How Do I Calculate the Angle Between a Line and the Horizontal Axis in Programming?

Calculate the angle between the straight line and the horizontal axis in the program

In programming languages, determining the angle between a straight line and a horizontal axis is crucial for various graphics operations. Given two points: (P1x, P1y) and (P2x, P2y), let's explore a simple and efficient way to calculate this angle.

Steps:

1. Calculate the difference vector (DeltaX, DeltaY):

   • deltaX = P2x - P1x
   • deltaY = P2y - P1y

2. Determine the angle:

   • General situation:

     • angleInDegrees = arctan(deltaY / deltaX) * 180 / PI

   • Improve accuracy (using atan2 function):

     • angleInDegrees = atan2(deltaY, deltaX) * 180 / PI

Other notes:

1. Determine the quadrant:

   • The signs of deltaX and deltaY will indicate the quadrant in which the angle lies.
   • Positive deltaX and deltaY represent angles between 0 and 90 degrees, negative deltaX and deltaY represent angles between 180 and 270 degrees, and so on.

2. Normalization (optional):

   • By dividing deltaX and deltaY by the length of the vector (sqrt(deltaX^2 deltaY^2)), you can obtain unit vectors representing the cosine and sine of the angle. This step simplifies calculations and avoids potential division by zero.

Example:

<code class="language-python">import math

def calculate_angle(P1x, P1y, P2x, P2y):
  deltaX = P2x - P1x
  deltaY = P2y - P1y
  angle = math.atan2(deltaY, deltaX) * 180 / math.pi
  return angle</code>

Conclusion:

Using the provided method you can accurately calculate the angle between a straight line and the horizontal axis. This algorithm is both simple and efficient, allowing you to implement it in a variety of programming languages ​​for use in graphics applications or geometric calculations.

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