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.
This question is related to
c#
python
trigonometry
The answer is
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)->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 < 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
matlab function:
function [lineAngle] = getLineAngle(x1, y1, x2, y2)
deltaY = y2 - y1;
deltaX = x2 - x1;
lineAngle = rad2deg(atan2(deltaY, deltaX));
if deltaY < 0
lineAngle = lineAngle + 360;
end
end
deltaY = Math.Abs(P2.y - P1.y);
deltaX = Math.Abs(P2.x - P1.x);
angleInDegrees = Math.atan2(deltaY, deltaX) * 180 / PI
if(p2.y > p1.y) // Second point is lower than first, angle goes down (180-360)
{
if(p2.x < p1.x)//Second point is to the left of first (180-270)
angleInDegrees += 180;
else //(270-360)
angleInDegrees += 270;
}
else if (p2.x < p1.x) //Second point is top left of first (90-180)
angleInDegrees += 90;
import math
from collections import namedtuple
Point = namedtuple("Point", ["x", "y"])
def get_angle(p1: Point, p2: Point) -> 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 < 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) < epsilon
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)
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)))
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.
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)); }
Source: Stackoverflow.com