orbit demo

for beginners needing a quick demo of using cos and sin to locate a point at an angle in degrees and radius distance away from another point (xOrigin, yOrigin) from sub the located point is (xOut, yOut) last 2 arguments to sub orbit. also this illustrates that 0 Degrees is due east and as the angle is increased the angle goes clockwise from east to south to west to north and finally returning to east at 360 degrees.

Option _Explicit
_Title "orbit demo" 'b+ 2024-05-10

'============================== Main
Const Xmax = 1000, Ymax = 700
Const Thick = 2
Const Arc_Radius = 100
Const Sin_color = _RGB32(0, 0, 255)
Const Cos_color = _RGB32(0, 128, 0)
Const Radius_color = _RGB32(255, 0, 0)
Const Ang_color = _RGB32(255, 255, 0)
Const White = _RGB32(255, 255, 255)
Const Origin_color = _RGB32(255, 128, 0)
Dim cx, cy, mx, my, stepX, stepY, Radius, dAng, xOut, yOut, x, y
cx = Xmax / 2: cy = Ymax / 2
Screen _NewImage(Xmax, Ymax, 32)
_ScreenMove 60, 0
_PrintMode _KeepBackground
_MouseMove cx + 100, cy + 100 ' get ball rolling
While 1
   Cls
   Color White
   Locate 2, 18
   Print "Move your mouse clockwise starting at 0 due East to see Basics Angle in Degrees increase."
   Locate 5, 68
   Print "Orbit ";
   Color Origin_color
   Print "X_Origin, Y_Origin,";
   Color Ang_color
   Print " Degrees,";
   Color Radius_color
   Print " Radius,";
   Color White
   Print " xOut, yOut"
   'draw horizontal through center of screen
   Line (70, cy)-(Xmax - 70, cy), Cos_color
   ' draw vertical line through center of screen
   Line (cx, 70)-(cx, Ymax - 70), Sin_color
   'poll mouse
   While _MouseInput: Wend ' updates all mouse stuff except wheel
   mx = _MouseX: my = _MouseY 'get mouse location

   'draw our Color Coded Trig Triangle
   ThickLine cx, cy, mx, cy, 1, Cos_color
   ThickLine mx, cy, mx, my, 1, Sin_color
   ThickLine cx, cy, mx, my, Thick, Radius_color

   stepX = mx - cx: stepY = my - cy
   Radius = (stepX ^ 2 + stepY ^ 2) ^ .5

   'to draw angle need to do some math
   'dAng = mouse angle to 0 Degrees due East
   dAng = _R2D(_Atan2(my - cy, mx - cx))
   If dAng < 0 Then dAng = dAng + 360

   Color Ang_color
   ThickArc cx, cy, Radius, 0, dAng, Thick

   'report all numbers color coded
   Color Ang_color
   Locate 5, 3: Print "Yellow Angle (in Degrees) ~ "; dAng \ 1
   Color Radius_color
   Locate 7, 7: Print "    Length red Radius ~ "; Radius \ 1
   Color Sin_color
   Locate 9, 7: Print " Length blue Opp side ~ "; Abs(stepY) \ 1
   Color Cos_color
   Locate 8, 7: Print "Length green Adj side ~ "; Abs(stepX) \ 1
   Color White
   Locate 11, 1: Print " Ratios: (if no division by 0)"
   If Radius <> 0 Then
       Color Cos_color
       Locate 12, 8: Print "COS = Adj ";
       Color Radius_color
       Print "/ Radius ";
       Color White
       Print "~ "; Left$(Str$(stepX / Radius), 6) '; Cos(_D2R(dAng))  ' double check

       Color Sin_color
       Locate 13, 8: Print "SIN = Opp ";
       Color Radius_color
       Print "/ Radius ";
       Color White
       Print "~ "; Left$(Str$(stepY / Radius), 6) '; Sin(_D2R(dAng)) ' double check
   End If
   Color White
   orbit cx, cy, dAng, Radius, xOut, yOut ' mouse here
   orbit cx, cy, dAng, Radius + 50, x, y ' set label here
   label x, y, "(xOut, yOut) = (" + _Trim$(Str$(xOut \ 1)) + "," + Str$(yOut \ 1) + ")"
   Color Origin_color
   label cx, cy - 10, "(X_Origin, Y_Origin) = (" + _Trim$(Str$(cx)) + "," + Str$(cy) + ")"
   _Display
   _Limit 60
Wend


'      !!!!!!   featuring the use of this SUB routine   !!!!
Sub orbit (X_Origin, Y_Origin, Degrees, Radius, xOut, yOut) ' all default single  should be ok
   xOut = X_Origin + Radius * Cos(_D2R(Degrees))
   yOut = Y_Origin + Radius * Sin(_D2R(Degrees))
End Sub

Sub label (xc, yc, text$)
   Dim th2, pw2
   th2 = _FontHeight / 2
   pw2 = _PrintWidth(text$) / 2
   _PrintString (xc - pw2 + 1.25, yc - th2 + .5), text$
End Sub

Sub ThickArc (xCenter, yCenter, arcRadius, dAngleStart, dAngleEnd, rThick)
   Dim rAngle, rAngleStart, rAngleEnd, x1, y1, Stepper
   'draws an Arc with center at xCenter, yCenter, Radius from center is arcRadius

   'for SmallBASIC angle 0 Degrees is due East and angle increases clockwise towards South

   'THIS SUB IS SETUP TO DRAW AN ARC IN CLOCKWISE DIRECTION

   'dAngleStart is where to start Angle in Degrees
   ' so make the dAngleStart the first ray clockwise from 0 Degrees that starts angle drawing clockwise

   'dAngleEnd is where the arc ends going clockwise with positive Degrees
   ' so if the arc end goes past 0 Degrees clockwise from dAngleStart
   '  express the end angle as 360 + angle

   'rThick is the Radius of the many,many tiny circles this will draw to make the arc thick
   ' so if rThick = 2 the circles will have a Radius of 2 pixels and arc will be 4 pixels thick
   If arcRadius < 1 Then PSet (xCenter, yCenter): Exit Sub
   rAngleStart = _D2R(dAngleStart): rAngleEnd = _D2R(dAngleEnd)
   If Int(rThick) = 0 Then Stepper = 1 / (arcRadius * _Pi) Else Stepper = rThick / (arcRadius * _Pi / 2)
   For rAngle = rAngleStart To rAngleEnd Step Stepper
       x1 = arcRadius * Cos(rAngle): y1 = arcRadius * Sin(rAngle)
       If Int(rThick) < 1 Then
           PSet (xCenter + x1, yCenter + y1)
       Else
           fcirc xCenter + x1, yCenter + y1, rThick, Ang_color
       End If
   Next
End Sub

Sub ThickLine (x1, y1, x2, y2, rThick, K As _Unsigned Long)
   Dim length, stepx, stepy, dx, dy, i

   'x1,y1 is one endpoint of line
   'x2,y2 is the other endpoint of the line
   'rThick is the Radius of the tiny circles that will be drawn
   '   from one end point to the other to create the thick line
   'Yes, the line will then extend beyond the endpoints with circular ends.

   stepx = x2 - x1
   stepy = y2 - y1
   length = (stepx ^ 2 + stepy ^ 2) ^ .5
   If length Then
       dx = stepx / length: dy = stepy / length
       For i = 0 To length
           fcirc x1 + dx * i, y1 + dy * i, rThick, K
       Next
   End If
End Sub

Sub fcirc (CX As Long, CY As Long, R As Long, C As _Unsigned Long)
   Dim Radius As Long, RadiusError As Long
   Dim X As Long, Y As Long
   Radius = Abs(R): RadiusError = -Radius: X = Radius: Y = 0
   If Radius = 0 Then PSet (CX, CY), C: Exit Sub
   Line (CX - X, CY)-(CX + X, CY), C, BF
   While X > Y
       RadiusError = RadiusError + Y * 2 + 1
       If RadiusError >= 0 Then
           If X <> Y + 1 Then
               Line (CX - Y, CY - X)-(CX + Y, CY - X), C, BF
               Line (CX - Y, CY + X)-(CX + Y, CY + X), C, BF
           End If
           X = X - 1
           RadiusError = RadiusError - X * 2
       End If
       Y = Y + 1
       Line (CX - X, CY - Y)-(CX + X, CY - Y), C, BF
       Line (CX - X, CY + Y)-(CX + X, CY + Y), C, BF
   Wend
End Sub

this sub has some useful drawing routines along with fill circle, fcir(x, y, r, color) there is also thick line and thick arc