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**Drawing Labels**
The code divides the previous and next vectors' components by their lengths to get vectors of length 1. It then averages these unit vectors to get a new vector pointing halfway between the original vectors. To complete the operation, the code divides this vector's components by its length and multiplies by half the desired tick mark width. The result is a vector that the program can use to draw a tick mark at this point.

The

DrawLabels method shown in the following code also uses

GetTickVector; however this code draws text, so it has some special needs. The Graphics object uses transformations to make drawing the data relatively straightforward. In particular, it scales the drawing to flip Y coordinates. That allows world coordinates to start with (0, 0) in the lower left corner and increase upwards as you normally expect on a graph. Unfortunately that means that any text you draw on the Graphics object appears flipped upside down. To fix this, the

DrawLabels method adds another transformation to flip the text right-side up:

```
Private Sub DrawLabels(ByVal gr As Graphics)
If Labels Is Nothing Then Exit Sub
' Save the original transformation.
Dim old_transform As Matrix = gr.Transform
' Flip the transformation vertically.
gr.ScaleTransform(1, -1, MatrixOrder.Prepend)
' Draw the labels.
For i As Integer = 0 To Points.Length - 1
' Get the tick mark direction vector.
Dim tx, ty As Single
GetTickVector(i, tx, ty)
' Lengthen the tick mark vector to
' add extra room for the text.
Dim lbl_size As SizeF = _
gr.MeasureString(Labels(i), LabelFont)
Dim extra_len As Single = 0.375 * _
Sqrt(lbl_size.Width * lbl_size.Width + _
lbl_size.Height * lbl_size.Height)
Dim tick_len As Single = Sqrt(tx * tx + ty * ty)
tx *= (1 + extra_len / tick_len)
ty *= (1 + extra_len / tick_len)
' Draw the label.
Using sf As New StringFormat()
sf.Alignment = StringAlignment.Center
sf.LineAlignment = StringAlignment.Center
Dim x, y As Single
If LabelsOnLeft Then
x = Points(i).X + tx
y = -(Points(i).Y + ty)
Else
x = Points(i).X - tx
y = -(Points(i).Y - ty)
End If
gr.DrawString(Labels(i), _
LabelFont, LabelBrush, x, y, sf)
End Using
Next i
' Restore the original transformation.
gr.Transform = old_transform
End Sub
```

The method starts by saving the Graphics object's current transformation matrix in the variable

old_transform. It then adds a scaling transformation at the beginning of the Graphics object's sequence of transformations to flip all Y coordinates. Now, when the code draws text, this transformation flips the text upside down. Then the original transformations that map world coordinates to device coordinates flip the text right-side up again.

After adding the new transformation, the code loops through the object's data points. For each point, it calls

GetTickVector to find the tick mark vector for the point. It measures the point's label text and uses the size to add some extra length to the vector to make room for the label.

The code then draws the label. To draw on the right side of the data, the code switches the sign of the lengthened tick mark vector. Because the newly added scaling transformation flips Y coordinates, the code also switches the sign of the label's target Y position so it appears in its correct location. The new transformation flips the Y coordinate, inverting the string and placing it at the desired location in world coordinates. Then the Graphics object's original transformations map the new point to its correct final destination in device coordinates, flipping the text back in the process.

Finally

DrawLabels restores the Graphics object's original transformation so other DataSeries objects can correctly map from world to device coordinates when drawing their data.