What is the difference between atan and atan2 in C

Question

User · Answer

With atan2 you can determine the quadrant as stated here      You can use atan2 if you need to   determine the quadrant

User · Answer

Another thing to mention is that atan2 is more stable when computing tangents using an expression like atan y   x  and x is 0 or close to 0

User · Answer

I guess the main question tries to figure out   when should I use one or the other   or  which should I use   or  Am I using the right one    I guess the important point is atan only was intended to feed positive values in a right-upwards direction curve like for time-distance vectors  Cero is always at the bottom left  and thigs can only go up and right  just slower or faster  atan doesn t return negative numbers  so you can t trace things in the 4 directions on a screen just by adding subtracting its result   atan2 is intended for the origin to be in the middle  and things can go backwards or down  That s what you d use in a screen representation  because it DOES matter what direction you want the curve to go  So atan2 can give you negative numbers  because its cero is in the center  and its result is something you can use to trace things in 4 directions

User · Answer

With atan2 you can determine the quadrant as stated here      You can use atan2 if you need to   determine the quadrant

User · Answer

Consider a right angled triangle  We label the hypotenuse r  the horizontal side y and the vertical side x  The angle of interest  alpha  is the angle between x and r   C   atan2 y  x  will give us the value of angle  alpha  in radians  atan is used if we only know or are interested in y x not y and x individually  So if p   y x then to get  alpha  we d use atan p    You cannot use atan2 to determine the quadrant  you can use atan2 only if you already know which quadrant your in  In particular positive x and y imply the first quadrant  positive y and negative x  the second and so on  atan or atan2 themselves simply return a positive or a negative number  nothing more

User · Answer

atan x     Returns the principal value of the arc tangent of x  expressed in radians   atan2 y x  Returns the principal value of the arc tangent of y x  expressed in radians   Notice that because of the sign ambiguity  a function cannot determine with certainty in which quadrant the angle falls only by its tangent value  atan alone   You can use atan2 if you need to determine the quadrant

User · Answer

The actual values are in radians but to interpret them in degrees it will be    atan   gives angle value between -90 and 90 atan2   gives angle value between -180 and 180   For my work which involves computation of various angles such as heading and bearing in navigation  atan2 in most cases does the job

User · Answer

The actual values are in radians but to interpret them in degrees it will be    atan   gives angle value between -90 and 90 atan2   gives angle value between -180 and 180   For my work which involves computation of various angles such as heading and bearing in navigation  atan2 in most cases does the job

User · Answer

atan x     Returns the principal value of the arc tangent of x  expressed in radians   atan2 y x  Returns the principal value of the arc tangent of y x  expressed in radians   Notice that because of the sign ambiguity  a function cannot determine with certainty in which quadrant the angle falls only by its tangent value  atan alone   You can use atan2 if you need to determine the quadrant

User · Answer

I guess the main question tries to figure out   when should I use one or the other   or  which should I use   or  Am I using the right one    I guess the important point is atan only was intended to feed positive values in a right-upwards direction curve like for time-distance vectors  Cero is always at the bottom left  and thigs can only go up and right  just slower or faster  atan doesn t return negative numbers  so you can t trace things in the 4 directions on a screen just by adding subtracting its result   atan2 is intended for the origin to be in the middle  and things can go backwards or down  That s what you d use in a screen representation  because it DOES matter what direction you want the curve to go  So atan2 can give you negative numbers  because its cero is in the center  and its result is something you can use to trace things in 4 directions

User · Answer

In atan2  the output is  -pi  lt  atan2 y x   lt pi  and in atan  the output is  -pi 2  lt  atan y x   lt  pi 2    it dose NOT consider the quarter  If you want to get the orientation between 0 and 2 pi  like the high-school math   we need to use the atan2 and for negative values add the 2 pi to get the final result between 0 and 2 pi  Here is the Java source code to explain it clearly   System out println Math atan2 1 1      pi 4 in the 1st quarter System out println Math atan2 1 -1       pi 4   pi 2  3  pi 4  in the 2nd quarter  System out println Math atan2 -1 -1      -3  pi 4  and it is less than 0  System out println Math atan2 -1 -1  2 Math PI     5 pi 4  in the 3rd quarter  System out println Math atan2 -1 1      -pi 4 and it is less than 0  System out println Math atan2 -1 1  2 Math PI     7  pi 4  in the 4th quarter  System out println Math atan 1      pi 4 System out println Math atan -1      -pi 4

User · Answer

atan x     Returns the principal value of the arc tangent of x  expressed in radians   atan2 y x  Returns the principal value of the arc tangent of y x  expressed in radians   Notice that because of the sign ambiguity  a function cannot determine with certainty in which quadrant the angle falls only by its tangent value  atan alone   You can use atan2 if you need to determine the quadrant

User · Answer

With atan2 you can determine the quadrant as stated here      You can use atan2 if you need to   determine the quadrant

User · Answer

std  atan2 allows calculating the arctangent of all four quadrants  std  atan only allows calculating from quadrants 1 and 4

User · Answer

From school mathematics we know that the tangent has the definition  tan a    sin a    cos a    and we differentiate between four quadrants based on the angle that we supply to the functions  The sign of the sin  cos and tan have the following relationship  where we neglect the exact multiples of p 2      Quadrant    Angle              sin   cos   tan -------------------------------------------------   I           0     lt  a  lt  p 2                      II          p 2   lt  a  lt  p              -     -   III         p     lt  a  lt  3p 2     -     -         IV          3p 2  lt  a  lt  2p       -           -   Given that the value of tan a  is positive  we cannot distinguish  whether the angle was from the first or third quadrant and if it is negative  it could come from the second or fourth quadrant  So by convention  atan   returns an angle from the first or fourth quadrant  i e  -p 2  lt   atan    lt   p 2   regardless of the original input to the tangent   In order to get back the full information  we must not use the result of the division sin a    cos a  but we have to look at the values of the sine and cosine separately  And this is what atan2   does  It takes both  the sin a  and cos a  and resolves all four quadrants by adding p to the result of atan   whenever the cosine is negative   Remark  The atan2 y  x  function actually takes a y and a x argument  which is the projection of a vector with length v and angle a on the y- and x-axis  i e    y   v   sin a  x   v   cos a    which gives the relation  y x   tan a    Conclusion  atan y x  is held back some information and can only assume that the input came from quadrants I or IV  In contrast  atan2 y x  gets all the data and thus can resolve the correct angle

User · Answer

Another thing to mention is that atan2 is more stable when computing tangents using an expression like atan y   x  and x is 0 or close to 0

User · Answer

In atan2  the output is  -pi  lt  atan2 y x   lt pi  and in atan  the output is  -pi 2  lt  atan y x   lt  pi 2    it dose NOT consider the quarter  If you want to get the orientation between 0 and 2 pi  like the high-school math   we need to use the atan2 and for negative values add the 2 pi to get the final result between 0 and 2 pi  Here is the Java source code to explain it clearly   System out println Math atan2 1 1      pi 4 in the 1st quarter System out println Math atan2 1 -1       pi 4   pi 2  3  pi 4  in the 2nd quarter  System out println Math atan2 -1 -1      -3  pi 4  and it is less than 0  System out println Math atan2 -1 -1  2 Math PI     5 pi 4  in the 3rd quarter  System out println Math atan2 -1 1      -pi 4 and it is less than 0  System out println Math atan2 -1 1  2 Math PI     7  pi 4  in the 4th quarter  System out println Math atan 1      pi 4 System out println Math atan -1      -pi 4

User · Answer

Consider a right angled triangle  We label the hypotenuse r  the horizontal side y and the vertical side x  The angle of interest  alpha  is the angle between x and r   C   atan2 y  x  will give us the value of angle  alpha  in radians  atan is used if we only know or are interested in y x not y and x individually  So if p   y x then to get  alpha  we d use atan p    You cannot use atan2 to determine the quadrant  you can use atan2 only if you already know which quadrant your in  In particular positive x and y imply the first quadrant  positive y and negative x  the second and so on  atan or atan2 themselves simply return a positive or a negative number  nothing more

User · Answer

Mehrwolf below is correct  but here is a heuristic which may help   If you are working in a 2-dimensional coordinate system  which is often the case for programming the inverse tangent  you should use definitely use atan2  It will give the full 2 pi range of angles and take care of zeros in the x coordinate for you   Another way of saying this is that atan y x  is virtually always wrong  Only use atan if the argument cannot be thought of as y x

User · Answer

Another thing to mention is that atan2 is more stable when computing tangents using an expression like atan y   x  and x is 0 or close to 0

User · Answer

std  atan2 allows calculating the arctangent of all four quadrants  std  atan only allows calculating from quadrants 1 and 4

User · Answer

atan x     Returns the principal value of the arc tangent of x  expressed in radians   atan2 y x  Returns the principal value of the arc tangent of y x  expressed in radians   Notice that because of the sign ambiguity  a function cannot determine with certainty in which quadrant the angle falls only by its tangent value  atan alone   You can use atan2 if you need to determine the quadrant

User · Answer

Another thing to mention is that atan2 is more stable when computing tangents using an expression like atan y   x  and x is 0 or close to 0

User · Answer

atan2 y x  is generally used if you want to convert cartesian coordinates to polar coordinates  It will give you the angle  while sqrt x x y y  or  if available  hypot y x  will give you the size   atan x  is simply the inverse of tan  In the annoying case you have to use atan y x  because your system doesn t provide atan2  you would have to do additional checks for the signs of x and y  and for x 0  in order to get the correct angle   Note  atan2 y x  is defined for all real values of y and x  except for the case when both arguments are zero

User · Answer

Mehrwolf below is correct  but here is a heuristic which may help   If you are working in a 2-dimensional coordinate system  which is often the case for programming the inverse tangent  you should use definitely use atan2  It will give the full 2 pi range of angles and take care of zeros in the x coordinate for you   Another way of saying this is that atan y x  is virtually always wrong  Only use atan if the argument cannot be thought of as y x

User · Answer

From school mathematics we know that the tangent has the definition  tan a    sin a    cos a    and we differentiate between four quadrants based on the angle that we supply to the functions  The sign of the sin  cos and tan have the following relationship  where we neglect the exact multiples of p 2      Quadrant    Angle              sin   cos   tan -------------------------------------------------   I           0     lt  a  lt  p 2                      II          p 2   lt  a  lt  p              -     -   III         p     lt  a  lt  3p 2     -     -         IV          3p 2  lt  a  lt  2p       -           -   Given that the value of tan a  is positive  we cannot distinguish  whether the angle was from the first or third quadrant and if it is negative  it could come from the second or fourth quadrant  So by convention  atan   returns an angle from the first or fourth quadrant  i e  -p 2  lt   atan    lt   p 2   regardless of the original input to the tangent   In order to get back the full information  we must not use the result of the division sin a    cos a  but we have to look at the values of the sine and cosine separately  And this is what atan2   does  It takes both  the sin a  and cos a  and resolves all four quadrants by adding p to the result of atan   whenever the cosine is negative   Remark  The atan2 y  x  function actually takes a y and a x argument  which is the projection of a vector with length v and angle a on the y- and x-axis  i e    y   v   sin a  x   v   cos a    which gives the relation  y x   tan a    Conclusion  atan y x  is held back some information and can only assume that the input came from quadrants I or IV  In contrast  atan2 y x  gets all the data and thus can resolve the correct angle

User · Answer

std  atan2 allows calculating the arctangent of all four quadrants  std  atan only allows calculating from quadrants 1 and 4

User · Answer

atan2 y x  is generally used if you want to convert cartesian coordinates to polar coordinates  It will give you the angle  while sqrt x x y y  or  if available  hypot y x  will give you the size   atan x  is simply the inverse of tan  In the annoying case you have to use atan y x  because your system doesn t provide atan2  you would have to do additional checks for the signs of x and y  and for x 0  in order to get the correct angle   Note  atan2 y x  is defined for all real values of y and x  except for the case when both arguments are zero

User · Answer

With atan2 you can determine the quadrant as stated here      You can use atan2 if you need to   determine the quadrant

User · Answer

std  atan2 allows calculating the arctangent of all four quadrants  std  atan only allows calculating from quadrants 1 and 4

[c++] What is the difference between atan and atan2 in C++?

Examples related to c++

Examples related to math.h