How to calculate the angle in 2 coordinates?

Question

PHP

Good afternoon! I'm having trouble solving a small math problem, so I'm asking for the community's help.
So, I have a transport tracking service. For each car on the map, you need to set the rotation angle via transform: rotate(<angle>).
For each car, I have its past X1, Y1 coordinate and current X2, Y2 coordinate.
Question. What is the formula for calculating this angle?

Answer 1

alpha = arccos (deltaX / deltaY)
PS and "higher mathematics" in the tags to the question - is it marketing? :)
UPD: oyblin, sorry... all the math teachers of my youth, forgive me :/ of
course alpha = atan ( deltaY / deltaX )
but with deltaX=0, alpha = sign(deltaY) * pi/2;

Answer 2

Draw it on a piece of paper - and you will understand. In essence, you have a right triangle, where the hypotenuse is a segment from (x1, y1) to (x2, y2), and the legs are projections onto the corresponding axes. Next, find the desired angle from the formulas for the ratio of angles and sides of a right triangle.

Answer 3

So, I have a transport tracking service.

I can't solve a little math problem

Hand over the didactic material and go learn the lessons!

X = x0 + (x - x0) * cos(a) - (y - y0) * sin(a);
Y = y0 + (y - y0) * cos(a) + (x - x0) * sin(a);

Answer 4

Here, about the angle between the vectors
, angle(a, b) = arccos((a * b) / (|a| * |b|))
a * b is the dot product (the sum of the products of coordinates)
|a| - the length of the vector (the root of the sum of the squares of its coordinates)

Answer 5

As I understand it, you need the angle of the vector (x1,y1)→(x2,y2).
Any school "arch", if they act on the forehead, in a certain range of angles is not defined or unstable.
But this is precisely what most languages ​​have a function for.
atan2(y2 - y1, x2 - x1)

Answer 6

If the task sounds exactly like this, then it comes down to finding the angle between vectors (see the scalar product of vectors):

const getScalarProduct = ([xA, ...restA], [xB, ...restB]) => 
   (restA.length === 0 || restB.length === 0)
      ? xA * xB
      : xA * xB + getScalarProduct(restA, restB)
  
const getSquareModule = ([x, ...rest]) =>
   (rest.length === 0)
      ? x * x
      : x * x + getSquareModule(rest)

const getModule = (A) => Math.sqrt(getSquareModule(A))
  
const getCosOfAngle = (A, B) => getScalarProduct(A, B) / (getModule(A) * getModule(B))

getCosOfAngle([1, 0],[0, 1]) - two-dimensional case, but you can find the angle for any dimension
P.S.: JavaScript code , the getCosOfAngle function returns the cosine of the angle

Answer 7

It's never too late, possible exceptions are yours.

<?php 
  $x1 = 10;
  $y1 = 10;
  $x2 = 5;
  $y2 = 5;

  $alpha = rad2deg(atan2($y1 > $y2 ? $y1 - $y2 : ($y1 == $y2 ? $y1 : $y2 - $y1), $x1 > $x2 ? $x1 - $x2 : ($x1 == $x2 ? $x1 : $x2 - $x1)));

  echo($alpha)
?>

UPD: In this solution, you can get the angle, if the coordinates change in distance from each other, the solution will be correct.
UPD2: An example, if it's a radar type and the angles are 0 - 180 and 0 - -180:

$alpha = (($y1 > $y2 ? 180 : -180) - rad2deg(atan2($y1 - $y2, $x1 - $x2))) * -1;