两个运动物体的交点

Question

I'm trying to use the answer provided here: Intersection of two Moving Objects with Latitude/Longitude Coordinates

But I have some questions..

What is this angle:

var angle = Math.PI + dir - target.dir

I was thinking that the angle that should be used in the law of cosines is already "alpha or target.dir".. What is that line doing? Also in these two steps:

 var x = target.x + target.vel * time * Math.cos(target.dir); 
 var y = target.y + target.vel * time * Math.sin(target.dir);  

Shouldn't the code be using the angle between x- or y-axis and the target velocity vector? Why is the author using alpha here?

Answer 1

What is this angle:

 var angle = Math.PI + dir - target.dir 

The variable named angle is indeed the angle alpha . Because the direction dir is the direction from chaser to target, and we need it the other way round for this calculation, we add π to it before we subtract target.dir .

Maybe using the word angle as a variable name was a bit vague; I'll change it to alpha , the name I used for this angle in the images.

Shouldn't the code be using the angle between x- or y-axis and the target velocity vector? Why is the author using alpha here?

 var x = target.x + target.vel * time * Math.cos(target.dir); var y = target.y + target.vel * time * Math.sin(target.dir); 

We are indeed using target.dir , which is the direction of the target, ie the angle between the x-axis and the target vector, to calculate the coordinates of the interception point, and not the angle alpha.