Compute Two Bounding Boxes

gistfile1.txt

--[[
	Micro-optimized code for computing a local space and the global space
	bounding box for a set of parts and attachments as fast as possible.
]]
local function computeTwoBoundingBoxes(basisCFrame1, allParts, allAttachments)
	local basisX, basisY, basisZ = basisCFrame1.X, basisCFrame1.Y, basisCFrame1.Z
	local inverseBasis1 = basisCFrame1:Inverse()
	local xmin1, xmax1 = math.huge, -math.huge
	local ymin1, ymax1 = math.huge, -math.huge
	local zmin1, zmax1 = math.huge, -math.huge
	local xmin2, xmax2 = math.huge, -math.huge
	local ymin2, ymax2 = math.huge, -math.huge
	local zmin2, zmax2 = math.huge, -math.huge

	for _, part in ipairs(allParts) do
		if not part:IsA("Terrain") then
			local cframe = part.CFrame
			local size = part.Size
			local sx, sy, sz = size.X, size.Y, size.Z

			-- Calculation for bounding box in the space of basisCFrame1
			local localCFrame1 = inverseBasis1 * cframe -- put cframe in our local basis
			local _, _, _,
				t00, t01, t02,
				t10, t11, t12,
				t20, t21, t22 = localCFrame1:components()
			local hw1 = 0.5 * (math.abs(sx * t00) + math.abs(sy * t10) + math.abs(sz * t20))
			local hh1 = 0.5 * (math.abs(sx * t01) + math.abs(sy * t11) + math.abs(sz * t21))
			local hd1 = 0.5 * (math.abs(sx * t02) + math.abs(sy * t12) + math.abs(sz * t22))
			local at1x, at1y, at1z = localCFrame1.X, localCFrame1.Y, localCFrame1.Z
			xmin1 = math.min(xmin1, at1x - hw1)
			xmax1 = math.max(xmax1, at1x + hw1)
			ymin1 = math.min(ymin1, at1y - hh1)
			ymax1 = math.max(ymax1, at1y + hh1)
			zmin1 = math.min(zmin1, at1z - hd1)
			zmax1 = math.max(zmax1, at1z + hd1)

			-- Calculation for the bounding box in the global coordinate space
			_, _, _,
			t00, t01, t02,
			t10, t11, t12,
			t20, t21, t22 = cframe:components()
			local hw2 = 0.5 * (math.abs(sx * t00) + math.abs(sy * t01) + math.abs(sz * t02))
			local hh2 = 0.5 * (math.abs(sx * t10) + math.abs(sy * t11) + math.abs(sz * t12))
			local hd2 = 0.5 * (math.abs(sx * t20) + math.abs(sy * t21) + math.abs(sz * t22))
			local at2x, at2y, at2z = cframe.X, cframe.Y, cframe.Z
			xmin2 = math.min(xmin2, at2x - hw2)
			xmax2 = math.max(xmax2, at2x + hw2)
			ymin2 = math.min(ymin2, at2y - hh2)
			ymax2 = math.max(ymax2, at2y + hh2)
			zmin2 = math.min(zmin2, at2z - hd2)
			zmax2 = math.max(zmax2, at2z + hd2)
		end
	end
	for _, attachment in ipairs(allAttachments) do
		local worldPosition = attachment.WorldPosition

		local localPosition = inverseBasis1 * worldPosition
		local localx, localy, localz = localPosition.X, localPosition.Y, localPosition.Z
		xmin1 = math.min(xmin1, localx)
		xmax1 = math.max(xmax1, localx)
		ymin1 = math.min(ymin1, localy)
		ymax1 = math.max(ymax1, localy)
		zmin1 = math.min(zmin1, localz)
		zmax1 = math.max(zmax1, localz)

		local globalx, globaly, globalz = worldPosition.X, worldPosition.Y, worldPosition.Z
		xmin2 = math.min(xmin2, globalx)
		xmax2 = math.max(xmax2, globalx)
		ymin2 = math.min(ymin2, globaly)
		ymax2 = math.max(ymax2, globaly)
		zmin2 = math.min(zmin2, globalz)
		zmax2 = math.max(zmax2, globalz)
	end

	local localBoundingBoxOffset = Vector3.new(
		0.5 * (xmin1 + xmax1),
		0.5 * (ymin1 + ymax1),
		0.5 * (zmin1 + zmax1)
	)
	local localBoundingBoxSize = Vector3.new(
		xmax1 - xmin1,
		ymax1 - ymin1,
		zmax1 - zmin1
	)

	local globalBoundingBoxOffset = Vector3.new(
		0.5 * (xmin2 + xmax2) - basisX,
		0.5 * (ymin2 + ymax2) - basisY,
		0.5 * (zmin2 + zmax2) - basisZ
	)
	local globalBoundingBoxSize = Vector3.new(
		xmax2 - xmin2,
		ymax2 - ymin2,
		zmax2 - zmin2
	)

	return localBoundingBoxOffset, localBoundingBoxSize,
		globalBoundingBoxOffset, globalBoundingBoxSize
end