How to calculate the point of intercept in 3D space

Questions & Answers
1

So I have been wracking my brain trying to figure this out. So I need to calculate how far ahead to aim for 1 spaceship to fire and hit another spaceship. I need to know this so when the player targets another ship a targeting bracket shows up where the player needs to fire at that point in time.
I know there is a code already written to do this on the wiki, however I am not understanding how it works. I am scripting in JS. Any help with this would be greatly appreciated.

2

Ok, i don’t see your problem… Do you want to understand how it works or how you can use it?

Just copy the code in this section:

into a new C-sharp script that is located in Standard Assets. Then you can use the function even in JS.

using UnityEngine;
using System.Collections;

public class Intercept
{

    //first-order intercept using absolute target position
    
    public static Vector3 FirstOrderIntercept(  Vector3 shooterPosition,
                                                Vector3 shooterVelocity,
                                                float shotSpeed,
                                                Vector3 targetPosition,
                                                Vector3 targetVelocity) {
        Vector3 targetRelativeVelocity = targetVelocity - shooterVelocity;
        float t = FirstOrderInterceptTime(  shotSpeed,
                                            targetPosition - shooterPosition,
                                            targetRelativeVelocity);
        return targetPosition + t*(targetRelativeVelocity);
    }
    //first-order intercept using relative target position
    public static float FirstOrderInterceptTime(float shotSpeed,
                                                Vector3 targetRelativePosition,
                                                Vector3 targetRelativeVelocity) {
        float velocitySquared = targetRelativeVelocity.sqrMagnitude;
        if(velocitySquared < 0.001f)
            return 0f;
    
        float a = velocitySquared - shotSpeed*shotSpeed;
    
        //handle similar velocities
        if (Mathf.Abs(a) < 0.001f) {
            float t = -targetRelativePosition.sqrMagnitude
                        /(2f*Vector3.Dot(   targetRelativeVelocity,
                                            targetRelativePosition));
            return Mathf.Max(t, 0f); //don't shoot back in time
        }
    
        float   b = 2f*Vector3.Dot(targetRelativeVelocity, targetRelativePosition),
                c = targetRelativePosition.sqrMagnitude,
                determinant = b*b - 4f*a*c;
       
        if (determinant > 0f) { //determinant > 0; two intercept paths (most common)
            float   t1 = (-b + Mathf.Sqrt(determinant))/(2f*a),
                    t2 = (-b - Mathf.Sqrt(determinant))/(2f*a);
            if (t1 > 0f) {
                if (t2 > 0f)
                    return Mathf.Min(t1, t2); //both are positive
                else
                    return t1; //only t1 is positive
            } else
                return Mathf.Max(t2, 0f); //don't shoot back in time
        } else if (determinant < 0f) //determinant < 0; no intercept path
            return 0f;
        else //determinant = 0; one intercept path, pretty much never happens
            return Mathf.Max(-b/(2f*a), 0f); //don't shoot back in time
    }
}

In JS you can use it like this:

// I'll assume that both target and shooter are rigidbodies
var target : Transform;
var shotSpeed : float;

function Update()
{
    var interceptionPoint = Intercept.FirstOrderIntercept(transform.position, rigidbody.velocity, shotSpeed, target.position, target.rigidbody.velocity);
    // Do what you want
}