Addendum to Blue Noise through Optimal Transport*-3mm
نویسندگان
چکیده
Notation: A power diagram for a weighted point set (X = {xi},W = {wi}) is a partition of a domain D into convex cells V i such that V i = {x ∈ D | ‖x − xi‖ − wi ≤ ‖x − xj‖ − wj ,∀j}. The dual of power diagram defines the regular triangulation of (X,W ). We denote by eij the regular edge between two adjacent points xi and xj , and by eij the dual (orthogonal and clipped byD) edge separating the partition regions V i and V j ; therefore x ∈ eij iff ‖x − xi‖ − wi = ‖x − xj‖ − wj and x ∈ D. We further indicate by |e| the length of the edge e and by Ωi the one-ring of xi in the regular triangulation (X,W ). We also denote by cij the intersecting point between the supporting lines of eij and eij . As in our main paper, we will refer to the density field in the domain D as ρ, and denote the average value of ρ over eij as ρ̄ij , and mi as the integrated value of ρ over V i .
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