Determining the Angle of a Triangle

[thejoecole]

I'm working on a small app for work to determine what depression angle I need to set a camera for oblique aerial photography.

I'm not strong in math, but my wife is and she showed me a formula using Tangent. I looked in the JB Help and saw an example to use Tangent:

TAN( n )

This function returns the tangent of the angle n. The angle n should be expressed in radians

Usage:

 for t = 1 to 45

   print "The tangent of "; t; " is "; tan(t)

 next t
I understand this OK enough, but the formula I have requires the use of an inverse Tangent. Not sure how to do this with code.
Also, my desired output will be in degrees and as I understand the example above, the output is in radians and I'll have to convert to degrees.

Does anyone have experience with this?

Thanks,
Joe

[B+]

pi = acs(-1) 'quick way for pi

radianAngle * 180/pi = degreeAngle


It is handy to make some coversion numbers GLOBAL:
global PI, DEG, RAD
PI = acs(-1)
DEG = 180 / PI
RAD = PI / 180


Put the GLOBAL definitions at the top of your program, then you can use these anywhere in a program.

To convert a radian angle to a degree angle multiply by DEG.

To convert a degree angle to radian angle multiply by RAD.



Now another name for Inverse Tangent is Arc Tangent.

It is the angle in radians whose Tangent is some ratio usually a y difference in height divded by an x difference in horizontal measure, usually and atan2( y difference, x difference) will usually get you that.

The tangent is the side opposite the angle in question (of a right triangle = one angle is 90 degrees) divided by the side adjacent to the angle (connects to the angle.) Tangent is ratio of the two side lengths = y/x, arc tangent is the angle that produces that ratio.

[thejoecole]

Thanks B+

I'll give this a whirl and see if I can put together something useful.

[bluatigro]

maybe you can use this :


function v3d.dot( x1 , y1 , z1 , x2 , y2 , z2 )
 v3d.dot = x1 * x2 + y1 * y2 + z1 * z2
end function

function v3d.angle( x1 , y1 , z1 , x2 , y2 , z2 )
 dot = v3d.dot( x1 , y1 , z1 , z2 , y2 , x2 )
 l1 = v3d.lenght( x1 , y1 , z1 )
 l2 = v3d.lenght( x2 , y2 , z2 )
 v3d.angle = acs( dot / ( l1 * l2 ) )
end function

function v3d.lenght( x , y , z )
 v3d.lenght = sqr( x * x + y * y + z * z )
end function



[tsh73]

Have a look at this.
It uses built-in ATN.
(it will fail if dy = 0 , by using atan2 you avoid that)
nomainwin
open "click somewhere" for graphics_nsb_nf as #gr
#gr "trapclose [quit]"
#gr "down"

#gr "home; posxy cx cy"
#gr "circle 10"
#gr "when mouseMove [move]"
#gr "when leftButtonUp [mUp]"

lastX=cx+1:lastY=0
pi=acs(-1)
'notice pi
wait

[move]
#gr "color white"
#gr "home; goto ";lastX;" ";lastY
lastX=MouseX
lastY=MouseY
#gr "color black"
#gr "home; goto ";lastX;" ";lastY
wait

[mUp]

lastX=MouseX
lastY=MouseY
dy=lastY-cy
dx=lastX-cx
#gr "color red"
#gr "home"
#gr "\dy=";dy;"   "
#gr "\dx=";dx;"   "
'#gr "\ATN(dy/dx)=";using("####.##", atn(dy/dx));"   "    'rad
#gr "\ATN(dy/dx)=";using("####.##", atn(dy/dx)*180/pi);"   "  'degrees
#gr "home; goto ";lastX;" ";lastY



wait
[quit]
   close #gr
end


[B+]

Hi Joe,

How are you coming along? bluatigro has given code for 3D calculations but you need a system origin for those x, y, z.

Ha! well I guess you need that for 2D too.

tsh73 has a calculator but instead of key presses you can draw the angle in question with mouse click.



OK I just looked up a diagram of what you are trying and tangent of angle in question is x/y ratio as I have labeled diagram:


So atan2(x, y) should give you the angle in radians  A * 180 / pi is angle in degrees.

x and y are positive number lengths.  x is the side opposite angle in question, y is side adjacent to angle in question tan = opposite/adjacent. 

It looks as if for "oblique aerial photographs", we are talking about the angle at the other end of a right triangle for the camera.
We had been giving you angles from the ground to the camera.


A picture is worth a 1000 replies!

[B+]

I have modified tsh73 code for Joe's angle question.

See if this looks right now?

nomainwin
open "click below circle 4 angle" for graphics_nsb_nf as #gr
#gr "trapclose [quit]"
#gr "down"

#gr "home; posxy cx cy"
#gr "circle 10"
#gr "when mouseMove [move]"
#gr "when leftButtonUp [mUp]"

lastX=cx+1:lastY=0
pi=acs(-1)
'notice pi
wait

[move]
#gr "color white"
#gr "home; goto ";lastX;" ";lastY
lastX=MouseX
lastY=MouseY
#gr "color black"
#gr "home; goto ";lastX;" ";lastY
wait

[mUp]

lastX=MouseX
lastY=MouseY
dy=lastY-cy
dx=abs(lastX-cx)
#gr "place 0 50"
#gr "color red"
'#gr "home"
#gr "\height = ";dy;"   "
#gr "\ground to plumb = ";dx;"   "
'#gr "\ATN(dy/dx)=";using("####.##", atn(dy/dx));"   "    'rad
#gr "\ATN(ground to plumb / height) = ";using("####.##", atn(dx/dy)*180/pi);"   "  'degrees
#gr "home; goto ";lastX;" ";lastY



wait
[quit]
   close #gr
end


You should now get the camera angle to target shot on ground.

Camera angle in degrees = atan2( distance target to plumb on ground, height of camera ) * 180 / pi

[thejoecole]

Thanks for all the help. I will definitely share the final product.