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Small Basic: Coordinate

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This article describes about coordinates in Microsoft Small Basic programming language.

Coordinate

A coordinate (or co-ordinate) is a number represents a position in a line.  With two lines that are called x-axis and y-axis, any position can be described in a 2-D surface as a couple of coordinates such like (10, 20).  In Small Basic, there are two types of coordinates.  One is for Desktop.  Another is for GraphicsWindow.

Desktop Coordinate

The origin of the Desktop coordinate is the left top corner of the desktop.  Properties Mouse.MouseX, Mouse.MouseY, GraphicsWindow.Left, and GraphicsWindow.Top show positions in Desktop coordinates.

GraphicsWindow Coordinate

The origin of the GraphicsWindow coordinate is the left top corner of the graphics window application pain.  GraphicsWindow coordinate is used in many properties and operations in GraphicsWindow and Shapes objects.  Following figure shows Desktop coordinate and GraphicsWindow coordinate.

Coordinate Transformation

Many application programs have their own coordinates.  So coordinate transformation is needed to convert application coordinate such as (x, y) to the graphics window coordinate such as (gx, gy).  In Maths, y-axis goes from bottom to top, but in the graphics window, y-axis goes from top to bottom.  Following figure shows a sample of Maths coordinate.

Program JKM186-0 is a sample program that transform Maths coordinate to GraphicsWindow coordinate with a subroutine Map().

' Maths Coordiante Sample
' Copyright © 2019 Nonki Takahashi. The MIT License.
' Last update 2019-12-29
' Program ID JKM186-0
 
GraphicsWindow.Title = "Maths Coordinate Sample"
Init()
DrawGrid()
GraphicsWindow.PenColor = c2
While "True"
  AddCircle()
  Remove()
  AddParabola()
  Remove()
  AddSin()
  Remove()
  AddCos()
  Remove()
EndWhile
 
Sub AddCos
  For x =  xMin To xMax Step 0.1
    y = Math.Cos(x)
    Map()
    If xMin <  x Then
      n = n  + 1
      shp[n] = Shapes.AddLine(_gx, _gy,  gx, gy)
    EndIf
    _gx = gx
    _gy = gy
  EndFor
  n = n  + 1
  shp[n] = Shapes.AddText("y = cos x")
  Shapes.Move(shp[n], 10,  10)
EndSub
 
Sub AddCircle
  For a =  0 To 360 Step 5
    _a = Math.GetRadians(a)
    x = Math.Cos(_a)
    y = Math.Sin(_a)
    Map()
    If 0 <  a Then
      n = n  + 1
      shp[n] = Shapes.AddLine(_gx, _gy,  gx, gy)
    EndIf
    _gx = gx
    _gy = gy
  EndFor
  n = n  + 1
  shp[n] = Shapes.AddText("x² + y² = 1")
  Shapes.Move(shp[n], 10,  10)
EndSub
 
Sub AddParabola
  For x =  -1.6 To 1.6 Step 0.1
    y = Math.Power(x, 2)
    Map()
    If -1.6  < x Then
      n = n  + 1
      shp[n] = Shapes.AddLine(_gx, _gy,  gx, gy)
    EndIf
    _gx = gx
    _gy = gy
  EndFor
  n = n  + 1
  shp[n] = Shapes.AddText("y = x²")
  Shapes.Move(shp[n], 10,  10)
EndSub
 
Sub AddSin
  For x =  xMin To xMax Step 0.1
    y = Math.Sin(x)
    Map()
    If xMin <  x Then
      n = n  + 1
      shp[n] = Shapes.AddLine(_gx, _gy,  gx, gy)
    EndIf
    _gx = gx
    _gy = gy
  EndFor
  n = n  + 1
  shp[n] = Shapes.AddText("y = sin x")
  Shapes.Move(shp[n], 10,  10)
EndSub
 
Sub DrawGrid
  GraphicsWindow.BrushColor = c2
  GraphicsWindow.FontName = "Arial"
  GraphicsWindow.FontSize = 14
  For x =  xMin To xMax Step 0.1
    Map()
    If x =  0 Then
      pc = c2
      GraphicsWindow.DrawText(gx, gh /  2, Math.Round(x))
    ElseIf Math.Remainder(x, 1) = 0 Then
      pc = c1
      If x <> 3 Then
        GraphicsWindow.DrawText(gx, gh /  2, Math.Round(x))
      EndIf
    Else
      pc = c0
    EndIf
    GraphicsWindow.PenColor = pc
    GraphicsWindow.DrawLine(gx, 0, gx, gh)
  EndFor
  For y =  yMin To yMax Step 0.1
    Map()
    If y =  0 Then
      pc = c2
      GraphicsWindow.DrawText(gw / 2, gy,  Math.Round(y))
    ElseIf Math.Remainder(y, 1) = 0 Then
      pc = c1
      GraphicsWindow.DrawText(gw / 2, gy,  Math.Round(y))
    Else
      pc = c0
    EndIf
    GraphicsWindow.PenColor = pc
    GraphicsWindow.DrawLine(0, gy,  gw, gy)
  EndFor
  GraphicsWindow.PenColor = c2
  GraphicsWindow.DrawLine(gw - 10, gh /  2 - 4, gw,  gh / 2)
  GraphicsWindow.DrawLine(gw - 10, gh /  2 + 4, gw,  gh / 2)
  GraphicsWindow.DrawText(gw - 20, gh /  2, "x")
  GraphicsWindow.DrawLine(gw / 2, 0, gw / 2  - 4, 10)
  GraphicsWindow.DrawLine(gw / 2, 0, gw / 2  + 4, 10)
  GraphicsWindow.DrawText(gw / 2, 10,  "y")
EndSub
 
Sub Init
  c2 = "#FF666666"
  c1 = "#660099CC"
  c0 = "#330099CC"
  gw = 640
  gh = 480
  GraphicsWindow.Width = gw
  GraphicsWindow.Height = gh
  xMin = -3.2
  xMax = 3.2
  yMin = -2.4
  yMax = 2.4
  scale = 100
  gxOffset = gw  / 2
  gyOffset = gh  / 2
EndSub
 
Sub Map
  gx = scale  * x + gxOffset
  gy = -scale * y  + gyOffset 
EndSub
 
Sub Remove
  Program.Delay(3000)
  For i =  1 To n
    Shapes.Remove(shp[i])
  EndFor
  n = 0
EndSub

See Also

  • [[articles:Wiki: Small Basic Portal]]
  • [[articles:Small Basic: GraphicsWindow Basics]]
  • [[articles:Small Basic Getting Started Guide: Chapter 6: Beginning Graphics]]