Unity, Projectile Motion, Angle Required to Hit Coordinate (X, Y, Z)

projectile-motion-angle-required-to-hit-xyz.cs

public static class PhysicsCalculator 
{
    // https://en.wikipedia.org/wiki/Projectile_motion#Angle_%CE%B8_required_to_hit_coordinate_(x,_y)
    public static float CalculateAngleToHitXYZ(Vector3 from, Vector3 to, float v, float g)
    {
        g = Mathf.Abs(g); // According to the wikipedia article, g is acceleration due to gravity and is |g|
        Vector3 s = (to - from); // Non-normalized so that we only get an angle if the velocity is enough to reach target.

        float x = new Vector3(s.x, 0, s.z).magnitude;
        float y = s.y;

        float v2 = v * v;
        float v4 = v2 * v2;

        float fac = v4 - g*(g*x*x + 2*y*v2);
        if (fac < 0) // Can't reach target with given velocity
        {
            return Mathf.Infinity;
        }

        /*
            There are two possible launch angles for reaching the target e.g. v2 +- sqrt(fac)

            theta1 = High arc angle, for big lobs
            theta2 = Low arc angle, for shallow lobs
        */

        //float theta1 = Mathf.Atan((v2 + Mathf.Sqrt(fac)) / (g * x)) * Mathf.Rad2Deg;
        float theta2 = Mathf.Atan((v2 - Mathf.Sqrt(fac)) / (g * x)) * Mathf.Rad2Deg;

        // Returning shallow arc
        return theta2;
    }

    public static float CalculateMaxRangeFromVelocity(float v, float g) => (v*v)/Mathf.Abs(g);
}