' 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
' 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
sub drawXit
local c, i
'for mouse clicks
'mx > mxborder=xmax-60
'my < myborder=30
c = rgb(190, 0, 0)
rect xmax - 60, 10 step 51, 21, 0 filled
rect xmax - 60, 10 step 50, 20, c filled
for i = 0 to 2
line xmax - 40 + i, 15, xmax - 33 + i, 25, 15
line xmax - 40 + i, 25, xmax - 33 + i, 15, 15
next i
end
sub ThickArc(xCenter, yCenter, arcRadius, dAngleStart, dAngleEnd, rThick)
local 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 func
rAngleStart = rad(dAngleStart) : rAngleEnd = rad(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
circle xCenter + x1, yCenter + y1, rThick filled
fi
next
end
sub ThickLine(x1, y1, x2, y2, rThick)
local 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
circle x1 + dx * i, y1 + dy * i, rThick filled
next
end if
end
'============================== Main
const thick = 2
const arc_radius = 100
const hor_color = rgb(30,30,30)
const sin_color = rgb(0,0,255)
const cos_color = rgb(255,0,0)
const hyp_color = rgb(0,192,0)
const ang_color = rgb(255,255,0)
const white = rgb(255,255,255)
cx = xmax / 2 : cy = ymax / 2
while 1
if asc(inkey) = 27 then end else pen on 'did user press esc to quit?
cls
'draw eXit sign
drawXit
'draw horizontal through center of screen
line 0, cy, xmax, cy, hor_color
'get mouse
mx = pen(4) : my = pen(5) 'get mouse location
'check if eXit was clicked, if so then end
if mx > xmax - 60 and my < 30 and pen(3) then end
'draw our Color Coded Trig Triangle
color cos_color
ThickLine cx, cy, mx, cy, thick
color sin_color
ThickLine mx, cy, mx, my, thick
color hyp_color
ThickLine cx, cy, mx, my, thick
stepx = abs(cx - mx) : stepy = abs(cy - my)
hyp = ( (stepx ^ 2 + stepy ^ 2) ^.5 )\1
'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 = ( deg(atan( (my - cy) / (mx - cx) ) )+.5 ) \ 1
if mx < cx then dAng = dAng + 180
if my < cy and mx > cx then dAng = dAng + 360
if dAng <= 90 then
startA = 0 : endA = dAng : reportA = dAng
elif dAng <= 180
startA = dAng : endA = 180 : reportA = 90 - (dAng - 90)
elif dAng <= 270
startA = 180 : endA = dAng : reportA = dAng - 180
elif dAng <= 360
startA = dAng : endA = 360 : reportA = 90 - (dAng - 270)
fi
color ang_color
ThickArc cx, cy, arc_radius, startA, endA, thick
'report all numbers color coded
color ang_color
locate 0, 0 : ? "yellow Angle (degrees) ~ "; reportA
color white
locate 2, 0 : ? "Lengths:"
color Hyp_Color
locate 3, 0 : ? "green Hyp ~ "; hyp
color SIN_Color
locate 4, 0 : ? " blue Opp ~ "; stepy \ 1
color COS_Color
locate 5, 0 : ? " red Adj ~ "; stepx \ 1
color white
locate 7, 0 : ? "Ratios: (if no division by 0)"
if hyp <> 0 then
color COS_Color
locate 8, 0 : ? "COS = Adj ";
color Hyp_Color
? "/ Hyp ";
color white
? "~ "; left(str(stepx / hyp), 6)
color SIN_Color
locate 9, 0 : ? "SIN = Opp ";
color Hyp_Color
? "/ Hyp ";
color white
? "~ "; left(str(stepy / hyp), 6)
fi
if stepx <> 0 then
locate 10, 0 : ? "TAN = ";
color SIN_Color
? "Opp ";
color COS_Color
? "/ Adj ";
color white
? "~ "; left(str(stepy / stepx), 6)
fi
showpage
delay 100
pen off
wend
