// Token: 0x06002966 RID: 10598 RVA: 0x001C0DF0 File Offset: 0x001BEFF0
public static Vector2 CalculateAccelerationToReachPoint(Vector2 deltaPosition, Vector2 targetVelocity, Vector2 currentVelocity, float forwardsAcceleration, float rotationSpeed, float maxSpeed, Vector2 forwardsVector)
{
if (forwardsAcceleration <= 0f)
{
return(Vector2.zero);
}
float magnitude = currentVelocity.magnitude;
float a = magnitude * rotationSpeed * 0.0174532924f;
a = Mathf.Max(a, forwardsAcceleration);
deltaPosition = VectorMath.ComplexMultiplyConjugate(deltaPosition, forwardsVector);
targetVelocity = VectorMath.ComplexMultiplyConjugate(targetVelocity, forwardsVector);
currentVelocity = VectorMath.ComplexMultiplyConjugate(currentVelocity, forwardsVector);
float num = 1f / (forwardsAcceleration * forwardsAcceleration);
float num2 = 1f / (forwardsAcceleration * forwardsAcceleration);
if (targetVelocity == Vector2.zero)
{
float num3 = 0.01f;
float num4 = 10f;
while (num4 - num3 > 0.01f)
{
float num5 = (num4 + num3) * 0.5f;
Vector2 vector = (6f * deltaPosition - 4f * num5 * currentVelocity) / (num5 * num5);
Vector2 a2 = 6f * (num5 * currentVelocity - 2f * deltaPosition) / (num5 * num5 * num5);
Vector2 vector2 = vector + a2 * num5;
if (vector.x * vector.x * num + vector.y * vector.y * num2 > 1f || vector2.x * vector2.x * num + vector2.y * vector2.y * num2 > 1f)
{
num3 = num5;
}
else
{
num4 = num5;
}
}
Vector2 vector3 = (6f * deltaPosition - 4f * num4 * currentVelocity) / (num4 * num4);
vector3.y *= 2f;
float num6 = vector3.x * vector3.x * num + vector3.y * vector3.y * num2;
if (num6 > 1f)
{
vector3 /= Mathf.Sqrt(num6);
}
return(VectorMath.ComplexMultiply(vector3, forwardsVector));
}
float num7;
Vector2 a3 = VectorMath.Normalize(targetVelocity, out num7);
float magnitude2 = deltaPosition.magnitude;
Vector2 vector4 = ((deltaPosition - a3 * Math.Min(0.5f * magnitude2 * num7 / (magnitude + num7), maxSpeed * 1.5f)).normalized * maxSpeed - currentVelocity) * 10f;
float num8 = vector4.x * vector4.x * num + vector4.y * vector4.y * num2;
if (num8 > 1f)
{
vector4 /= Mathf.Sqrt(num8);
}
return(VectorMath.ComplexMultiply(vector4, forwardsVector));
}
/** Calculate an acceleration to move deltaPosition units and get there with approximately a velocity of targetVelocity */
public static Vector2 CalculateAccelerationToReachPoint(Vector2 deltaPosition, Vector2 targetVelocity, Vector2 currentVelocity, float forwardsAcceleration, float rotationSpeed, float maxSpeed, Vector2 forwardsVector)
{
// Guard against div by zero
if (forwardsAcceleration <= 0)
{
return(Vector2.zero);
}
float currentSpeed = currentVelocity.magnitude;
// Convert rotation speed to an acceleration
// See https://en.wikipedia.org/wiki/Centripetal_force
var sidewaysAcceleration = currentSpeed * rotationSpeed * Mathf.Deg2Rad;
// To avoid weird behaviour when the rotation speed is very low we allow the agent to accelerate sideways without rotating much
// if the rotation speed is very small. Also guards against division by zero.
sidewaysAcceleration = Mathf.Max(sidewaysAcceleration, forwardsAcceleration);
sidewaysAcceleration = forwardsAcceleration;
// Transform coordinates to local space where +X is the forwards direction
// This is essentially equivalent to Transform.InverseTransformDirection.
deltaPosition = VectorMath.ComplexMultiplyConjugate(deltaPosition.ToPFV2(), forwardsVector.ToPFV2()).ToUnityV2();
targetVelocity = VectorMath.ComplexMultiplyConjugate(targetVelocity.ToPFV2(), forwardsVector.ToPFV2()).ToUnityV2();
currentVelocity = VectorMath.ComplexMultiplyConjugate(currentVelocity.ToPFV2(), forwardsVector.ToPFV2()).ToUnityV2();
float ellipseSqrFactorX = 1 / (forwardsAcceleration * forwardsAcceleration);
float ellipseSqrFactorY = 1 / (sidewaysAcceleration * sidewaysAcceleration);
// If the target velocity is zero we can use a more fancy approach
// and calculate a nicer path.
// In particular, this is the case at the end of the path.
if (targetVelocity == Vector2.zero)
{
// Run a binary search over the time to get to the target point.
float mn = 0.01f;
float mx = 10;
while (mx - mn > 0.01f)
{
var time = (mx + mn) * 0.5f;
// Given that we want to move deltaPosition units from out current position, that our current velocity is given
// and that when we reach the target we want our velocity to be zero. Also assume that our acceleration will
// vary linearly during the slowdown. Then we can calculate what our acceleration should be during this frame.
//{ t = time
//{ deltaPosition = vt + at^2/2 + qt^3/6
//{ 0 = v + at + qt^2/2
//{ solve for a
// a = acceleration vector
// q = derivative of the acceleration vector
var a = (6 * deltaPosition - 4 * time * currentVelocity) / (time * time);
var q = 6 * (time * currentVelocity - 2 * deltaPosition) / (time * time * time);
// Make sure the acceleration is not greater than our maximum allowed acceleration.
// If it is we increase the time we want to use to get to the target
// and if it is not, we decrease the time to get there faster.
// Since the acceleration is described by acceleration = a + q*t
// we only need to check at t=0 and t=time.
// Note that the acceleration limit is described by an ellipse, not a circle.
var nextA = a + q * time;
if (a.x * a.x * ellipseSqrFactorX + a.y * a.y * ellipseSqrFactorY > 1.0f || nextA.x * nextA.x * ellipseSqrFactorX + nextA.y * nextA.y * ellipseSqrFactorY > 1.0f)
{
mn = time;
}
else
{
mx = time;
}
}
var finalAcceleration = (6 * deltaPosition - 4 * mx * currentVelocity) / (mx * mx);
// Boosting
{
// The trajectory calculated above has a tendency to use very wide arcs
// and that does unfortunately not look particularly good in some cases.
// Here we amplify the component of the acceleration that is perpendicular
// to our current velocity. This will make the agent turn towards the
// target quicker.
// How much amplification to use. Value is unitless.
const float Boost = 1;
finalAcceleration.y *= 1 + Boost;
// Clamp the velocity to the maximum acceleration.
// Note that the maximum acceleration constraint is shaped like an ellipse, not like a circle.
float ellipseMagnitude = finalAcceleration.x * finalAcceleration.x * ellipseSqrFactorX + finalAcceleration.y * finalAcceleration.y * ellipseSqrFactorY;
if (ellipseMagnitude > 1.0f)
{
finalAcceleration /= Mathf.Sqrt(ellipseMagnitude);
}
}
return(VectorMath.ComplexMultiply(finalAcceleration.ToPFV2(), forwardsVector.ToPFV2()).ToUnityV2());
}
else
{
// Here we try to move towards the next waypoint which has been modified slightly using our
// desired velocity at that point so that the agent will more smoothly round the corner.
// How much to strive for making sure we reach the target point with the target velocity. Unitless.
const float TargetVelocityWeight = 0.5f;
// Limit to how much to care about the target velocity. Value is in seconds.
// This prevents the character from moving away from the path too much when the target point is far away
const float TargetVelocityWeightLimit = 1.5f;
float targetSpeed;
var normalizedTargetVelocity = VectorMath.Normalize(targetVelocity.ToPFV2(), out targetSpeed);
var distance = deltaPosition.magnitude;
var targetPoint = deltaPosition.ToPFV2() - normalizedTargetVelocity * System.Math.Min(TargetVelocityWeight * distance * targetSpeed / (currentSpeed + targetSpeed), maxSpeed * TargetVelocityWeightLimit);
// How quickly the agent will try to reach the velocity that we want it to have.
// We need this to prevent oscillations and jitter which is what happens if
// we let the constant go towards zero. Value is in seconds.
const float TimeToReachDesiredVelocity = 0.1f;
// TODO: Clamp to ellipse using more accurate acceleration (use rotation speed as well)
var finalAcceleration = (targetPoint.normalized * maxSpeed - currentVelocity.ToPFV2()) * (1f / TimeToReachDesiredVelocity);
// Clamp the velocity to the maximum acceleration.
// Note that the maximum acceleration constraint is shaped like an ellipse, not like a circle.
float ellipseMagnitude = finalAcceleration.x * finalAcceleration.x * ellipseSqrFactorX + finalAcceleration.y * finalAcceleration.y * ellipseSqrFactorY;
if (ellipseMagnitude > 1.0f)
{
finalAcceleration /= Mathf.Sqrt(ellipseMagnitude);
}
return(VectorMath.ComplexMultiply(finalAcceleration, forwardsVector.ToPFV2()).ToUnityV2());
}
}