[v8i vba] Detect if shapes are coplanar?

Unknown said:

I cannot find a function that tells me if either:

1. Two shapes are coplanar, or
2. Two plane3d are coplanar

We wrote a VBA project answering your question that is explained in this article.

Unknown said:

From what I read, the essence is that we have to do math.  Do I really need to do math?

No: in this case MicroStation VBA does the hard work for you.  However, you need to understand the geometric 3D concepts of points, planes and normals for the solution to make sense.

Unknown said:

I cannot find a function that tells me if either:

1. Two shapes are coplanar, or
2. Two plane3d are coplanar

We wrote a VBA project answering your question that is explained in this article.

Unknown said:

From what I read, the essence is that we have to do math.  Do I really need to do math?

No: in this case MicroStation VBA does the hard work for you.  However, you need to understand the geometric 3D concepts of points, planes and normals for the solution to make sense.

Hi Guys,

Wow! Thanks for all the nice work. I am sure that will save a few future math-questions around here! :)
As stated earlier I went with this semi built-in functionality:

Function isCoplanar(a As Element, b As Element) As Boolean

    On Error Resume Next

    isCoplanar = True
    
    Dim aa(0) As Element
    Set aa(0) = a
    Dim ab(0) As Element
    Set ab(0) = b
    
    GetRegionUnion aa, ab, Nothing
    If Err.Number <> 0 Then
        isCoplanar = False
        Err.Clear
    End If
    
    Erase aa
    Erase ab
    
End Function

Solution no longer available. Please re-share.

Oto said:

Please re-share

Planes and Normals

A plane is defined by its normal and a point on that plane. MicroStation VBA provides the Plane3d user-defined-type (UDT). The two data members of Plane3d are its Normal and Origin.

Shapes, Normals and Planes

A MicroStation VBA ClosedElement, such as a ShapeElement or an EllipseElement, has a Normal property. It's therefore very easy to derive a Plane3d from a ClosedElement. The normal of the plane is the normal of the closed shape, and any point on that closed shape can be the origin of the plane …

Dim oShape As ShapeElement
... get shape from somewhere
Dim plane As Plane3d
plane.Normal = oShape.Normal
plane.Origin = oShape.Vertex (1)

CoPlanar Planes

Two planes may be parallel but not necessarily coplanar. They are parallel if their normals are identical. If they are not parallel then they intersect.

Two planes are coplanar if two conditions are satisfied …

1. Their normals are identical
2. A point on one plane also lies on the other plane

VBA Methods to Test Planes

VBA provides many methods that deal with 3D objects. Often, it's hard to work out those methods that will help in a given situation.

In this case, we want first to find whether two planes are coplanar. VBA method Plane3dIntersectsPlane3d tells us if two planes intersect. Therefore, the Boolean inverse of that function tells us whether two planes are parallel …

Dim plane1 As Plane3d
Dim plane2 As Plane3d
... get planes from somewhere
Dim intersectionRay As Ray3d
Dim intersection  As Boolean
intersection = Plane3dIntersectsPlane3d (intersectionRay, plane1, plane2)
Dim parallel As Boolean
parallel = Not intersection

Expressing that test more concisely …

Dim parallel  As Boolean
parallel = Not Plane3dIntersectsPlane3d (intersectionRay, plane1, plane2)

We can test if a point on one plane lies on another plane using VBA method Point3dProjectToPlane3d. If we project the origin of plane 1 onto plane 2 and the result is identical, then the planes must be coplanar. Here's a function to perform that test …

Function TestPlanesCoplanar( _
    ByRef plane0 As Plane3d, ByVal label0 As String, _
    ByRef plane1 As Plane3d, ByVal label1 As String) As Boolean
    TestPlanesCoplanar = False

    Const TrueProjection                    As Variant = 0
    Const ModelCoordinates                  As Boolean = False
    Dim projection                          As Point3d
    projection = Point3dProjectToPlane3d(plane0.Origin, plane1, TrueProjection, ModelCoordinates)
    If Point3dEqual(projection, plane0.Origin) Then
        TestPlanesCoplanar = True
        Debug.Print "Plane" & label0 & " is coplanar with plane" & label1
    Else
        Debug.Print "Plane" & label0 & " is not coplanar with plane" & label1
    End If
End Function

Is the full project "CoPlanarShapes.zip" lost?