As if Trig is not confusing enough, the confusion is made far worse because in the Basic screen Y increases going down screen whereas in math graphing, you learned Y increases going up.
To make matters still more confusing, there are 2 unit measures for angles, Degrees and Radians.
Degrees go full circle from 0 to 360 in nice easy to understand way with integers giving a pretty accurate picture of the angle.
Radians go full circle from 0 to 2 * _Pi and with not so easy to picture angle measures unless you express them in fractions of 2*_Pi eg _Pi is 180 Degrees half a circle = 2*Pi / 2 which is just _Pi, _Pi / 2 = 90 one quarter of a circle 2*_PI / 4 same as _PI / 2.
120 Degrees is 1/3 of circle same as 2*_Pi / 3
60 Degrees is 1/6 of circle same as 2*_PI /6 = _Pi / 3
30 Degrees is 1/12 of circle same as 2 *_Pi / 12 = _PI / 6
Anyway here is maybe a Rosetta Stone for Math's Trig Comparing to Basic's Trig with pictures to show WTH? is what!
I sure hope this helps and does not add to the confusion.
To make matters still more confusing, there are 2 unit measures for angles, Degrees and Radians.
Degrees go full circle from 0 to 360 in nice easy to understand way with integers giving a pretty accurate picture of the angle.
Radians go full circle from 0 to 2 * _Pi and with not so easy to picture angle measures unless you express them in fractions of 2*_Pi eg _Pi is 180 Degrees half a circle = 2*Pi / 2 which is just _Pi, _Pi / 2 = 90 one quarter of a circle 2*_PI / 4 same as _PI / 2.
120 Degrees is 1/3 of circle same as 2*_Pi / 3
60 Degrees is 1/6 of circle same as 2*_PI /6 = _Pi / 3
30 Degrees is 1/12 of circle same as 2 *_Pi / 12 = _PI / 6
Anyway here is maybe a Rosetta Stone for Math's Trig Comparing to Basic's Trig with pictures to show WTH? is what!
Code: (Select All)
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 SubI sure hope this helps and does not add to the confusion.
b = b + ...
