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+---- Forum: bplus (https://staging.qb64phoenix.com/forumdisplay.php?fid=36)
+---- Thread: Math's Trig Versus Basic's Trig Functions (/showthread.php?tid=700)
RE: Math's Trig Versus Basic's Trig Functions - bplus - 10-07-2022
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 SubRE: Math's Trig Versus Basic's Trig Functions - Pete - 10-08-2022
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
LOOPI'm not sure I have the exact degrees worked out, but it seems to be pretty close.
Pete
RE: Math's Trig Versus Basic's Trig Functions - bplus - 10-08-2022
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
LoopAnd 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
LoopRE: Math's Trig Versus Basic's Trig Functions - Pete - 10-08-2022
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/showthread.php?tid=700&pid=4631#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
RE: Math's Trig Versus Basic's Trig Functions - bplus - 10-08-2022
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.
RE: Math's Trig Versus Basic's Trig Functions - Pete - 10-08-2022
