# Angle of rotation formula depending on sprite position

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ElyasMachera    102
Hi, I'm new to the gamedev.net and hope to know you guys
I'm just going over game basics to get the hang of it.
I have a 2d spaceship please see attached file.
I was using the one the right initially, but then I was messing with the rotation when I decided to use the one on the left.
To calculate the direction (velocity) vector based on that right sprite position I used this formula,

playerVel.X = Math.Sin(rotAngle) ;
playerVel.Y = -Math.Cos(rotAngle) ;

That worked fine, until I let the sprite's initial position look like that of the left. To calculate the direction I was guessing the formula..until I tried the original formula of finding direction based on angle of rotation. The one that makes sense.

playerVel.X = Math.Cos(rotAngle);
playerVel.Y = Math.Sin(rotAngle) ;

now this makes sense! Cos is used to find the X value and Sin to find the Y value. My question is, how does switching how the sprite's initial direction in a 2d image change the formula to find the new direction vector?
If I knew how to plot this on a graph paper I'd be able to derive the formula instead of guessing..I was never good at trigonometry so can someone please make this clear using some pictures of a graph or something..hopefully?
Thanks

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Postie    1559
It's all based on how you're defining your rotation angle. Your initial orientations differ by 90 degrees, so your definition of the where angle = 0 is differs, which means the formulas are going to differ slightly.

Incidentally, rotating by 90 degrees in 2D can be achieved by swapping the X & Y coordinates, and then negating one of the coordinates. If you look at the difference between the two formulas you've come up with you'll notice you've done exactly that.

Hopefully that makes sense.

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haegarr    7372
There are 2 ways:

1. An offset of the angle by -90° (in this case) compared to the original

[code]
playerVel.X = Math.Sin(rotAngle-90) ;
playerVel.Y = -Math.Cos(rotAngle-90);
[/code]
(ignoring that sin and cos usually need radian instead of degree) and using the correspondences

[code]
sin( a-90° ) == cos( a ), sin( a+90° ) == -cos( a ), cos( a-90° ) == -sin( a ), cos( a+90° ) == sin( a )
[/code]
because the sine and cosine curves are the same but just 90° shifted.

2. Rotating the original vector as Postie has already mentioned above:

[code]
[ cos( 90° ) -sin( 90° ) ] * [ sin( a ) ] = [ 0 -1 ] * [ sin( a ) ] = [ cos( a ) ]
[ sin( 90° ) cos( 90° ) ] [ -cos( a ) ] [ 1 0 ] [ -cos( a ) ] [ sin( a ) ]
[/code]

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ElyasMachera    102
thanks guys..sorry for late reply, I didn't know I got a reply. The second answer was very difficult to follow, I am not good at maths like that...but I get it now thanks
By the way I was also wondering why when I am trying to get the direction vector of the enemy to look at the player..
I use atan2(y2-y1,x2-x1)
the code works well if the angle of the player is at 0 degrees pointing to the right..it will point directly at the player..
however if the sprites heading is upwards at 90 degrees..the atan2 doesn't give me the correct results.
so I am wondering for the enemy sprite to rotate at the player correctly does the ship sprite need to have an initial angle of 0 degrees (must it be facing right on the spritesheet)?
Because even if I subtracted 90 from the atan2 results the ship still doesn't look directly at the player, if its initial angle was at 90 degrees on the spritesheet..
any insights on this?
Thanks..

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haegarr    7372
[quote name='Elyas_321' timestamp='1307037752' post='4818776']
... The second answer was very difficult to follow, I am not good at maths like that...but I get it now thanks
[/quote]
Sorry for that, but unfortunately things are inherently math. And so is your next question, too:

[quote name='Elyas_321' timestamp='1307037752' post='4818776']
By the way I was also wondering why when I am trying to get the direction vector of the enemy to look at the player..
I use atan2(y2-y1,x2-x1)
the code works well if the angle of the player is at 0 degrees pointing to the right..it will point directly at the player..
[/quote]
The atan2 is a improved function of the atan (i.e. "arc tangent" or "inverse tangent") function. To understand atan2, you need to understand the tangent function.

The tangent function of an angle is defined as [url="http://en.wikipedia.org/wiki/Tangens#Overview"]the ratio of the opposite to the adjacent[/url] leg. With atan2(y,x) the corresponding arc tangent function is atan(y/x). Because the arc tangent is the inverse of the tangent, y plays the role of the opposite and x the role of the adjacent leg.

Hence the result of atan2(y,x) will be
* angle==0 where y==0 and x>0 (i.e. straight to the right),
* angle==90° where y>0 and x==0 (i.e. straight up),
* angle==180° where y==0 and x<0 (i.e. straight to the left),
* angle==-90° where y<0 and x==0 (i.e. straight down).

If this is not what you want, you have to adapt the values. E.g. by exchanging the values, i.e. using atan2(x,y) instead, you'll get
* angle==0 where x==0 and y>0 (i.e. straight up),
* angle==90° where x>0 and y==0 (i.e. straight to the right),
* angle==180° where x==0 and y<0 (i.e. straight down),
* angle==-90° where x<0 and y==0 (i.e. straight to the left).

You can also alter the sign of one or both values. E.g. atan2(-y,x) yields in
* angle==0 where y==0 and x>0 (i.e. straight to the right),
* angle==90° where y<0 and x==0 (i.e. straight down),
* angle==180° where y==0 and x<0 (i.e. straight to the left),
* angle==-90° where y>0 and x==0 (i.e. straight up).

...

So you can rotate the axes by 90° when swapping y and x, and you can mirror up/down and/or left/right by negating one or both arguments. If you need further help, please tell us what angles you desire at what combination of x and y (like I've done above).

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ElyasMachera    102
Hi Haegar thanks for reply..I know maths is but I'm sure you've met people like myself where sin and cos puts them off..but I'd really like to understand it so I can make cool games ha ha you might have heard that a lot..
The angle of the sprite in the sprite sheet is at 90 degrees...but I can't tell where the x and y positions of the player or enemy will be as it is random.

To make things simple..we know that the sprite both enemy and player looking up at 90 degrees (12 o'clock)..and to calculate the angle of rotation for the enemy to face the player I would need the
atan function...since the x and y coordinates are random...
how do I decide which formula to use
atan2(x,y) atan2(y,x) atan2(-y,x)
Maybe if we start from there...I'd slowly but surely come to understand why it is happening..I hope you're patient enough to help me as I am very slow.
Thanks

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jyk    2094
Just a general recommendation: stick with '0 degrees/radians points along the +x axis' for all your game objects and game object visuals (e.g. sprites), and things will be much simpler. (Following this convention, you would use 'atan2(y, x)'.)

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haegarr    7372
[quote name='Elyas_321' timestamp='1307048866' post='4818852']
The angle of the sprite in the sprite sheet is at 90 degrees...but I can't tell where the x and y positions of the player or enemy will be as it is random.
[/quote]
Well, although the positions are arbitrary w.r.t. the definition range, the correspondence between the delta of the positions and the angle is not arbitrary; and that is what we're looking for.

[quote name='Elyas_321' timestamp='1307048866' post='4818852']
To make things simple..we know that the sprite both enemy and player looking up at 90 degrees (12 o'clock)..and to calculate the angle of rotation for the enemy to face the player I would need the
atan function...since the x and y coordinates are random...
how do I decide which formula to use
atan2(x,y) atan2(y,x) atan2(-y,x)
[/quote]
The 3 functions I've listed are just 3 examples out of a set of 8 possibilities. However ... let's go into the details:

You want to know the angle of rotation with which the sprite of ship A has to be transformed to let its forward vector point to the position of target ship B. The sprite has a default forward vector (i.e. the forward vector when the sprite is unrotated) of f[sub]x[/sub]=0 and f[sub]y[/sub]=1. Please notice that these values denote a direction, not a position! I.e. it is irrelevant where the sprite is placed; its default forward direction is ever the same.

The default forward direction can be written in vector notation as:
[ f[sub]x[/sub] f[sub]y[/sub] ] = [ 0 1 ]
If you apply the atan2(y,x) function to these values, you'll get that the default forward direction is at
atan2( f[sub]y[/sub] , f[sub]x[/sub] ) = atan2( 1, 0 ) = 90° =: a[sub]f[/sub]
what we'll define as the angle a[sub]f[/sub].
(Attention: The atan2 function, when used in computer programs, deals with radian values (i.e. 2 pi means 360°), while I use degree here for simplicity!)

If you check out some values, you'll find that the angle of 0° is returned by atan2( y,x ) when y==0 and x>0. Hence, the reference angle 0° is to the right (for the constellation (y,x) of arguments). Because we've found above that +90° is straight up, atan2(y,x) gives us increasing angles when rotating in counter clockwise (CCW) direction.

The function atan(y/x) is working inside atan2(y,x). As you can see, the argument to atan is a quotient. One consequence is that if both y and x are scaled by the same factor (unequal to 0), the quotient and hence the resulting angle from atan is the same. E.g. atan( 3/5 ) gives the same angle as atan( (2*3)/(2*5) ). The same is true for atan2 in principle, but remember that atan2 is able to distinguish which signs each of y and x has. That means that for atan2 the factor must be >0 (and not only !=0).

That said, what would scaling of [ x y ] mean? It would mean that the distance of the both ships is irrelevant when computing the angle; only the direction is relevant.

So we can compute the difference between the positions from ship A to ship B as
[ x[sub]B[/sub] y[sub]B[/sub] ] - [ x[sub]A[/sub] y[sub]A[/sub] ] = [ x[sub]B[/sub]-x[sub]A [/sub]y[sub]B[/sub]-y[sub]A[/sub] ]
as you already know, an put this into atan2 without bothering the absolute distance, and compute the angle of this direction as
a[sub]d[/sub] := atan2( y[sub]B[/sub]-y[sub]A[/sub] , x[sub]B[/sub]-x[sub]A [/sub])
which denotes the angle to the targeted ship.

When looking at the difference of the default angle a[sub]f[/sub] and this target angle a[sub]d[/sub], we see that
* for y[sub]B[/sub]-y[sub]A[/sub] == 0, x[sub]B[/sub]-x[sub]A [/sub]> 0, i.e. ship B is straight to the right of ship A, we get a[sub]d[/sub]-a[sub]f[/sub] = 0°-90° == -90°, i.e. rotate A by 90° in CW direction to target B,
* for y[sub]B[/sub]-y[sub]A[/sub] == 0, x[sub]B[/sub]-x[sub]A [/sub]< 0, i.e. ship B is straight to the left of ship A, we get a[sub]d[/sub]-a[sub]f[/sub] = 180°-90° == +90°, i.e. rotate A by 90° in CCW direction to target B,
* for y[sub]B[/sub]-y[sub]A[/sub] > 0, x[sub]B[/sub]-x[sub]A [/sub]== 0, i.e. ship B is straight above ship A, we get a[sub]d[/sub]-a[sub]f[/sub] = 90°-90° == 0°, i.e. don't rotate A to target B,
* for y[sub]B[/sub]-y[sub]A[/sub] < 0, x[sub]B[/sub]-x[sub]A [/sub]== 0, i.e. ship B is straight below ship A, we get a[sub]d[/sub]-a[sub]f[/sub] = -90°-90° == -180°, i.e. rotate A by 180° to target B.

All of these 4 (straight forward and therefore chosen) cases work fine. The receipt you're looking for is hence:
1. compute the difference angle from the both ship positions (B - A) using the atan2(y,x),
2. subtract the default forward angle of 90° from it,
3. use the resulting angle for rotation.
[sub][/sub]

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ElyasMachera    102
hello, @jyk I get what you mean..but it wouldn't hurt to have this knowledge
@haegar I think I get what you mean

if the ship is facing right, then its original look vector irrespective of it its position is (1,0) and atan2(0) is always 90
if it is up at 90 (0,-1) in reference to your first post should it not be x==0, y<0 for the ship looking up?

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haegarr    7372
[quote name='Elyas_321' timestamp='1307098311' post='4819006']
if the ship is facing right, then its original look vector irrespective of it its position is (1,0) and atan2(0) is always 90
[/quote]
It would be better to say that the [i]original[/i] (or default, i.e. unrotated) look vector is [ 0 1 ] (but see below), and that the [i]current[/i] look vector is [ 1 0 ] when facing to the right, and all this regardless of the location of the ship. This distinction is necessary because we need the default (or original) vector to be constant. One can say that it is the look direction in the model's local space but expressed in global co-ordinates, and as such it is fixed.

atan2(0) is not defined, because atan2 requires 2 parameters. But atan2(y,0) for any y>0 is always 90°, correct.

[quote name='Elyas_321' timestamp='1307098311' post='4819006']
if it is up at 90 (0,-1) in reference to your first post should it not be x==0, y<0 for the ship looking up?
[/quote]
Err, does this mean that y increases from top to bottom rather than from bottom to top? Until now I assumed here and in any post above that y increases from the bottom of the screen to its top, because AFAIK it is the way D3D handles this! Please clarify.

If that assumption is wrong, then the vector [ 0 1 ] and its belonging angle +90° will point down, while the vector [ 0 -1 ] and its belonging angle -90° will point up. Moreover, positive angles mean to rotate in CW direction, while negative angles mean to rotate in CCW direction. This can be overcome simply by negating the angle after its computation by atan2, [i]where necessary[/i].

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ElyasMachera    102
[quote name='haegarr' timestamp='1307101111' post='4819017']
[quote name='Elyas_321' timestamp='1307098311' post='4819006']
if the ship is facing right, then its original look vector irrespective of it its position is (1,0) and atan2(0) is always 90
[/quote]
It would be better to say that the [i]original[/i] (or default, i.e. unrotated) look vector is [ 0 1 ] (but see below), and that the [i]current[/i] look vector is [ 1 0 ] when facing to the right, and all this regardless of the location of the ship. This distinction is necessary because we need the default (or original) vector to be constant. One can say that it is the look direction in the model's local space but expressed in global co-ordinates, and as such it is fixed.

atan2(0) is not defined, because atan2 requires 2 parameters. But atan2(y,0) for any y>0 is always 90°, correct.

[quote name='Elyas_321' timestamp='1307098311' post='4819006']
if it is up at 90 (0,-1) in reference to your first post should it not be x==0, y<0 for the ship looking up?
[/quote]
Err, does this mean that y increases from top to bottom rather than from bottom to top? Until now I assumed here and in any post above that y increases from the bottom of the screen to its top, because AFAIK it is the way D3D handles this! Please clarify.
[/quote]

[quote]
If that assumption is wrong, then the vector [ 0 1 ] and its belonging angle +90° will point down, while the vector [ 0 -1 ] and its belonging angle -90° will point up. Moreover, positive angles mean to rotate in CW direction, while negative angles mean to rotate in CCW direction. This can be overcome simply by negating the angle after its computation by atan2, [i]where necessary[/i].
[/quote]
When going up in XNA you need to subtract the y axis, and when going down you need to add to the y axis..yeah it is screwed up..the same with C++ allegro...the graph is upside down...

so if the y<0 and x==0 (0,-1) looking up at 90, if its current look vector is (1, 0) then I need to subtract -90 to make it look right...yeah?

so the code
angle = atan2(y2-y1,x2-x1) - Pi/2 ;

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Burnt_Fyr    1665
[quote] Moreover, positive angles mean to rotate in CW direction, while negative angles mean to rotate in CCW direction. [/quote]

This would depend quite a bit on handedness of the system. A positive rotation of 90 on Z should rotate X to Y and Y to -X but whether this is clockwise or not is relative to the handedness of the system and the position of the viewer in respect to the object rotating.

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ElyasMachera    102
ha ha I'm so lost here..."handedness of he system?" what?! lol...
I think I will just draw an arrow and let it follow the sprite...with different initial directions

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haegarr    7372
[quote name='Elyas_321' timestamp='1307102845' post='4819026']
When going up in XNA you need to subtract the y axis, and when going down you need to add to the y axis..yeah it is screwed up..the same with C++ allegro...the graph is upside down...

so if the y<0 and x==0 (0,-1) looking up at 90, if its current look vector is (1, 0) then I need to subtract -90 to make it look right...yeah?

so the code
angle = atan2(y2-y1,x2-x1) - Pi/2 ;
[/quote]
Yes (with the small mistake that up is at -90°, not at +90°, because atan2(-1,0)==-90°).

However, there is still the possibility that the rotation code uses positive angles for a CCW rotation instead of the CW rotation (as is needed here). If so, then the angle need to be negated before being fed to a rotation matrix generation.

BTW: I'm writing all this from a theoretical point of view. Maybe I'm wrong in the one of other statement, so double check all what I wrote.

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ElyasMachera    102
[quote name='haegarr' timestamp='1307104817' post='4819031']
[quote name='Elyas_321' timestamp='1307102845' post='4819026']
When going up in XNA you need to subtract the y axis, and when going down you need to add to the y axis..yeah it is screwed up..the same with C++ allegro...the graph is upside down...

so if the y<0 and x==0 (0,-1) looking up at 90, if its current look vector is (1, 0) then I need to subtract -90 to make it look right...yeah?

so the code
angle = atan2(y2-y1,x2-x1) - Pi/2 ;
[/quote]
Yes (with the small mistake that up is at -90°, not at +90°, because atan2(-1,0)==-90°).

However, there is still the possibility that the rotation code uses positive angles for a CCW rotation instead of the CW rotation (as is needed here). If so, then the angle need to be negated before being fed to a rotation matrix generation.

BTW: I'm writing all this from a theoretical point of view. Maybe I'm wrong in the one of other statement, so double check all what I wrote.
[/quote]

oh yeah...so I need to subtract [i]-90 [/i]from the atan2 results, I am not sure if it takes positive angles
angle = atan2(y2-y1,x2-x1) - (-90); //this doesn't seem right to me
or
angle = atan2(y2-y1,x2-x1) +(-90); //this makes more sense..but the arrow doesn't look at the mouse
either way the sprite isn't looking

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haegarr    7372
[quote name='Burnt_Fyr' timestamp='1307103112' post='4819027']
[quote] Moreover, positive angles mean to rotate in CW direction, while negative angles mean to rotate in CCW direction. [/quote]

This would depend quite a bit on handedness of the system. A positive rotation of 90 on Z should rotate X to Y and Y to -X but whether this is clockwise or not is relative to the handedness of the system and the position of the viewer in respect to the object rotating.
[/quote]
Sorry, but this is IMHO not true. The axes are definitely given so that x increases from left to right, and y increases from top to bottom. Based on a direction vector in this system, the use of atan2(y,x) to compute the orientation angle and a[sub]d[/sub]-a[sub]f[/sub] to compute the rotation (i.e. difference) angle, we have [i]defined[/i] that positive angles rotate in CW direction! And it doesn't make sense to look at the screen [i]from behind it[/i] to be able to say "it's CCW".

But as I've written in previous posts, when actually doing the rotation, one has 2 possibilities to generate a (usually) rotation matrix. The one rotates in CW direction for positive angles and the other in CCW direction. Again, this is no consequence of the handedness but a convention. Your statement "positive rotation of 90 on Z [i]should[/i] rotate ..." (emphasis done by me) already stresses this.

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ElyasMachera    102
mmn
rotAngle = (float)Math.Atan2(Mouse.GetState().Y-arrowPos.Y, Mouse.GetState().X-arrowPos.X)+90.0f;
odd it worked, I forgot that atan2 returned radians, and rotation parameter takes radians
rotAngle = (float)Math.Atan2(Mouse.GetState().Y-arrowPos.Y, Mouse.GetState().X-arrowPos.X)+Math.Pi/2 did the trick;

EDIT:
I rotated the sprite again at 180 degrees
so its look vector is (-1,0)
hence atan2(0/-1) = 0
using the normal atan2 formula did not work.. although it should work? :S

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haegarr    7372
[quote name='Elyas_321' timestamp='1307105886' post='4819035']
oh yeah...so I need to subtract [i]-90 [/i]from the atan2 results, I am not sure if it takes positive angles
angle = atan2(y2-y1,x2-x1) - (-90); //this doesn't seem right to me
or
angle = atan2(y2-y1,x2-x1) +(-90); //this makes more sense..but the arrow doesn't look at the mouse
either way the sprite isn't looking
[/quote]
From said theoretical point of view (;)), the formula to use should be
angle = atan2(y2-y1,x2-x1) - (-90);
what is equivalent to
angle = atan2(y2-y1,x2-x1)+90;

But, as said somewhere above, atan2 usually works with radian (and XNA seems me to do so, too) but "90" is a value in degree! So, if you use the above in actual code, you probably add apples to oranges! Please check whether XNA's atan2 returns radian or degree. In the former case you need to use something like
angle = atan2(y2-y1,x2-x1)+0.5*Math::PI;
or whatever the usual way in XNA is.

Even then, the rotation may be wrong due to the convention XNA uses when generating rotations. After ensuring that the above issue with Math::PI is okay, and the rotation is done so that ship A turns to the left instead of to the right (and vice-versa), please try
angle = -(atan2(y2-y1,x2-x1)+0.5*Math::PI);
(notice the minus in front).

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ElyasMachera    102
[quote name='haegarr' timestamp='1307107098' post='4819043']
[quote name='Elyas_321' timestamp='1307105886' post='4819035']
oh yeah...so I need to subtract [i]-90 [/i]from the atan2 results, I am not sure if it takes positive angles
angle = atan2(y2-y1,x2-x1) - (-90); //this doesn't seem right to me
or
angle = atan2(y2-y1,x2-x1) +(-90); //this makes more sense..but the arrow doesn't look at the mouse
either way the sprite isn't looking
[/quote]
From said theoretical point of view (;)), the formula to use should be
angle = atan2(y2-y1,x2-x1) - (-90);
what is equivalent to
angle = atan2(y2-y1,x2-x1)+90;

But, as said somewhere above, atan2 usually works with radian (and XNA seems me to do so, too) but "90" is a value in degree! So, if you use the above in actual code, you probably add apples to oranges! Please check whether XNA's atan2 returns radian or degree. In the former case you need to use something like
angle = atan2(y2-y1,x2-x1)+0.5*Math::PI;
or whatever the usual way in XNA is.

Even then, the rotation may be wrong due to the convention XNA uses when generating rotations. After ensuring that the above issue with Math::PI is okay, and the rotation is done so that ship A turns to the left instead of to the right (and vice-versa), please try
angle = -(atan2(y2-y1,x2-x1)+0.5*Math::PI);
(notice the minus in front).
[/quote]

lol I assume you didn't see my previous post..I noticed that error myself and I didn't have to negate it:(
However, the sprite is now at 180 degrees at 9 o'clock...current look vector is [-1,0]
so atan2(0,-1) returns 0..
which is the original formula..but that didn't work..nor did negating it :S

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haegarr    7372
[quote name='Elyas_321' timestamp='1307106854' post='4819041']
...
EDIT:
I rotated the sprite again at 180 degrees
so its look vector is (-1,0)
hence atan2(0/-1) = 0
using the normal atan2 formula did not work.. although it should work? :S
[/quote]
I assume you meant atan2(0,-1) instead of atan2(0/-1) ...
atan2(0,-1) returns PI (a.k.a. 180°). That's absolutely okay!

EDIT
[font=arial, verdana, tahoma, sans-serif][size=2][quote name='Elyas_321' timestamp='1307108071' post='4819047']
lol I assume you didn't see my previous post..I noticed that error myself and I didn't have to negate it:(
However, the sprite is now at 180 degrees at 9 o'clock...current look vector is [-1,0]
so atan2(0,-1) returns 0..
which is the original formula..but that didn't work..nor did negating it :S
[/quote]
I saw it, but at that moment my answer was already written and send. Posting is just no realtime communication [/size][/font]

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ElyasMachera    102
[quote name='haegarr' timestamp='1307108115' post='4819049']
[quote name='Elyas_321' timestamp='1307106854' post='4819041']
...
EDIT:
I rotated the sprite again at 180 degrees
so its look vector is (-1,0)
hence atan2(0/-1) = 0
using the normal atan2 formula did not work.. although it should work? :S
[/quote]
I assume you meant atan2(0,-1) instead of atan2(0/-1) ...
atan2(0,-1) returns PI (a.k.a. 180°). That's absolutely okay!
[/quote]

yeah..wtf! when I did atan2(y,x) - Math.Pi and it worked!..I'm so confused lol
atan(0/-1) returned 0 on google..my calculator crashes..how do you work it out?

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haegarr    7372
[quote name='Elyas_321' timestamp='1307108385' post='4819052']
yeah..wtf! when I did atan2(y,x) - Math.Pi and it worked!..I'm so confused lol
atan(0/-1) returned 0 on google..my calculator crashes...
[/quote]
atan by itself is not suitable to do the computation we're looking for. atan cannot distinguish between all 4 quadrant but only between 2 of them. As an effect, atan can compute only angles in a range of 180°. As an example, atan(0/-1) returns 0 as well as atan(0/+1) does. atan2(0,+1) returns 0 as well, but atan2(0,-1) returns PI a.k.a. 180°. See [url="http://en.wikipedia.org/wiki/Atan2#Definition"]this wikipedia article[/url] on how atan2 and atan (therein named arctan) are related.

[quote name='Elyas_321' timestamp='1307108385' post='4819052']
...how do you work it out?
[/quote]
Head, pen & paper, calculator, and if required by writing little program.

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ElyasMachera    102
[quote name='haegarr' timestamp='1307108115' post='4819049'][font="arial, verdana, tahoma, sans-serif"][size="2"]
I saw it, but at that moment my answer was already written and send. Posting is just no realtime communication [/size][/font]
[/quote]

true
by the way how do you calculate your atan results..I keep getting 0 of instead of 180

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haegarr    7372
[quote name='Elyas_321' timestamp='1307112281' post='4819064']
by the way how do you calculate your atan results..I keep getting 0 of instead of 180

[/quote]
Well, as already written: atan(0/-1) [i]actually returns[/i] [i]0[/i]. But atan2(0,-1) returns PI. Please read my previous post carefully. Its first section explains the difference between atan and atan2, and therein is the reason for what you observe.

The last resort (and proof, if you wish so) is this:

[code]
// test.c

#include <stdio.h>
#include <math.h>

int
main() {
printf("%f\n", atan2(0,-1));
return 0;
}

[/code]
Compile and run. With gcc and a shell and using a Unix like OS it looks like this:

[code]
> gcc test.c
> ./a.out
3.141593
[/code]

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ElyasMachera    102
[quote name='haegarr' timestamp='1307113670' post='4819078']
[quote name='Elyas_321' timestamp='1307112281' post='4819064']
by the way how do you calculate your atan results..I keep getting 0 of instead of 180

[/quote]
Well, as already written: atan(0/-1) [i]actually returns[/i] [i]0[/i]. But atan2(0,-1) returns PI. Please read my previous post carefully. Its first section explains the difference between atan and atan2, and therein is the reason for what you observe.

The last resort (and proof, if you wish so) is this:

[code]
// test.c

#include <stdio.h>
#include <math.h>

int
main() {
printf("%f\n", atan2(0,-1));
return 0;
}

[/code]
Compile and run. With gcc and a shell and using a Unix like OS it looks like this:

[code]
> gcc test.c
> ./a.out
3.141593
[/code]
[/quote]

sorry I didn't see your previous post.
Thanks very much..I'm sure I'll be back..