I'm at X,Y - target at X,Y - How calculate angle to face target?

Question

Hello there!

1. I am at 10, 25 (x,y)
2. target at 5, -10 (x,y)
3. I'm facing 0º

How can I calculate the correct angle to face the target?

About this question: I am building a script on javascritp, so I guess I really need to use vanilla maths here,

if I were coding/scrip in some 3D software it would be easy as use something like "transform,x,y"...

EDIT: Got it working, thanks for the Tutors! Here's the code I'm using:

function getAngleDeg(ax,ay,px,py)

{

var angel = {

x: ax,

y: ay

};

var player = {

x: px,

y: py

};

var x = player.x - angel.x;

var y = player.y - angel.y;

var radianAngle = Math.atan2(x, y);

var northUpAngle = radianAngle * 128 / Math.PI;

if (northUpAngle < 0) northUpAngle += 256;

return northUpAngle.toFixed(0);

}

ps: Instead of 380º the game reads that as 256units (probably because needs to be sent as Unsigned Integers of bits) and needed te result to be 0-256 (wihtout negative numbers)

Answer 1

If you are at position (x₀,y₀) and your target is at position (x₁,y₁), then your problem is equivalent to calculating the angle between v=(x₁-x₀, y₁-y₀) and e_1=(1,0). The vector v is based at (0,0) and points in the direction from your position to the target's. The vector e_1 points faces 0° from (0,0).

Recall that the angle between two vectors v=(v₁,v₂),w=(w₁,w₂) can be calculated via the dot product: v·w=v₁w₁+v₂w₂=|v||w|cos(θ), where θ is the angle between the two vectors. Thus, we find

cos(θ)=(v₁w₁+v₂w₂)/(|v||w|)

⇒ θ = arccos((v₁w₁+v₂w₂)/(|v||w|))

Recall also that the length of the vector v=(v_1,v_2) is calculated via the pythagorean theorem: |v|=√(v₁²+v₂²).

For your particular problem, we have v=(-5,-35) and w=(1,0). Thus, we get

θ=arccos(-5/√(5²+35²))≈98.13°

This is only the magnitude of the angle. It is not immediate whether this angle is to be traversed in the clockwise or counterclockwise direction. This is determined by what quadrant v lives in. If v is in the upper half plane (quadrants 1 and 2), then the angle should be traversed counterclockwise. If v is in the lower half plane (quadrants 3 and 4), the angle should be traversed clockwise. So for your particular problem:

A person facing 0° at position (10,25) must turn 98.13° clockwise to aim at a target positioned at (5,-35).

Answer 2

tan of the base angle is the same as the slope

(10,25) vs (5, -10)

slope is (25 - -10)/(5 - 10) = 35/ -5 = -7

tan x = -7

x =| inverse tangent(-7)| = 81.87 degrees

the complement is 8.13 degrees