Math's Trig Versus Basic's Trig Functions

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Option _Explicit

_Title "A Look at Math's Trig and Comparing to Basic's Trig Functions" 'b+ trans from:

' Another look at Trig functions.bas  SmallBASIC 0.12.2 [B+=MGA] 2016-05-01

' inspired by PeterMaria's simple code for Atan2 on Aurels' forum BasicPro

' 2017-09-23 Modified to run again on Android



' Here is another effort in a continuing series to demystify Trig functions:



' Move your mouse around the center point of the screen and see the right triangles

' created with the mouse and a horizontal line from the center.



' See all the parts of the triangle expressed in numbers:

' Angles to the horizontal line, lengths of the sides and hypotenuse of the right

' and the COS, SIN and TAN ratios



'============================== Main

Const Xmax = 800, Ymax = 700

Const Thick = 2

Const Arc_radius = 100

Const Sin_color = _RGB32(0, 0, 255)

Const Cos_color = _RGB32(255, 0, 0)

Const Hyp_color = _RGB32(0, 192, 0)

Const Ang_color = _RGB32(255, 255, 0)

Const White = _RGB32(255, 255, 255)

Dim cx, cy, mx, my, stepX, stepY, hyp, dAng, startA, endA, reportA

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



    'draw horizontal through center of screen

    Line (0, cy)-(Xmax, cy), Cos_color

    ' draw vertical line through center of screen

    Line (cx, 0)-(cx, Ymax), 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, Thick, Cos_color

    ThickLine mx, cy, mx, my, Thick, Sin_color

    ThickLine cx, cy, mx, my, Thick, Hyp_color



    stepX = Abs(cx - mx): stepY = Abs(cy - my)

    hyp = Int(((stepX ^ 2 + stepY ^ 2) ^ .5))



    'to draw angle need to do some math

    'dAng = mouse angle to 0 degrees due East

    ' other Angles:  StartA, EndA and reportA are for the Trig Ratios of triangle

    dAng = Int(_R2D(_Atan2(my - cy, mx - cx)) + .5)

    If dAng < 0 Then dAng = dAng + 360



    If dAng <= 90 Then

        startA = 0: endA = dAng: reportA = dAng

    ElseIf dAng <= 180 Then

        startA = dAng: endA = 180: reportA = 90 - (dAng - 90)

    ElseIf dAng <= 270 Then

        startA = 180: endA = dAng: reportA = dAng - 180

    ElseIf dAng <= 360 Then

        startA = dAng: endA = 360: reportA = 90 - (dAng - 270)

    End If

    Color Ang_color

    ThickArc cx, cy, Arc_radius, startA, endA, Thick



    'report all numbers color coded

    Color Ang_color

    Locate 1, 1: Print " Yellow Angle (in degrees) ~ "; reportA

    Color White

    Locate 3, 1: Print "    Lengths:"

    Color Hyp_color

    Locate 4, 1: Print " green Hyp ~ "; hyp

    Color Sin_color

    Locate 5, 1: Print "  blue Opp ~ "; stepY \ 1

    Color Cos_color

    Locate 6, 1: Print "   red Adj ~ "; stepX \ 1

    Color White

    Locate 8, 1: Print " Ratios: (if no division by 0)"

    If hyp <> 0 Then

        Color Cos_color

        Locate 9, 2: Print "COS = Adj ";

        Color Hyp_color

        Print "/ Hyp ";

        Color White

        Print "~ "; Left$(Str$(stepX / hyp), 6)



        Color Sin_color

        Locate 10, 2: Print "SIN = Opp ";

        Color Hyp_color

        Print "/ Hyp ";

        Color White

        Print "~ "; Left$(Str$(stepY / hyp), 6)

    End If

    If stepX <> 0 Then

        Locate 11, 2: Print "TAN = ";

        Color Sin_color

        Print "Opp ";

        Color Cos_color

        Print "/ Adj ";

        Color White

        Print "~ "; Left$(Str$(stepY / stepX), 6)

    End If



    Color &H55FFFFFF

    Locate 33, 2: Print "QB64 Coding Notes for Basic Graphics without Window( ):"

    Print "   The Screen center Center X, Center Y is "; _Trim$(Str$(cx)); ", "; _Trim$(Str$(cy))

    Print "   Mouse X ="; mx; "   MouseX - Center X = "; _Trim$(Str$(mx - cx))

    Print "   Mouse Y ="; my; "   MouseY = Center Y = "; _Trim$(Str$(my - cx))

    Print "   So Mouse Angle in Radians = _Atan2(my - cy, mx - cx) ="; _Atan2(my - cy, mx - cx)

    Print "   Mouse Angle converted to Degrees rounding to nearest 1 = Int(_R2D(Radian Angle) +.5) = ";

    Print _Trim$(Str$(Int(_R2D(_Atan2(my - cy, mx - cx)) + .5)))

    Print "   BUT! if Degrees < 0 add 360 to see angle in postive numbers from Basic's 0 (due East) = ";

    If Int(_R2D(_Atan2(my - cy, mx - cx)) + .5) < 0 Then

        Print _Trim$(Str$(Int(_R2D(_Atan2(my - cy, mx - cx)) + .5) + 360))

    Else

        Print _Trim$(Str$(Int(_R2D(_Atan2(my - cy, mx - cx)) + .5)))

    End If

    Print

    Print "  Move your mouse clockwise starting at 0 due East to see Basics Angle in Degrees increase."

    _Display

    _Limit 60

Wend



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