2D rotation of an object along a custom axis

Question

I'm attempting to figure out how to rotate a 2D object along any axis, which could be outside of the shape itself or somewhere else.

Any pseudocode will do; I just happen to use the VBA programming language for this.

I am looking for a function similar to this:

function rotate(obj, axisX, axisY, angle)
    obj.rotate(angle)
    obj.x = ?
    obj.y = ?

I'm not sure if it matters, but let's suppose it does for the sake of simplicity that the shape is a rectangle.

And when the shape has been rotated, the x, y coordinates would be those of a square containing the rotated shape.

Answer 1

Use this:

Option Explicit
Type ObjLocData
    X As Long
    Y As Long
End Type
Sub Rotate_Object_About_Axis()

    Dim RotObj As Shape
    Dim RotLoc1 As ObjLocData
    Dim RotLoc2 As ObjLocData
    Dim AxisObj As Shape
    Dim AxisLoc As ObjLocData
    Dim R_Rad As Double
    Dim Pi As Double
    
    R_Rad = 0.1
    Pi = 3.14159
    
    Set AxisObj = ActiveSheet.Shapes("AxisObj")
    AxisLoc = ObjectLocation(AxisObj)
    Set RotObj = ActiveSheet.Shapes("RotObj")
    RotLoc1 = ObjectLocation(RotObj)
    Debug.Print AxisLoc.X
    
    RotLoc2 = RotateCoordinates(AxisLoc.X, AxisLoc.Y, RotLoc1.X, RotLoc1.Y, R_Rad)
    With RotObj
        .Left = RotLoc2.X - (.Width / 2)
        .Top = RotLoc2.Y - (.Height / 2)
        .Rotation = .Rotation + (R_Rad * 360 / (2 * Pi))
    End With
    
End Sub
Function ObjectLocation(Shp As Object) As ObjLocData
    ObjectLocation.X = Shp.Left + (Shp.Width / 2)
    ObjectLocation.Y = Shp.Top + (Shp.Height / 2)
End Function
Function RotateCoordinates(Xa, Ya, X, Y, R) As ObjLocData
    RotateCoordinates.X = ((X - Xa) * Cos(R)) - ((Y - Ya) * Sin(R)) + Xa
    RotateCoordinates.Y = ((X - Xa) * Sin(R)) + ((Y - Ya) * Cos(R)) + Ya
End Function
'Location Formulas
'X'=(x-p)cos(?)-(y-q)sin(?)+p,
'y'=(x-p)sin(?)+(y-q)cos(?)+q.

Example: