Math's Trig Versus Basic's Trig Functions

[bplus]

Oh look it's almost that time of the month!

Code: (Select All)

_Title "Halloween Time" 'B+ 2019-10-22
' 2019-10-23 attempt to change transparency gradually to loose blinking

Const m = 350
Screen _NewImage(720, 720, 32)
_ScreenMove 500, 10

Dim Shared sprt(15, 15)
For y = 0 To 15
    For x = 0 To 15
        Read sprt(x, y)
    Next
Next

Dim Shared sprt2(15, 15)
For y = 0 To 15
    For x = 0 To 15
        Read sprt2(x, y)
    Next
Next
Dim Shared bx, by, bf
dt = 1
Do
    Cls

    'angles
    hour% = Int(t# / 3600)
    If hour% > 12 Then showHr# = t# / 3600 - 12 Else showHr# = t# / 3600
    min# = t# / 60 - hour% * 60
    sec# = t# - hour% * 3600 - Int(min#) * 60

    'face
    For r = 340 To 0 Step -1
        If r < 150 Then
            c~& = _RGB32(200 - 50 * r / 100, 150 - 100 * r / 100, 0)
        Else
            c~& = _RGB32(200 - 50 * r / 100, 150 - 100 * r / 100, 40 - r / 340)
        End If
        fcirc m, m, r, c~&
    Next
    For i = 0 To 59
        If i Mod 5 = 0 Then r = 2 Else r = 1
        Circle (350 + 330 * Cos(i * _Pi(2 / 60)), 350 + 330 * Sin(i * _Pi(2 / 60))), r
    Next
    'some triangles
    t = t + dt
    If t > 180 Then dt = -dt: t = 180
    If t < 1 Then dt = -dt: t = 1
    ry~& = _RGBA32(255, 255, 140, t)
    ftri 290, 335, 305, 365, 335, 350, ry~&
    ftri 410, 335, 395, 365, 365, 350, ry~&
    ftri 330, 380, 350, 360, 370, 380, ry~&
    ftri 290, 420, 350, 400, 350, 410, ry~&
    ftri 410, 420, 350, 400, 350, 410, ry~&
    fcirc m, m, 150, ry~& 'more orange glow

    'arms and legs
    x1 = 210 * Cos(showHr# * _Pi(2 / 12) - _Pi / 2)
    y1 = 210 * Sin(showHr# * _Pi(2 / 12) - _Pi / 2)
    x2 = 260 * Cos(min# * _Pi(2 / 60) - _Pi / 2)
    y2 = 260 * Sin(min# * _Pi(2 / 60) - _Pi / 2)
    Line (m, m)-Step(x1, y1), _RGB32(255, 255, 255, 50)
    Line (m, m)-Step(x2, y2), _RGB32(255, 255, 255, 50)
    drawSpinner m + x1, m + y1, .5, _Atan2(y1, x1), &HFF331800
    drawSpinner m + x2, m + y2, .3, _Atan2(y2, x2), &HFF221100

    'seconds fly by...
    bx = 350 + 290 * Cos(sec# * _Pi(2 / 60) - _Pi / 2)
    by = 350 + 290 * Sin(sec# * _Pi(2 / 60) - _Pi / 2)
    drawb

    _Display
    _Limit 5
    t# = Timer
Loop Until _KeyDown(27)

Data 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
Data 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
Data 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
Data 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
Data 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
Data 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
Data 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
Data 0,0,1,1,0,0,0,0,0,0,0,1,1,0,0,0
Data 1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0
Data 0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0
Data 0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0
Data 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
Data 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
Data 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
Data 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
Data 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0

Data 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
Data 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
Data 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
Data 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
Data 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
Data 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
Data 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
Data 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
Data 0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0
Data 0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0
Data 0,0,0,0,1,0,1,1,1,0,0,1,0,0,0,0
Data 0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0
Data 0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0
Data 0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0
Data 0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0
Data 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0

Sub drawb
    bf = (bf + 1) Mod 5
    sz = 3
    If bf = 0 Then
        For y = 0 To 15
            For x = 0 To 15
                If sprt2(x, y) Then Line (x * sz + bx - 7.5 * sz, .5 * y * sz + by - 7.5 * sz)-Step(sz, sz), _RGB32(0, 0, 0), BF
            Next
        Next
    Else
        For y = 0 To 15
            For x = 0 To 15
                If sprt(x, y) Then Line (x * sz + bx - 7.5 * sz, y * sz + by - 7.5 * sz)-Step(sz, sz), _RGB32(0, 0, 0), BF
            Next
        Next
    End If
End Sub

Sub drawSpinner (x As Integer, y As Integer, scale As Single, heading As Single, c As _Unsigned Long)
    Dim x1, x2, x3, x4, y1, y2, y3, y4, r, a, a1, a2, lg, d, rd, red, blue, green
    Static switch As Integer
    switch = switch + 2
    switch = switch Mod 16 + 1
    red = _Red32(c): green = _Green32(c): blue = _Blue32(c)
    r = 10 * scale
    x1 = x + r * Cos(heading): y1 = y + r * Sin(heading)
    r = 2 * r 'lg lengths
    For lg = 1 To 8
        If lg < 5 Then
            a = heading + .9 * lg * _Pi(1 / 5) + (lg = switch) * _Pi(1 / 10)
        Else
            a = heading - .9 * (lg - 4) * _Pi(1 / 5) - (lg = switch) * _Pi(1 / 10)
        End If
        x2 = x1 + r * Cos(a): y2 = y1 + r * Sin(a)
        drawLink x1, y1, 3 * scale, x2, y2, 2 * scale, _RGB32(red + 20, green + 10, blue + 5)
        If lg = 1 Or lg = 2 Or lg = 7 Or lg = 8 Then d = -1 Else d = 1
        a1 = a + d * _Pi(1 / 12)
        x3 = x2 + r * 1.5 * Cos(a1): y3 = y2 + r * 1.5 * Sin(a1)
        drawLink x2, y2, 2 * scale, x3, y3, scale, _RGB32(red + 35, green + 17, blue + 8)
        rd = Int(Rnd * 8) + 1
        a2 = a1 + d * _Pi(1 / 8) * rd / 8
        x4 = x3 + r * 1.5 * Cos(a2): y4 = y3 + r * 1.5 * Sin(a2)
        drawLink x3, y3, scale, x4, y4, scale, _RGB32(red + 50, green + 25, blue + 12)
    Next
    r = r * .5
    fcirc x1, y1, r, _RGB32(red - 20, green - 10, blue - 5)
    x2 = x1 + (r + 1) * Cos(heading - _Pi(1 / 12)): y2 = y1 + (r + 1) * Sin(heading - _Pi(1 / 12))
    fcirc x2, y2, r * .2, &HFF000000
    x2 = x1 + (r + 1) * Cos(heading + _Pi(1 / 12)): y2 = y1 + (r + 1) * Sin(heading + _Pi(1 / 12))
    fcirc x2, y2, r * .2, &HFF000000
    r = r * 2
    x1 = x + r * .9 * Cos(heading + _Pi): y1 = y + r * .9 * Sin(heading + _Pi)
    TiltedEllipseFill 0, x1, y1, r, .7 * r, heading + _Pi, _RGB32(red, green, blue)
End Sub

Sub drawLink (x1, y1, r1, x2, y2, r2, c As _Unsigned Long)
    Dim a, a1, a2, x3, x4, x5, x6, y3, y4, y5, y6
    a = _Atan2(y2 - y1, x2 - x1)
    a1 = a + _Pi(1 / 2)
    a2 = a - _Pi(1 / 2)
    x3 = x1 + r1 * Cos(a1): y3 = y1 + r1 * Sin(a1)
    x4 = x1 + r1 * Cos(a2): y4 = y1 + r1 * Sin(a2)
    x5 = x2 + r2 * Cos(a1): y5 = y2 + r2 * Sin(a1)
    x6 = x2 + r2 * Cos(a2): y6 = y2 + r2 * Sin(a2)
    fquad x3, y3, x4, y4, x5, y5, x6, y6, c
    fcirc x1, y1, r1, c
    fcirc x2, y2, r2, c
End Sub

'need 4 non linear points (not all on 1 line) list them clockwise so x2, y2 is opposite of x4, y4
Sub fquad (x1 As Integer, y1 As Integer, x2 As Integer, y2 As Integer, x3 As Integer, y3 As Integer, x4 As Integer, y4 As Integer, c As _Unsigned Long)
    ftri x1, y1, x2, y2, x4, y4, c
    ftri x3, y3, x4, y4, x1, y1, c
End Sub

Sub ftri (x1, y1, x2, y2, x3, y3, K As _Unsigned Long)
    Dim a&
    a& = _NewImage(1, 1, 32)
    _Dest a&
    PSet (0, 0), K
    _Dest 0
    _MapTriangle _Seamless(0, 0)-(0, 0)-(0, 0), a& To(x1, y1)-(x2, y2)-(x3, y3)
    _FreeImage a& '<<< this is important!
End Sub

Sub fcirc (CX As Integer, CY As Integer, R As Integer, C As _Unsigned Long)
    Dim Radius As Integer, RadiusError As Integer
    Dim X As Integer, Y As Integer
    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

Sub TiltedEllipseFill (destHandle&, x0, y0, a, b, ang, c As _Unsigned Long)
    Dim max As Integer, mx2 As Integer, i As Integer, j As Integer, k As Single, lasti As Single, lastj As Single
    Dim prc As _Unsigned Long, tef As Long
    prc = _RGB32(255, 255, 255, 255)
    If a > b Then max = a + 1 Else max = b + 1
    mx2 = max + max
    tef = _NewImage(mx2, mx2)
    _Dest tef
    _Source tef 'point wont read without this!
    For k = 0 To 6.2832 + .05 Step .1
        i = max + a * Cos(k) * Cos(ang) + b * Sin(k) * Sin(ang)
        j = max + a * Cos(k) * Sin(ang) - b * Sin(k) * Cos(ang)
        If k <> 0 Then
            Line (lasti, lastj)-(i, j), prc
        Else
            PSet (i, j), prc
        End If
        lasti = i: lastj = j
    Next
    Dim xleft(mx2) As Integer, xright(mx2) As Integer, x As Integer, y As Integer
    For y = 0 To mx2
        x = 0
        While Point(x, y) <> prc And x < mx2
            x = x + 1
        Wend
        xleft(y) = x
        While Point(x, y) = prc And x < mx2
            x = x + 1
        Wend
        While Point(x, y) <> prc And x < mx2
            x = x + 1
        Wend
        If x = mx2 Then xright(y) = xleft(y) Else xright(y) = x
    Next
    _Dest destHandle&
    For y = 0 To mx2
        If xleft(y) <> mx2 Then Line (xleft(y) + x0 - max, y + y0 - max)-(xright(y) + x0 - max, y + y0 - max), c, BF
    Next
    _FreeImage tef
End Sub

[Pete]

Well I think I learned something here. Working with the angular formula and mouse coordinates I was able to make a mouse mimic a joystick.

Hold right button to down to move in the direction of the mouse pointer or click left button to just move all at once.

Code: (Select All)

yy = 3: xx = 1
LOCATE yy, xx: PRINT "*";
DO
    _LIMIT 60
    WHILE _MOUSEINPUT: WEND
    mx = _MOUSEX
    my = _MOUSEY
    lb = _MOUSEBUTTON(1)
    rb = _MOUSEBUTTON(2)
    b$ = INKEY$
    IF LEN(b$) THEN
        SELECT CASE b$
            CASE CHR$(0) + "K"
                IF POS(0) > 1 THEN LOCATE , POS(0) - 1
            CASE CHR$(0) + "M"
                IF POS(0) < _WIDTH THEN LOCATE , POS(0) + 1
            CASE CHR$(0) + "H"
                IF CSRLIN > 1 THEN LOCATE CSRLIN - 1, POS(0)
            CASE CHR$(0) + "P"
                IF CSRLIN < _HEIGHT THEN LOCATE CSRLIN + 1, POS(0)
        END SELECT
    END IF
    IF ABS(z1 - TIMER) > .2 THEN
        z1 = TIMER
        IF rb THEN
            ' Angle formula by bplus ------------------------------
            cx = POS(0): cy = CSRLIN
            stepX = ABS(cx - mx): stepY = ABS(cy - my)

            dAng = INT(_R2D(_ATAN2(my - cy, mx - cx)) + .5)
            IF dAng < 0 THEN dAng = dAng + 360

            IF dAng <= 90 THEN
                startA = 0: endA = dAng: ra = dAng
            ELSEIF dAng <= 180 THEN
                startA = dAng: endA = 180: ra = 90 - (dAng - 90)
            ELSEIF dAng <= 270 THEN
                startA = 180: endA = dAng: ra = dAng - 180
            ELSEIF dAng <= 360 THEN
                startA = dAng: endA = 360: ra = 90 - (dAng - 270)
            END IF
            '-------------------------------------------------------
            m_y = 0: m_x = 0
            IF ra <= 90 AND ra >= 50 THEN
                IF my > CSRLIN THEN
                    x$ = "down": m_y = 1: m_x = 0
                ELSE
                    x$ = "up": m_y = -1: m_x = 0
                END IF
            ELSEIF ra < 50 AND ra >= 15 THEN
                IF mx > POS(0) AND my > CSRLIN THEN
                    x$ = "down right": m_y = 1: m_x = 2
                ELSEIF mx < POS(0) AND my > CSRLIN THEN
                    x$ = "down left": m_y = 1: m_x = -2
                ELSEIF mx > POS(0) AND my < CSRLIN THEN
                    x$ = "up right": m_y = -1: m_x = 2
                ELSEIF mx < POS(0) AND my < CSRLIN THEN
                    x$ = "up left": m_y = -1: m_x = -2
                END IF
            ELSEIF ra < 15 AND ra >= 0 THEN
                IF mx > POS(0) THEN
                    x$ = "right": m_y = 0: m_x = 2
                ELSE
                    x$ = "left": m_y = 0: m_x = -2
                END IF
            END IF
            y2 = CSRLIN: x2 = POS(0): LOCATE 1, 1: PRINT x1; " "; x2; "  "; ra; "  "; x$; "              ";: LOCATE y2, x2
            LOCATE yy, xx: PRINT " ";: yy = yy + m_y: xx = xx + m_x: LOCATE yy, xx: PRINT "*";
        END IF
    END IF
    IF lb THEN LOCATE yy, xx: PRINT " ";: LOCATE my, mx: PRINT "*";: yy = my: xx = mx
LOOP

I'm not sure I have the exact degrees worked out, but it seems to be pretty close.

Pete

[bplus]

What is all this?

Code: (Select All)

            IF dAng <= 90 THEN
                startA = 0: endA = dAng: ra = dAng
            ELSEIF dAng <= 180 THEN
                startA = dAng: endA = 180: ra = 90 - (dAng - 90)
            ELSEIF dAng <= 270 THEN
                startA = 180: endA = dAng: ra = dAng - 180
            ELSEIF dAng <= 360 THEN
                startA = dAng: endA = 360: ra = 90 - (dAng - 270)
            END IF
            '-----

Not something I wrote.  Update: I did write that but it was for comparing to a Cartesia graph, angles as positive arcs from x-axis. Sigh

This should be easy to understand:

Code: (Select All)

Screen _NewImage(800, 600, 32)
stepSize = 15: x = _Width / 2: y = _Height / 2 ' got to start somewhere
Do
    Cls
    _PrintString (x - 4, y - 8), "*"
    While _MouseInput: Wend
    mx = _MouseX: my = _MouseY: mb1 = _MouseButton(1): mb2 = _MouseButton(2)
    If mb1 Then ' relocate at mouse
        x = mx: y = my: _Delay .25
    ElseIf mb2 Then  ' move position towards mouse
        angle = _Atan2(my - y, mx - x) ' angle of mouse to current x, y position
        x = x + stepSize * Cos(angle): y = y + stepSize * Sin(angle)
        _Delay .25
    End If
    _Display
    _Limit 30
Loop

And here if you can only move left/right OR up/down like in a maze:

Code: (Select All)

Screen _NewImage(800, 600, 32)
stepSize = 15: x = _Width / 2: y = _Height / 2 ' got to start somewhere
Do
    Cls
    _PrintString (x - 4, y - 8), "*"
    While _MouseInput: Wend
    mx = _MouseX: my = _MouseY: mb1 = _MouseButton(1): mb2 = _MouseButton(2)
    If mb1 Then
        x = mx: y = my: _Delay .25
    ElseIf mb2 Then
        angle = _Atan2(my - y, mx - x) ' angle of mouse to current x, y position
        dx = stepSize * Cos(angle): dy = stepSize * Sin(angle)
        If Abs(dx) >= Abs(dy) Then
            x = x + stepSize * Sgn(dx)
        Else
            y = y + stepSize * Sgn(dy)
        End If
        _Delay .25
    End If
    _Display
    _Limit 30
Loop

[Pete]

The part enclosed in...
'----------------------------------------------------------------------
            cx = POS(0): cy = CSRLIN
            stepX = ABS(cx - mx): stepY = ABS(cy - my)

            dAng = INT(_R2D(_ATAN2(my - cy, mx - cx)) + .5)
            IF dAng < 0 THEN dAng = dAng + 360

            IF dAng <= 90 THEN
                startA = 0: endA = dAng: ra = dAng
            ELSEIF dAng <= 180 THEN
                startA = dAng: endA = 180: ra = 90 - (dAng - 90)
            ELSEIF dAng <= 270 THEN
                startA = 180: endA = dAng: ra = dAng - 180
            ELSEIF dAng <= 360 THEN
                startA = dAng: endA = 360: ra = 90 - (dAng - 270)
            END IF
            '----------------------------------------------------------------------

...is a portion of the code you posted in post #1 of this thread: https://staging.qb64phoenix.com/showthre...31#pid4631

I'll have a look at the other methods, too. I've never had the need to use trig functions in a program prior to this, so this is new and interesting stuff fr me, and I have a use for it now, to boot!

Thanks,

Pete

[bplus]

Crap! Sorry, thanks @Pete for link. I was figuring out the yellow arc to put the angle between 0 and 90 degrees from x axis. That was for comparing to Cartesia method, as you will notice the x and y axis in center of diagram. Raspberries!

Looks like my hope to not add to the confusion was a bust.

[Pete]