spzeros(ne(sd), nv(sd))
	for e in edges(sd)
	α, β = edge_vertices(sd,e)
	des = elementary_duals(1,sd,e)
	dvs = sd[des, :D_∂v0]
	tris = only.(incident(sd, dvs, :tri_center))
	γδ = map(tris) do t
	only(filter(x -> x ∉ [α,β], triangle_vertices(sd,t)))
	end
	ws = sd[des, :dual_length] ./ sum(sd[des, :dual_length])
	for (w,l) in zip(ws,γδ)
	m[e,α] += w*5/12
	m[e,β] += w*5/12
	m[e,l] += w*2/12
	end
	end
	m
	end