"Ancient Programmer has new question -- numeric / string sub

[2ndtrickop]

First off, thanks to  Rod, B+, and tsh for getting me started a few months ago; my routing-model  project is firming up nicely.

Now I have a question on converting the slope of a line (representing one or more legs(segments) of a trip into eight, or possibly sixteen. directions on a compass.


The first algorimtm  tried below converts the slope (negative for eastward movements and positive for westbound) into a direction expressed as a string variable; this can then be compared to the direction from the original point of origin or destination …..


as formulated below (where Jslp = the slope of the leg/segment and Jdir$ = the direction expressed as a string. 




if ((Jslp<1) and (Jslp>.875)) then (Jdir$="S")

if ((Jslp<.875) and (Jslp>.625)) then (Jdir$="SW")

if ((Jslp<.625) and (Jslp>.375)) then (Jdir$="W")

if ((Jslp<.375) and (Jslp>.125)) then (Jdir$="NW")

if ((Jslp<.125) and (Jslp>-.125)) then (Jdir$="N")

if ((Jslp<-.125) and (Jslp>-.375)) then (Jdir$="NE")

if ((Jslp<-.375) and (Jslp>-.625)) then (Jdir$="E")

if ((Jslp<-.625) and (Jslp>-.875)) then (Jdir$="SE")

if ((Jslp<-.875) and (Jslp>-1)) then (Jdir$="S") 

I'm trying to avoid eight (let alone sixteen) separate branching statements in this manner; Thanks, as before!

[B+]

What if you were given a formula to find the angle one point is to another?

The input would be the (x1, y1) coordinate of one place and the (x2, y2) coordinate of the 2nd.

The output would be the exact measure in degrees 0 to 360 in degrees or 0 to 2*pi in radians. PLUS you can have the same data return the distance as bonus information!

[2ndtrickop]

Thanks! --- that should work well as I currently use a 360-degree field for departures from points not used enough to justify a static table of mileages.

A couple of years ago, using the same hang-bells-and-whistles-until-it-overloads system, I came up with a program to simulate the actions of a rail dispatcher on single track.


It helps an aging introvert get through a dull winter.

[B+]

OK not a formula, nor even a function, here is a sub (angleAndDistance) that returns both angle and distance given the x, y coordinates of two points on a map. The main code is testing all the major compass directions for accuracy:

'atan2 and distance.txt B+ 2019-01-07

'the subs need the follwing global constants
global pi, d2r, r2d
pi = acs(-1)
d2r = pi/180 'convert degree angle units to radians
r2d = 180/pi 'convert radian angle units to degrees

'
'                    N
'                NW  |  NE
'                  \   /
'              W -       - E
'                  /   \
'                SW  |  SE
'                    S

'test standard compass directions with these simple map coordinates
ox = 0: oy = 0     'Origin
Nx = 0: Ny = -1    'North of Origin
NEx = 1: NEy = -1  'NE
Ex = 1: Ey = 0     'East of Origin
SEx = 1: SEy = 1   'SE
Sx = 0: Sy = 1     'South of Origin
SWx = -1: SWy = 1  'SW
Wx = -1: Wy = 0    'West of Origin
NWx = -1: NWy = -1 'NW

'going around the world
print "Test North of origin:"
call angleAndDistance ox, oy, Nx, Ny, ang, dist
print ang;" degrees", dist;" distance units"
print
print "Test North-East of origin:"
call angleAndDistance ox, oy, NEx, NEy, ang, dist
print ang;" degrees", dist;" distance units"
print
print "Test East of origin:"
call angleAndDistance ox, oy, Ex, Ey, ang, dist
print ang;" degrees", dist;" distance units"
print
print "Test South-East of origin:"
call angleAndDistance ox, oy, SEx, SEy, ang, dist
print ang;" degrees", dist;" distance units"
print
print "Test South of origin:"
call angleAndDistance ox, oy, Sx, Sy, ang, dist
print ang;" degrees", dist;" distance units"
print
print "Test South-West of origin:"
call angleAndDistance ox, oy, SWx, SWy, ang, dist
print ang;" degrees", dist;" distance units"
print
print "Test West of origin:"
call angleAndDistance ox, oy, Wx, Wy, ang, dist
print ang;" degrees", dist;" distance units"
print
print "Test North-West of origin:"
call angleAndDistance ox, oy, NWx, NWy, ang, dist
print ang;" degrees", dist;" distance units"

'this sub needs Atan2(y, x) Function and r2d gobal constant to convert radians to degrees
sub angleAndDistance x1, y1, x2, y2, byref angle, byref distance
   angle = r2d * Atan2(y2 - y1, x2 - x1)
   if angle < 0 then angle = angle + 360
   distance = sqr((x2 - x1)^2 + (y2 - y1)^2)
end sub

' this sub needs global constants pi and d2r for converting degrees to radians
Function Atan2(y, x)
   'Atan2 is a function which determines the angle between points
   'x1, y1 and x2, y2. The angle returned is in radians
   'The angle returned is always in the range of
   '-PI to PI radians (-180 to 180 degrees)
   '==============================================================
   'NOTE the position of Y and X arguments
   'This keeps Atan2 function same as other language versions
   '==============================================================
  If x = 0 Then
      If y < 0 Then
           Atan2 = -1.5707963267948967
       Else
           Atan2 = 1.5707963267948967
       End If
  Else
      chk = atn(y/x)
      If x < 0 Then
          If y < 0 Then
               chk = chk - 3.1415926535897932
           Else
               chk = chk + 3.1415926535897932
           End If
      End If
       Atan2 = chk
  End If
  'thanks Andy Amaya

  'make the angle 0 degrees (or radians) due North to match maps and compass readings
  Atan2 = Atan2 - 270 * d2r

  'normalize angle between 0 and 2*pi
  if Atan2 < 0 then Atan2 = Atan2 + 2 * pi
End Function


"It helps an aging introvert get through a dull winter."

Yeah, same here!

[B+]

Dang! I just realized, maps probably have y, vertical values, increase from bottom to top, not top to bottom.

Well, this could be fixed for such maps...

[Rod]

Vector maths? point x,y point x1,y1 deltaX, deltaY, distance sqr(abs(dx^2+dy^2))
A practical example of the problem would save a lot of guessing.

[B+]

OK fixed the sub for y values increasing going up on map, just flip y values from + to - and vice versa!

Here is 10 random cities with their angle and distance calculated from the center (origin) of a map running 500 units East and 500 units West, 300 Units North and 300 units South.

'city map.txt for JB v2.0 B+ 2019-01-08

global pi, d2r, r2d, Directions$
pi = acs(-1)
d2r = pi/180 'convert degree angle units to radians
r2d = 180/pi 'convert radian angle units to degrees
Directions$ = "N NE E SE S SW W NW"

randomize 12 'get same random results

nCities = 10
xmax = 500
xmin = -500
ymax = 300
ymin = -300
centerx = 0
centery = 0

dim cityx(nCities), cityy(nCities)
Print "From the map center (0, 0):"
print "city X", "city Y", "angle", "distance", "~ direction"
for i = 1 to nCities
   cityx(i) = rand(xmin, xmax)
   cityy(i) = rand(ymin, ymax)
   call angleAndDistance 0, 0, cityx(i), cityy(i), a, d
   d$ = Direction$(a)
   print cityx(i), cityy(i), a, d, d$
next

function Direction$(degreeAngle)
   for i = 1 to 8
       if i = 1 then
           if degreeAngle < 27.5 or degreeAngle >= 315 + 27.5 then Direction$ = word$(Directions$, i) : exit function
       else
           if degreeAngle < 45 * (i - 1) + 27.5 then Direction$ = word$(Directions$, i) : exit function
       end if
   next
end function

'this sub needs Atan2(y, x) Function and r2d gobal constant to convert radians to degrees
sub angleAndDistance x1, y1, x2, y2, byref angle, byref distance
   angle = r2d * Atan2(y2 - y1, x2 - x1)
   if angle < 0 then angle = angle + 360
   if angle >= 360 then angle = angle - 360
   distance = sqr((x2 - x1)^2 + (y2 - y1)^2)
end sub

' this sub needs global constants pi and d2r for converting degrees to radians
Function Atan2(y, x)
   'Atan2 is a function which determines the angle between points
   'x1, y1 and x2, y2. The angle returned is in radians
   'The angle returned is always in the range of
   '-PI to PI radians (-180 to 180 degrees)
   '==============================================================
   'NOTE the position of Y and X arguments
   'This keeps Atan2 function same as other language versions
   '==============================================================

   'OK to reverse direction on y to fix increasing y values going from bottom to top of a map
   y = -1 * y

  If x = 0 Then
      If y < 0 Then
           Atan2 = -1.5707963267948967
       Else
           Atan2 = 1.5707963267948967
       End If
  Else
      chk = atn(y/x)
      If x < 0 Then
          If y < 0 Then
               chk = chk - 3.1415926535897932
           Else
               chk = chk + 3.1415926535897932
           End If
      End If
       Atan2 = chk
  End If
  'thanks Andy Amaya

  'make the angle 0 degrees (or radians) due North to match maps and compass readings
  Atan2 = Atan2 - 270 * d2r

  'normalize angle between 0 and 2*pi
  if Atan2 < 0 then Atan2 = Atan2 + 2 * pi
End Function

function rand(lo, hi)
   rand = int((hi - lo + 1) * rnd(0)) + lo
end function


output:
From the map center (0, 0):
city X        city Y        angle         distance      ~ direction
-54           -122          203.875281    133.416641    S
-426          -65           261.324598    430.930389    W
108           182           30.6851731    211.631756    NE
153           166           42.6663536    225.754291    NE
-242          97            291.842218    260.716321    W
-469          -292          238.093554    552.471719    SW
187           166           48.4045183    250.049995    NE
358           42            83.3087356    360.455268    E
-193          -42           257.722902    197.517088    W
-268          -208          232.184267    339.246223    SW


[2ndtrickop]

Thanks again, gentlemen ....... we'll have some fun tinkering with this.

[bluatigro]

somthing like this can be useful to

for i = 0 to 360 step 10
 print compas$( i )
next i
end
function compas$( deg )
 q$ = "N NNW NW WNW W WZW ZW ZZW Z ZZE ZE EZE E ENE NE NNE N"
 d = int( deg * 16 / 360 + 1.5 )
 compas$ = word$( q$ , d )
end function