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TitleDraw an hypotrochoid (and hypocycloid) in VB .NET
DescriptionThis example shows how to draw an hypotrochoid (and hypocycloid) in VB .NET.
Keywordshypotrochoid, hypocycloid, curve
CategoriesVB.NET, Graphics
The hypotrochoid is a curve drawn by rolling a circle (of radius B) around the inside circumference of another (of radius A). A point attached to the inner circle and distance C from its center draws the curve.

You can draw an hypotrochoid with the following parametric functions:

Private Function X(ByVal t As Single) As Single
    Return (m_A - m_B) * Cos(t) + m_C * Cos(t * (m_A - m_B) _
        / m_B)
End Function

Private Function Y(ByVal t As Single) As Single
    Return (m_A - m_B) * Sin(t) - m_C * Sin(t * (m_A - m_B) _
        / m_B)
End Function
Here the variable t ranges from 0 to m_B / GCD(m_A, m_B) * 2 * Pi. The program uses the following code to draw the complete curve when the form needs to be refreshed.
Private Sub DrawCurve(ByVal gr As Graphics, ByVal xmin As _
    Integer, ByVal ymin As Integer, ByVal xmax As Integer, _
    ByVal ymax As Integer)
    If Not m_FormLoaded Then Exit Sub

    ' Get A, B, C, and num_segments.
    m_A = Integer.Parse(txtA.Text)
    m_B = Integer.Parse(txtB.Text)
    m_C = Single.Parse(txtC.Text)
    Dim num_segments = Integer.Parse(txtNumSegs.Text)

    ' Scale and translate to center the drawing.
    Dim r As Single = m_A - m_B + m_C
    MapGraphicsWindow(gr, -r, -r, r, r, _
        xmin, ymin, xmax, ymax)

    ' Clear the canvas.

    ' Draw the geometry for debugging.
    If chkShowGeometry.Checked Then
        Dim red_pen As New Pen(Color.Red, 0)
        gr.DrawEllipse(red_pen, -m_A, -m_A, 2 * m_A, 2 * _
        gr.DrawEllipse(red_pen, m_A - 2 * m_B, -m_B, 2 * _
            m_B, 2 * m_B)
        gr.DrawLine(red_pen, m_A - m_B, 0, m_A - m_B + m_C, _
    End If

    Dim num_revs As Integer = m_B / GCD(m_A, m_B)
    Dim dt As Single = num_revs * 2 * PI / num_segments
    Dim t As Single = 0
    Dim x1, y1, x2, y2 As Single
    Dim i As Integer
    Dim thin_pen As New Pen(Color.Blue, 0)

    ' Draw the curve.
    x2 = X(0)
    y2 = Y(0)
    For i = 1 To num_segments
        t += dt
        x1 = x2
        y1 = y2
        x2 = X(t)
        y2 = Y(t)
        gr.DrawLine(thin_pen, x1, y1, x2, y2)
    Next i

    x1 = X(0)
    y1 = Y(0)
    gr.DrawLine(thin_pen, x1, y1, x2, y2)

End Sub

' Return the greatest common divisor of A and B.
Private Function GCD(ByVal A As Integer, ByVal B As _
    Integer) As Integer
    Dim R As Integer = A Mod B
    If R = 0 Then
        Return B
        Return GCD(B, R)
    End If
End Function
Special cases of the hypotrochoid include:

  • The hypocycloid where C = B.
  • A rose where:
        A = 2 * N * C / (N + 1)
        B = (N - 1) * C / (N + 1)
    for integer values of N.

For more information on graphics programming in Visual Basic (VB 6), see my book Ready-to-Run Visual Basic Graphics Programming.

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