The Polygon function

To draw a regular polygon as a symbol we first need to write a small function that will return the co-ordinates of the points of the corners of the polygon give its center and "radius".

This is easier to write than you might think, once you know  the equation for a circle in polar co-ordinates:

cx= r*Cos t + + x

cy= r*Sin t + y

which gives a point on the circle of radius r centered on x,y at angle t.

To generate the points of an n-sided polygon we simply need to evaluate the formulas for t equal to mulitples of 2Pi/n. For example for a triangle the angle is 2Pi/3:

The only complication is that a XML polygon has two extra requirements. The first is that you have to repeat the first point in its specification as the last point - i.e. to close the figure. The second is that the points have to be listed in a clockwise order.

With these two practicalities in mind we can write the polygon function. First we need to setup some basic variables and constants:

Private Function Polygon(
      x As Double, 
      y As Double, 
      r As Double, 
      n As Integer) As String
Dim Angle As Double
Dim Coords As String
Coords = ""
Angle = 2 * 3.141592654 / n

The number of points to be generated is given by n and the results are to be returned in the Coords string as a set in the format x,y,z with one point to a line.

The first and last points are best generated separately from the rest. The first point is:

px1 = r * Sin(Angle * i) + x
py1 = r * Cos(Angle * i) + y
Coords = Coords & px1 & "," & py1 & ",0 "

The final line converts the numeric values px1 and py1 into a comma separated string.

Next we use a for loop to generate the rest of the points in the polygon:

For i = 1 To n - 1
 px = r * Sin(Angle * i) + x
 py = r * Cos(Angle * i) + y
 Coords = Coords & px & "," & py & ",0 "
Next i

Finally we repeat the first point as the last point and return the result:

 Coords = Coords & px1 & "," & py1 & ",0"
 Polygon = Coords
End Function

The complete function is:

Private Function Polygon(
      x As Double, 
      y As Double, 
      r As Double, 
      n As Integer) As String
 Dim Angle As Double
 Dim Coords As String
 Coords = ""
 Angle = 2 * 3.141592654 / n

 px1 = r * Sin(Angle * i) + x
 py1 = r * Cos(Angle * i) + y
 Coords = Coords & px1 & "," & py1 & ",0 "

 For i = 1 To n - 1
  px = r * Sin(Angle * i) + x
  py = r * Cos(Angle * i) + y
  Coords = Coords & px & "," & py & ",0 "
 Next i

 Coords = Coords & px1 & "," & py1 & ",0"
 Polygon = Coords
End Function

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