How to calculate the angle between a line and the horizontal axis

Question

In a programming language  Python  C   etc  I need to determine how to calculate the angle between a line and the horizontal axis   I think an image describes best what I want     Given  P1x P1y  and  P2x P2y  what is the best way to calculate this angle  The origin is in the topleft and only the positive quadrant is used

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deltaY   Math Abs P2 y - P1 y   deltaX   Math Abs P2 x - P1 x    angleInDegrees   Math atan2 deltaY  deltaX    180   PI  if p2 y  gt  p1 y     Second point is lower than first  angle goes down  180-360      if p2 x  lt  p1 x   Second point is to the left of first  180-270      angleInDegrees    180    else    270-360      angleInDegrees    270    else if  p2 x  lt  p1 x    Second point is top left of first  90-180    angleInDegrees    90

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First find the difference between the start point and the end point  here  this is more of a directed line segment  not a  line   since lines extend infinitely and don t start at a particular point    deltaY   P2 y - P1 y deltaX   P2 x - P1 x   Then calculate the angle  which runs from the positive X axis at P1 to the positive Y axis at P1    angleInDegrees   arctan deltaY   deltaX    180   PI   But arctan may not be ideal  because dividing the differences this way will erase the distinction needed to distinguish which quadrant the angle is in  see below   Use the following instead if your language includes an atan2 function   angleInDegrees   atan2 deltaY  deltaX    180   PI   EDIT  Feb  22  2017   In general  however  calling atan2 deltaY deltaX  just to get the proper angle for cos and sin may be inelegant  In those cases  you can often do the following instead    Treat  deltaX  deltaY  as a vector  Normalize that vector to a unit vector  To do so  divide deltaX and deltaY by the vector s length  sqrt deltaX deltaX deltaY deltaY    unless the length is 0  After that  deltaX will now be the cosine of the angle between the vector and the horizontal axis  in the direction from the positive X to the positive Y axis at P1   And deltaY will now be the sine of that angle  If the vector s length is 0  it won t have an angle between it and the horizontal axis  so it won t have a meaningful sine and cosine     EDIT  Feb  28  2017   Even without normalizing  deltaX  deltaY     The sign of deltaX will tell you whether the cosine described in step 3 is positive or negative  The sign of deltaY will tell you whether the sine described in step 4 is positive or negative  The signs of deltaX and deltaY will tell you which quadrant the angle is in  in relation to the positive X axis at P1     deltaX   deltaY  0 to 90 degrees  -deltaX   deltaY  90 to 180 degrees  -deltaX  -deltaY  180 to 270 degrees  -180 to -90 degrees    deltaX  -deltaY  270 to 360 degrees  -90 to 0 degrees        An implementation in Python using radians  provided on July 19  2015 by Eric Leschinski  who edited my answer    from math import   def angle trunc a       while a  lt  0 0          a    pi   2     return a  def getAngleBetweenPoints x orig  y orig  x landmark  y landmark       deltaY   y landmark - y orig     deltaX   x landmark - x orig     return angle trunc atan2 deltaY  deltaX    angle   getAngleBetweenPoints 5  2  1 4  assert angle  gt   0   angle must be  gt   0  angle   getAngleBetweenPoints 1  1  2  1  assert angle    0   expecting angle to be 0  angle   getAngleBetweenPoints 2  1  1  1  assert abs pi - angle   lt   0 01   expecting angle to be pi  it is      str angle  angle   getAngleBetweenPoints 2  1  2  3  assert abs angle - pi 2   lt   0 01   expecting angle to be pi 2  it is      str angle  angle   getAngleBetweenPoints 2  1  2  0  assert abs angle -  pi pi 2    lt   0 01   expecting angle to be pi pi 2  it is      str angle  angle   getAngleBetweenPoints 1  1  2  2  assert abs angle -  pi 4    lt   0 01   expecting angle to be pi 4  it is      str angle  angle   getAngleBetweenPoints -1  -1  -2  -2  assert abs angle -  pi pi 4    lt   0 01   expecting angle to be pi pi 4  it is      str angle  angle   getAngleBetweenPoints -1  -1  -1  2  assert abs angle -  pi 2    lt   0 01   expecting angle to be pi 2  it is      str angle    All tests pass  See https   en wikipedia org wiki Unit circle

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Considering the exact question  putting us in a  special  coordinates system where positive axis means moving DOWN  like a screen or an interface view   you need to adapt this function like this  and negative the Y coordinates   Example in Swift 2 0  func angle between two points pa CGPoint pb CGPoint - gt Double      let deltaY Double    Double -pb y  - Double -pa y       let deltaX Double    Double pb x  - Double pa x       var a   atan2 deltaY deltaX      while a  lt  0 0           a   a   M PI 2           return a     This function gives a correct answer to the question  Answer is in radians  so the usage  to view angles in degrees  is    let p1   CGPoint x  1 5  y  2    estimated coords of p1 in question let p2   CGPoint x  2  y   3    estimated coords of p2 in question  print angle between two points p1  pb  p2     M PI 180     returns 296 56

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Sorry  but I m pretty sure Peter s answer is wrong  Note that the y axis goes down the page  common in graphics   As such the deltaY calculation has to be reversed  or you get the wrong answer   Consider   System out println  Math toDegrees Math atan2 1 1     System out println  Math toDegrees Math atan2 -1 1     System out println  Math toDegrees Math atan2 1 -1     System out println  Math toDegrees Math atan2 -1 -1       gives  45 0 -45 0 135 0 -135 0   So if in the example above  P1 is  1 1  and P2 is  2 2   because Y increases down the page   the code above will give 45 0 degrees for the example shown  which is wrong  Change the order of the deltaY calculation and it works properly

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matlab function   function  lineAngle    getLineAngle x1  y1  x2  y2       deltaY   y2 - y1      deltaX   x2 - x1       lineAngle   rad2deg atan2 deltaY  deltaX         if deltaY  lt  0         lineAngle   lineAngle   360      end end

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I have found a solution in Python that is working well    from math import atan2 degrees  def GetAngleOfLineBetweenTwoPoints p1  p2       return degrees atan2 p2 - p1  1    print GetAngleOfLineBetweenTwoPoints 1 3

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import math from collections import namedtuple   Point   namedtuple  Point     x    y      def get angle p1  Point  p2  Point  - gt  float         Get the angle of this line with the horizontal axis         dx   p2 x - p1 x     dy   p2 y - p1 y     theta   math atan2 dy  dx      angle   math degrees theta     angle is in  -180  180      if angle  lt  0          angle   360   angle     return angle   Testing  For testing I let hypothesis generate test cases     import hypothesis strategies as s from hypothesis import given    given s floats min value 0 0  max value 360 0   def test angle angle  float       epsilon   0 0001     x   math cos math radians angle       y   math sin math radians angle       p1   Point 0  0      p2   Point x  y      assert abs get angle p1  p2  - angle   lt  epsilon

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Based on reference  Peter O    Here is the java version  private static final float angleBetweenPoints PointF a  PointF b    float deltaY   b y - a y  float deltaX   b x - a x  return  float   Math atan2 deltaY  deltaX

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A formula for an angle from 0 to 2pi   There is x x2-x1 and y y2-y1 The formula is working for  any value of x and y  For x y 0 the result is undefined   f x y  pi  -pi   2  1 sign x    1-sign y 2         -pi   4  2 sign x   sign y        -sign x y  atan  abs x -abs y    abs x  abs y

[c#] How to calculate the angle between a line and the horizontal axis?

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