Open TK determine sphere (quadstrips) normals? - vb.net

Question

Introduction
I am somewhat new to using Open GL / Open TK. I have learned how to draw basic shapes, use matrices, lighting, shadowing, etc. I have a function that draws a sphere:
Private Sub drawSphere(r As Double, lats As Integer, longs As Integer)
Dim i As Integer, j As Integer
For i = 0 To lats
Dim lat0 As Double = PI * (-0.5 + CDbl(i - 1) / lats)
Dim z0 As Double = Sin(lat0)
Dim zr0 As Double = Cos(lat0)
Dim lat1 As Double = PI * (-0.5 + CDbl(i) / lats)
Dim z1 As Double = Sin(lat1)
Dim zr1 As Double = Cos(lat1)
GL.Begin(PrimitiveType.QuadStrip)
For j = 0 To longs
Dim lng As Double = 2 * PI * CDbl(j - 1) / longs
Dim x As Double = Cos(lng)
Dim y As Double = Sin(lng)
GL.Normal3(x * zr0 * r, y * zr0 * r, z0 * r)
GL.Vertex3(x * zr0 * r, y * zr0 * r, z0 * r)
GL.Normal3(x * zr1 * r, y * zr1 * r, z1 * r)
GL.Vertex3(x * zr1 * r, y * zr1 * r, z1 * r)
Next
GL.End()
Next
End Sub
I have other code that sets up the lights. I know the other code works because I have a separate function for drawing an STL object:
Dim texture As UInteger() = New UInteger(0) {}
Dim i As Integer = 0
If stl_table.Items.Count > 0 Then
find_center_of_part()
GL.Begin(PrimitiveType.Triangles)
GL.Color3(part_color.R, part_color.G, part_color.B)
Do Until i + 4 >= stl_table.Items.Count
GL.Normal3(Convert.ToSingle(stl_table.Items.Item(i).SubItems(0).Text), Convert.ToSingle(stl_table.Items.Item(i).SubItems(1).Text), Convert.ToSingle(stl_table.Items.Item(i).SubItems(2).Text))
GL.Vertex3(stl_table.Items.Item(i + 1).SubItems(0).Text - avgx, stl_table.Items.Item(i + 1).SubItems(1).Text - avgy, stl_table.Items.Item(i + 1).SubItems(2).Text - avgz)
GL.Vertex3(stl_table.Items.Item(i + 2).SubItems(0).Text - avgx, stl_table.Items.Item(i + 2).SubItems(1).Text - avgy, stl_table.Items.Item(i + 2).SubItems(2).Text - avgz)
GL.Vertex3(stl_table.Items.Item(i + 3).SubItems(0).Text - avgx, stl_table.Items.Item(i + 3).SubItems(1).Text - avgy, stl_table.Items.Item(i + 3).SubItems(2).Text - avgz)
i = i + 4
Loop
GL.End()
End If
This second function basically imports a CAD STL file and draws it as triangles. The normal vectors are simply an input from the CAD file (so they are already computed). This method's lighting works perfectly fine which makes me know my lighting code is correct.
Problem
The problem is that my sphere is not getting light correctly. I know through testing that this is due to my normal vectors.
With the current code, my sphere looks like this:
There is a "spot" of light which makes me think that is simply one of the quadstrips having the normal correct.
Does anybody have any suggestions on setting up the normal vectors correctly inside my function? Also before anybody suggests it, I can't use GLU or GLUT for what I am trying to accomplish, which is why I need the sphere function.