Huzzah!
Lua Code:
local current = select(5, C_ArtifactUI.GetEquippedArtifactInfo())
local numTraits = select(6, C_ArtifactUI.GetEquippedArtifactInfo())
local tier = select(13, C_ArtifactUI.GetEquippedArtifactInfo())
local nextCost = C_ArtifactUI.GetCostForPointAtRank(numTraits, tier)