spacing between two points in 3d cordinate system - vb.net

Question

i am a bit new to this but I'm trying to create a randomly generated 3d coordinate points with equal spacing, I've tried using for each loop but im confused on how to use in. the purpose is to generate sphere around that point but some sphere are overlapping each other. thanks in advance. the code below is to show how I'm generating the sphere
For i = 0 To noofsp - 1
x = Rnd(1) * maxDist
ws1.Cells(i + 5, 2) = x
y = Rnd(1) * maxDist
ws1.Cells(i + 5, 3) = y
z = Rnd(1) * maxDist
ws1.Cells(i + 5, 4) = z
centers.Add({x, y, z})
Next

Answer 1

You'll need to check the new point against all the other points to make sure that your new point is at a greater distance that the sum of the radii of your new sphere and each sphere you're checking against
You'll need to use pythagoras' theorem to check that the distances and I found the code below from this site. The code on the site is written in c#, but here is the vb.net version.
Public Function Distance3D(x1 As Double, y1 As Double, z1 As Double, x2 As Double, y2 As Double, z2 As Double) As Double
' __________________________________
'd = √ (x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2
'
'Our end result
Dim result As Double
'Take x2-x1, then square it
Dim part1 As Double = Math.Pow((x2 - x1), 2)
'Take y2-y1, then square it
Dim part2 As Double = Math.Pow((y2 - y1), 2)
'Take z2-z1, then square it
Dim part3 As Double = Math.Pow((z2 - z1), 2)
'Add both of the parts together
Dim underRadical As Double = part1 + part2 + part3
'Get the square root of the parts
result = Math.Sqrt(underRadical)
'Return our result
Return result
End Function
To generate the spheres, you would need to expand your code to include checking the new point against all the previously generated points. That code is below with comments.
I have assumed the definition of a variable called minDistance to specify how far apart the centre of the spheres should be. I'm also assuming that all the spheres are the same size. The number should be twice the radius of the spheres
Private Sub GenerateSpheres()
Randomize
For i As Integer = 0 To noofsp - 1
Dim distanceOK As Boolean = False
Dim x, y, z As Integer
'keep generating points until one is found that is
'far enough away. When it is, add it to your data
While distanceOK = False
x = Rnd(1) * maxDist
y = Rnd(1) * maxDist
z = Rnd(1) * maxDist
'If no other points have been generated yet, don't bother
'checking your new point
If centers.Count = 0 Then
distanceOK = True
Else
'If other points exist, loop through the list and check distance
For j As Integer = 0 To centers.Count - 1
'if the point is too close to any other, stop checking,
'exit the For Loop and the While Loop will generate a new
'coordinate for checking, and so on
Dim dist As Integer = Distance3D(centers(j)(0), centers(j)(1), centers(j)(2), x, y, z)
If dist <= minDistance Then
distanceOK = False
'exit the For loop and start the next iteration of the While Loop
Continue While
End If
Next
'If all previous points have been checked none are too close
'flag distanceOK as true
distanceOK = True
End If
End While
'ws1.Cells(i + 5, 2) = x
'ws1.Cells(i + 5, 3) = y
'ws1.Cells(i + 5, 4) = z
centers.Add({x, y, z})
Next
End Sub