Help with angles (0/360) - real comparison

[kingkwong]

This is a issue I've had with backstab and other similar triggers before in the past. I just played around with the numbers before until it worked but I didn;t really understand them.

So I have a conditions which are real comparisons.
I check whether it is greater than X_angle but less than Y_angle
What I don't get is when its around the 0 degrees/ 360 degrees.

Say I compared an angle which is less than X+90 and greater than X-90.
If X was in the 300s. Angle 350 would be less than X+90 but angle 10 would not be.

Can someone please explain to me how angles work in WE and if a real comparison is the correct thing to do.

Currently I am doing a homing missile trigger. It checks whether the unit is on the left or right of the missile and will change the angle to face it, taking the shortest turn (I don't want to make the unit have an order with a low turn rate).

 

[Dr Super Good]

You do not compare angles, you compare cosine or sine of angles.

For example the cosine of the angle is greater than 0. This gives you a 180 degree arc centred to the positive side of the x axis.

You get the angle between victim and the source and then subtract it by the facing of the victim. You then push it through cos. You can then compare that cos value if it is less than some cutoff cos value. For example a cutoff cos value of Cos(10 degrees) will give you a range of 10 degrees from the back of the unit.

 

[kingkwong]

You do not compare angles, you compare cosine or sine of angles.

For example the cosine of the angle is greater than 0. This gives you a 180 degree arc centred to the positive side of the x axis.

You get the angle between victim and the source and then subtract it by the facing of the victim. You then push it through cos. You can then compare that cos value if it is less than some cutoff cos value. For example a cutoff cos value of Cos(10 degrees) will give you a range of 10 degrees from the back of the unit.

hidden

• Angle test
  • Events
    • Time - Every 0.10 seconds of game time
  • Conditions
  • Actions
    • Set TempLoc[0] = (Position of Hero 0001 <gen>)
    • Set TempLoc[1] = (Position of Hero 0002 <gen>)
    • If (All Conditions are True) then do (Then Actions) else do (Else Actions)
      • If - Conditions
        • (Cos(((Angle from TempLoc[0] to TempLoc[1]) - (Facing of Hero 0001 <gen>)))) Less than or equal to Cos(90.00)
      • Then - Actions
        • Floating Text - Create floating text that reads (String((Angle from TempLoc[0] to TempLoc[1]))) above Hero 0001 <gen> with Z offset 0.00, using font size 10.00, color (0.00%, 100.00%, 0.00%), and 0.00% transparency
      • Else - Actions
        • Floating Text - Create floating text that reads (String((Angle from TempLoc[0] to TempLoc[1]))) above Hero 0001 <gen> with Z offset 0.00, using font size 10.00, color (100.00%, 0.00%, 0.00%), and 0.00% transparency
    • Floating Text - Change (Last created floating text): Disable permanence
    • Floating Text - Change the lifespan of (Last created floating text) to 0.11 seconds
    • Floating Text - Change the fading age of (Last created floating text) to 0.10 seconds
    • Custom script: call RemoveLocation(udg_TempLoc[0])
    • Custom script: call RemoveLocation(udg_TempLoc[1])

This is what I have but it's not really working. Its been a while since I've had tto use maths so I'm a bit rusty and can't really picture it in my head.

EDIT!! Don't worry, I got it. Thanks heaps. That Cos was really helpful

 

[Wietlol]

I prefer to substract angle X from angle Y and check if the result is both greater than -Z and lower than Z. (Where Z is the maximum angle difference allowed to both sides... for example a Z of 90 will result in half a circle.)
To make this work, the result of X - Y has to be between -180 and 180 for which I use a custom function.

I don't know about efficiency between 3 cosines but both should be pretty high performance solutions.

 

[kingkwong]

I prefer to substract angle X from angle Y and check if the result is both greater than -Z and lower than Z. (Where Z is the maximum angle difference allowed to both sides... for example a Z of 90 will result in half a circle.)
To make this work, the result of X - Y has to be between -180 and 180 for which I use a custom function.

I don't know about efficiency between 3 cosines but both should be pretty high performance solutions.

I used to do that too but the problem I had was that when going towards 360, it shifts from being a big number (360) to a small number (0). Thats why I think the real comparisons might have trouble.

 

[Wietlol]

You didn't read my post.

"has to be between -180 and 180 for which I use a custom function."
360 degree angles don't exist within those bounds.

That's why the read comparisons might have trouble.

 

[kingkwong]

Ahhh ... sorry, my bad. I get what you mean now. What did you mean about the efficiency of three cosines? Does it take a while to calculate?

 

[Wietlol]

It is still a calculation... 1+1 takes some processing time, 1*1 takes some processing time, 1%1 takes a bit more because of how it works, 1^1 takes a bit more than the first 2, etc.
Everything cost some processing time, but how much, I don't really know at this point and cosine may or may not be faster, but the differences are negligible.

 

[Dr Super Good]

The cosine approach is probably faster. It also only needs 1 cosine resolution (not 3).

 

[Bribe]

When using arithmatic with angles, use the Math - Mod function to modulate the result by 360 so you only get values between 0 and 360

 

[Zwiebelchen]

Or just add two more conditions:

if a < 0 then
set a = a + 360
elseif a > 360 then
set a = a - 360
endif

 

[Wietlol]

    function NormalizeAngle takes real angle returns real
        loop
            if angle < 0 then
                set angle = angle + 360
            elseif angle >= 360 then
                set angle = angle - 360
            else
                return angle
            endif
        endloop
        return 0.
    endfunction
    
    function DeNormalizeAngle takes real angle returns real
        loop
            if angle <= -180 then
                set angle = angle + 360
            elseif angle > 180 then
                set angle = angle - 360
            else
                return angle
            endif
        endloop
        return 0.
    endfunction

My custom function

 

[Bribe]

@Zwieb, And if the angle is less than -360 or greater than 720, the check fails. ModuloReal is superior.

@Wietlol: That first function is bulky; I have no idea why you won't simply use ModuloReal instead. The second function is something completely different, though.

 

[Wietlol]

ModuloReal does -180 -> 180 ?

ModuloReal(angle, 360) - 180 would work though.

Wait... does Modulo return negative values out of negative parameters? Cause in that case it would be "ModuloReal(Max(angle, -angle), 360) - 180".

I considered making my function with ModuloReal, but I guess this will do just fine... dunno about efficiency between 'em.

 

[Bribe]

@Wiet, sorry edited my post too late. I got busy and had to take a long break before I cpuld finish what I was writing.

Yes, ModuloReal is always 0 or greater. So you are right as well with your second function you could modulate by 360 and then subtract 180.

 

[Wietlol]

The second function isn't really more interesting than the first.
I didn't use modulo because I didn't think about it at that moment... I could use it, but I don't really care so much about which is faster than the other.

ModuloInteger and ModuloReal can return negative values when used: "call ModuloReal(-450, 360)" for example.
It is a rare occurence but the fact still remains that it will break the maths.

 

[Bribe]

Nope. The function would be useless in that case.

http://jass.wikia.com/wiki/Function_ModuloReal

-450/360 == -1. -1 * 360 == -360. -450 - -360 == -90. -90 + 360 == 270.

 

[Wietlol]

Ah, I misplaced a - and a +.

 

[Zwiebelchen]

@Zwieb, And if the angle is less than -360 or greater than 720, the check fails.

This only happens if you add more than 360 or less than -360 in an arithmetic operation, as none of the trigonometric functions will return an angle larger than 2*pi.

If you normalize every value individually when retrieved, there is no way you can have more than 720 or less than -360.

 

[Bribe]

Or you could avoid hacky and lenghier solutions and just call that function. I hate that every BJ function is red even if it's completely fine.

 

[Wietlol]

Look at my nice style:

(Source: TimerUtils)

 

[Zwiebelchen]

Or you could avoid hacky and lenghier solutions and just call that function. I hate that every BJ function is red even if it's completely fine.

How is that hacky or lenghty?
When do you ever add/substract more than 360 degrees?

And yes, Modulo is a good BJ. But if it's not needed, why add a pointless loop?

 

[Dr Super Good]

Why not just use Cos or Sin which does it all probably faster?

 

[kingkwong]

I've been using the sine and cosine so far and I understand it better.

So can someone tell me if I should be using modulo or the sin/cos? I want to learn the most effective method.

 

[Wietlol]

They all work fine.
As long as the result is good, you can use either.

 

[Dr Super Good]

Most efficient is probably sine/cosine approach because of how JASS works. Specifically there is no native modulo method (instead it is emulated) and the normal complexities of Sine/Cosine get drowned out so much by the JASS overhead that ultimately the time cost is mostly the function call.