CODEWITHSUNDEEP
geometry
Emma
Emma

Reputation: 2022

Overlapping cubes

I'm trying to determine if two cubes overlap. I've read up on overlapping rectangles, but I'm not sure how to translate it into the third dimension.

My goal is to generate a number of randomly positioned and sized non-overlapping cubes.

These cubes are represented on a x,y,z Cartesian plane.

Upvotes: 10

Views: 16123

Answers (5)

btilly
btilly

Reputation: 46497

You should be able to modify Determine if two rectangles overlap each other? to your purpose fairly easily.

Suppose that you have CubeA and CubeB. Any one of 6 conditions guarantees that no overlap can exist:

Cond1.  If A's left face is to the right of the B's right face,
           -  then A is Totally to right Of B
              CubeA.X2 < CubeB.X1
Cond2.  If A's right face is to the left of the B's left face,
           -  then A is Totally to left Of B
              CubeB.X2 < CubeA.X1
Cond3.  If A's top face is below B's bottom face,
           -  then A is Totally below B
              CubeA.Z2 < CubeB.Z1
Cond4.  If A's bottom face is above B's top face,
           -  then A is Totally above B
              CubeB.Z2 < CubeA.Z1
Cond5.  If A's front face is behind B's back face,
           -  then A is Totally behind B
              CubeA.Y2 < CubeB.Y1
Cond6.  If A's left face is to the left of B's right face,
           -  then A is Totally to the right of B
              CubeB.Y2 < CubeA.Y1

So the condition for no overlap is:

Cond1 or Cond2 or Cond3 or Cond4 or Cond5 or Cond6

Therefore, a sufficient condition for Overlap is the opposite (De Morgan)

Not Cond1 AND Not Cond2 And Not Cond3 And Not Cond4 And Not Cond5 And Not Cond6

Upvotes: 5

sanch
sanch

Reputation: 716

The accepted answer is wrong and very confusing. Here is what I have come up with.

Determining overlap in the x plane

    if (cubeA.maxX > cubeB.minX)
    if (cubeA.minX < cubeB.maxX)

Determining overlap in the y plane

    if (cubeA.maxY > cubeB.minY)
    if (cubeA.minY < cubeB.maxY)

Determining overlap in the z plane

    if (cubeA.maxZ > cubeB.minZ)
    if (cubeA.minZ < cubeB.maxZ)

if you AND all of these conditions together and the result is true, you know that the cubes intersect at some point.

Credit: https://silentmatt.com/rectangle-intersection/

Upvotes: 15

tink
tink

Reputation: 31

This is just the accepted answer rewritten with the correction. It tests to see if the two axis aligned cuboids have any segment of the X,Y, and Z axis in common, if they dont then it is impossible for them to have a collision. The function assumes there is a collision and performs the tests to check if there isnt.

Function func_Intersect(ByVal cuboid1_MinX As Double, ByVal cuboid1_MaxX As Double, ByVal cuboid1_MinY As Double, ByVal cuboid1_MaxY As Double, ByVal cuboid1_MinZ As Double, ByVal cuboid1_MaxZ As Double, ByVal cuboid2_MinX As Double, ByVal cuboid2_MaxX As Double, ByVal cuboid2_MinY As Double, ByVal cuboid2_MaxY As Double, ByVal cuboid2_MinZ As Double, ByVal cuboid2_MaxZ As Double) As Boolean
    func_Intersect = True
    If cuboid1_MaxX < cuboid2_MinX Then
        func_Intersect = False
    ElseIf cuboid2_MaxX < cuboid1_MinX Then
        func_Intersect = False
    ElseIf cuboid1_MaxY < cuboid2_MinY Then
        func_Intersect = False
    ElseIf cuboid2_MaxY < cuboid1_MinY Then
        func_Intersect = False
    ElseIf cuboid1_MaxZ < cuboid2_MinZ Then
        func_Intersect = False
    ElseIf cuboid2_MaxZ < cuboid1_MinZ Then
        func_Intersect = False
    End If
End Function

Upvotes: 0

Andrew
Andrew

Reputation: 24846

I suppose (did not think much, maybe my condition is not enough) check if all the vertices of first cube are out of the second and inverse: all vertices of second are out of the first.

To check if the vertex is in the cube or not, transform it's coordinates to cube-related coordinate system (apply translation to the cube center and cube rotation). Then simply check each coord (x, y, z) is smaller then half a side

Upvotes: 1

nmichaels
nmichaels

Reputation: 51019

Cubes are made up of 6 rectangular (okay, square) faces.

Two cubes do not intersect if the following conditions are met.

  • None of the faces of 2 cubes intersect.
  • One cube does not completely contain the other.

The post you linked can be easily extended. Just add Z.

Upvotes: 3

Related Questions