/** Clamps the velocity to the max speed and optionally the forwards direction. * \param velocity Desired velocity of the character. In world units per second. * \param maxSpeed Max speed of the character. In world units per second. * \param slowdownFactor Value between 0 and 1 which determines how much slower the character should move than normal. * Normally 1 but should go to 0 when the character approaches the end of the path. * \param slowWhenNotFacingTarget Prevent the velocity from being too far away from the forward direction of the character * and slow the character down if the desired velocity is not in the same direction as the forward vector. * \param forward Forward direction of the character. Used together with the \a slowWhenNotFacingTarget parameter. * * Note that all vectors are 2D vectors, not 3D vectors. * * \returns The clamped velocity in world units per second. */ public static Vector2 ClampVelocity(Vector2 velocity, float maxSpeed, float slowdownFactor, bool slowWhenNotFacingTarget, Vector2 forward) { // Max speed to use for this frame var currentMaxSpeed = maxSpeed * slowdownFactor; // Check if the agent should slow down in case it is not facing the direction it wants to move in if (slowWhenNotFacingTarget && (forward.x != 0 || forward.y != 0)) { float currentSpeed; var normalizedVelocity = VectorMath.Normalize(velocity.ToPFV2(), out currentSpeed); float dot = Vector2.Dot(normalizedVelocity.ToUnityV2(), forward); // Lower the speed when the character's forward direction is not pointing towards the desired velocity // 1 when velocity is in the same direction as forward // 0.2 when they point in the opposite directions float directionSpeedFactor = Mathf.Clamp(dot + 0.707f, 0.2f, 1.0f); currentMaxSpeed *= directionSpeedFactor; currentSpeed = Mathf.Min(currentSpeed, currentMaxSpeed); // Angle between the forwards direction of the character and our desired velocity float angle = Mathf.Acos(Mathf.Clamp(dot, -1, 1)); // Clamp the angle to 20 degrees // We cannot keep the velocity exactly in the forwards direction of the character // because we use the rotation to determine in which direction to rotate and if // the velocity would always be in the forwards direction of the character then // the character would never rotate. // Allow larger angles when near the end of the path to prevent oscillations. angle = Mathf.Min(angle, (20f + 180f * (1 - slowdownFactor * slowdownFactor)) * Mathf.Deg2Rad); float sin = Mathf.Sin(angle); float cos = Mathf.Cos(angle); // Determine if we should rotate clockwise or counter-clockwise to move towards the current velocity sin *= Mathf.Sign(normalizedVelocity.x * forward.y - normalizedVelocity.y * forward.x); // Rotate the #forward vector by #angle radians // The rotation is done using an inlined rotation matrix. // See https://en.wikipedia.org/wiki/Rotation_matrix return(new Vector2(forward.x * cos + forward.y * sin, forward.y * cos - forward.x * sin) * currentSpeed); } else { return(Vector2.ClampMagnitude(velocity, currentMaxSpeed)); } }