Algorithm 1 Algorithm to find a cluster

Require:$b>0$

Require: firstPoint ∈ pointCloud

1: while true do

2:    cluster = createEmptyCluster

3:    currentPoints = [firstPoint]

4:    boundingBox = point.coordinates ± b

5:    newPointsAdded = true

6:    while newPointsAdded do

7:       closePoints = fcp(boundingBox,b,root)

8:       if closePoints.size = 0 then

9:          newPointsAdded = false

10:       end if

11:       currentPoints ∪= closePoints

12:    end while

13:    return cluster(currentPoints)

14: end while

15: procedure FCP(boundingBox,b,node,result=[])

16:    if node.depth = 0 then

17:       currentLocation = node.location.x

18:    else

19:       if node.depth = 1 then

20:          currentLocation = node.location.y

21:       else

22:          currentLocation = node.location.z

23:       end if

24:    end if

25:    if !node.removed and boundingBox.contains(node) then

26:       result ∪= node

27:       node.removed = true

28:       boundingBox = expand(boundingBox, node, b)

29:    end if

30:    points ∪= fcp(boundingBox,b,node.left,result)

31:    points ∪= fcp(boundingBox,b,node.right,result)

32:    return points

33: end procedure

34: procedureexpand(boundingBox, node, b)

35:    boundingBox.minX = min(boundingBox.minX, node.x−b)

36:    boundingBox.maxX = min(boundingBox.maxX, node.x+b)

37:    boundingBox.minY = min(boundingBox.minY, node.y−b)

38:    boundingBox.maxY = min(boundingBox.maxY, node.y+b)

39:    boundingBox.minZ = min(boundingBox.minZ, node.z−b)

40:    boundingBox.maxZ = min(boundingBox.maxZ, node.z+b)

41: end procedure