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Wiki  >  TechNet Articles  >  Small Basic: How to Use Trigonometric Functions

Small Basic: How to Use Trigonometric Functions

Small Basic: How to Use Trigonometric Functions

Let's imagine to draw arc.
Assume center of the arc as x = 200, y = 300, start angle a1 = -30 and end angle = -60.
In mathematics, y axis goes up.  But in Small Basic GraphicsWindow, y axis goes down.  So sign of angle becomes opposite.



If you don't use trigonometric function, so use only 0, 30, 45, 60, 90, ...[degree].  Between these angles you can calculate height s from width c of the triangle while three edges of triangle r, c, s such as picture below have relationship r2 = s2 + c2 .  

But for any angle, use trigonometric function (sin, cos).


Be careful that trigonometric function needs [radian] but [degree] for Small Basic language.

You can use Math.GetRadians(degree) to convert from [degree] to [radian].

Following sample code shows how not to use or how to use trigonometric functions (sin, cos) for drawing arc.

gw = GraphicsWindow.Width
gh = GraphicsWindow.Height
DrawGrid()
x = 200
y = 300
r = 200
DrawArcwoTrigo()
Program.Delay(3000)
GraphicsWindow.Clear()
DrawGrid()
a1 = -30
a2 = -60
DrawArcwTrigo()
Sub DrawArcwoTrigo  ' draw arc without trigonometric functions
  GraphicsWindow.Title = "Arc without Trigonometric Functions"
  c1 = r * Math.SquareRoot(3) / 2   ' a1 = -30
  c2 = r / 2                        ' a2 = -60
  r2 = Math.Power(r, 2)
  For c = c1 To c2 Step -1
    s = Math.SquareRoot(r2 - Math.Power(c, 2))
    x2 = x + c
    y2 = y - s
    If c = c1 Then
      GraphicsWindow.PenColor = "Gray"
      GraphicsWindow.DrawLine(x, y, x2, y2)
    Else
      GraphicsWindow.PenColor = "Black"
      GraphicsWindow.DrawLine(x1, y1, x2, y2)
    EndIf
    If c - 1 < c2 Then
      GraphicsWindow.PenColor = "Gray"
      GraphicsWindow.DrawLine(x, y, x2, y2)
    EndIf
    x1 = x2
    y1 = y2
  EndFor
EndSub
Sub DrawArcwTrigo  ' draw arc with trigonometric functions
  GraphicsWindow.Title = "Arc with Trigonometric Functions"
  For a = a1 To a2 Step -0.3
    x2 = x + r * Math.Cos(Math.GetRadians(a))
    y2 = y + r * Math.Sin(Math.GetRadians(a))
    If a = a1 Then
      GraphicsWindow.PenColor = "Gray"
      GraphicsWindow.DrawLine(x, y, x2, y2)
    Else
      GraphicsWindow.PenColor = "Black"
      GraphicsWindow.DrawLine(x1, y1, x2, y2)
    EndIf
    If a - 0.3 < a2 Then
      GraphicsWindow.PenColor = "Gray"
      GraphicsWindow.DrawLine(x, y, x2, y2)
    EndIf
    x1 = x2
    y1 = y2
  EndFor
EndSub
Sub DrawGrid
  GraphicsWindow.PenColor = "MediumSeaGreen"
  GraphicsWindow.BrushColor = "MediumSeaGreen"
  For _x = 0 To gw Step 50
    GraphicsWindow.DrawLine(_x, 0, _x, gh)
    If gw - 50 < _x Then
      GraphicsWindow.DrawText(_x + 4, 4, "x")
    Else
      GraphicsWindow.DrawText(_x + 4, 4, _x)
    EndIf
  EndFor
  For _y = 0 To gh Step 50
    GraphicsWindow.DrawLine(0, _y, gw, _y)
    If gh - 50 < _y Then
      GraphicsWindow.DrawText(4, _y + 4, "y")
    Else
      GraphicsWindow.DrawText(4, _y + 4, _y)
    EndIf
  EndFor
EndSub
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  • 11 Jun 2013 2:05 AM

    Nonki Takahashi edited Revision 3. Comment: re-uploaded image

  • 5 Jun 2013 9:04 PM

    Nonki Takahashi edited Revision 1. Comment: typo

  • 5 Jun 2013 8:53 PM

    Nonki Takahashi edited Original. Comment: minor change

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