Vector3 pestDirection(
float planet_angle,
float planet_angle_speed,
Vector2 ship_pos,
float ship_speed
)
{
if (ship_speed == 0 || planet_angle_speed == 0)
{
return(Vector3.zero);
}
// Note: We will need to make sure that the units for time are the same for this function and the rest of the code.
// Note: This code is repetitive. Can you show me how one would make it nicer in Unity?
// Initial search interval
float t0 = 0.0f;
float t1 = 1.0f; // adjustable parameter
// Parameter
float t_scale = 1.2f; // upper bound search scale
float t_eps = 0.001f; // tolerance for finding the time of intersection
// Scale time upper bound (t1) until an intersect
float h; // arbitrary name
do
{
t1 *= t_scale;
Vector2 dxy = m_planet.NextPosition2d(planet_angle + t1 * planet_angle_speed) - ship_pos;
// float dx = orbit_x_radius * Mathf.Cos(planet_angle + t1 * planet_angle_speed) - ship_pos.x;
// float dy = orbit_y_radius * Mathf.Sin(planet_angle + t1 * planet_angle_speed) - ship_pos.y;
// float d2 = dx * dx + dy * dy;
float d2 = dxy.sqrMagnitude;
float ship_d = t1 * ship_speed;
float ship_d2 = ship_d * ship_d;
h = d2 - ship_d2;
} while (h > 0.0f);
// Bisect the search interval until its length is smaller than t_eps
float t_mid;
while (t1 - t0 > t_eps)
{
t_mid = 0.5f * (t0 + t1);
Vector2 dxy = m_planet.NextPosition2d((planet_angle + t_mid * planet_angle_speed)) - ship_pos;
// float dx = orbit_x_radius * Mathf.Cos((planet_angle + t_mid * planet_angle_speed) * Mathf.Deg2Rad) - ship_pos.x;
// float dy = orbit_y_radius * Mathf.Sin((planet_angle + t_mid * planet_angle_speed) * Mathf.Deg2Rad) - ship_pos.y;
// float d2 = dx * dx + dy * dy;
float d2 = dxy.sqrMagnitude;
float ship_d = t_mid * ship_speed;
float ship_d2 = ship_d * ship_d;
float h_mid = d2 - ship_d2;
if (h_mid > 0.0f)
{
t0 = t_mid;
}
else
{
t1 = t_mid;
}
}
// Get the position of the planet relative to the ship's starting position at the time of intersection
float intersect_t = 0.5f * (t0 + t1);
Vector2 intersect_dxy = m_planet.NextPosition2d((planet_angle + intersect_t * planet_angle_speed)) - ship_pos;
float intersect_length = intersect_dxy.magnitude;
// float intersect_dx = orbit_x_radius * Mathf.Cos((planet_angle * Mathf.Deg2Rad + intersect_t * planet_angle_speed)* Mathf.Deg2Rad) - ship_pos.x;
// float intersect_dy = orbit_y_radius * Mathf.Sin((planet_angle * Mathf.Deg2Rad + intersect_t * planet_angle_speed) * Mathf.Deg2Rad) - ship_pos.y;
// float intersect_length = Mathf.Sqrt(intersect_dx * intersect_dx + intersect_dy * intersect_dy);
Vector3 ship_heading;
if (intersect_length > 0.0f)
{
Vector2 intersect = intersect_dxy / intersect_length;
ship_heading = new Vector3(intersect.x, intersect.y, 0.0f);
}
else
{
ship_heading = new Vector3(0.0f, 0.0f, 0.0f);
}
return(ship_heading);
}