Rem	bbdoc: Face a target.	about:	given a target position, this Method rotates the entity's heading and	side vectors by an amount Not greater than m_dMaxTurnRate Until it	directly faces the target.	returns True when the heading is facing in the desired direction	EndRem	Method RotateHeadingToFacePosition:Byte(target:Vector2D)		Local toTarget:Vector2D = SubtractVector(target, position)		toTarget.Normalize()		  		Local dot:Double = heading.DOT(toTarget);  		'//some compilers lose acurracy so the value is clamped To ensure it  		'//remains valid For the ACos  		'Clamp(dot, -1, 1);  		'//first determine the angle between the heading vector And the target  		Local angle:Double = ACos(dot)  		'//Return True If the player is facing the target  		If angle < 0.00001 Then Return True  		'//clamp the amount To turn To the Max turn rate  		If angle > maxTurnRate Then angle = maxTurnRate;    		'//The Next few lines use a rotation matrix To rotate the player's heading  		'//vector accordingly		Local RotationMatrix:C2DMatrix = New C2DMatrix  				' TODO:  		'//notice how the direction of rotation has To be determined when creating  		'//the rotation matrix		RotationMatrix.Rotate(angle * heading.Sign(toTarget))	  		RotationMatrix.TransformVector2D(heading)  		RotationMatrix.TransformVector2D(velocity)  		'//finally recreate m_vSide  		side = heading.CreateRightNormal()  		Return False	End Method

	Rem	bbdoc:  Updates the vehicle's position from a series of steering behaviors	EndRem	Method Update(time_elapsed:Double)		'DebugLog "time_elapsed="+time_elapsed		'//update the time elapsed		timeElapsed = time_elapsed;				'//keep a record of its old position so we can update its cell later		'//in this Method		Local OldPos:Vector2D = GetPosition();				Local SteeringForce:Vector2D = Null				'//calculate the combined force from each steering behavior in the 		'//vehicle's list		SteeringForce = steeringb.Calculate();		'DebugLog "sf.x="+SteeringForce.X + " sf.y="+SteeringForce.Y+" sf.l="+SteeringForce.length()				'--------------------------------------		' I THINK THE CHANGE SHOUDL HAPPEN HERE		'--------------------------------------				'//Acceleration = Force/Mass		Local acceleration:Vector2D = SteeringForce.divide(mass)		'DebugLog "a.x="+acceleration.X + " a.y="+acceleration.Y+" a.l="+acceleration.length()				'//update velocity		velocity.Add(acceleration.Multiply(time_elapsed))				'//make sure vehicle does Not exceed maximum velocity		velocity.Truncate(maxSpeed);		'DebugLog "v.x="+velocity.X + " v.y="+velocity.Y+" v.l="+velocity.length()				'//update the position		position.Add(velocity.MultiplyCopy(time_elapsed))				'//update the heading If the vehicle has a non zero velocity		If velocity.LengthSquared() > 0.00000001 Then			heading = Vec2DNormalize(velocity);			side = heading.CreateRightNormal();		EndIf				'//EnforceNonPenetrationConstraint(this, World()->Agents());				'//treat the screen as a toroid		'WrapAround(m_vPos, m_pWorld->cxClient(), m_pWorld->cyClient());				'//update the vehicle's current cell if space partitioning is turned on		If steeringb.IsSpacePartitioningOn() Then'TODO			gworld.CellSpace().UpdateEntity(Self, OldPos);		EndIf				If IsSmoothingOn() Then			smoothedHeading = headingSmoother.Update(heading)		EndIf	End Method

Quote: Original post by Timkin
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// Helper functionsVector2D lerp(const Vector2D& a, const Vector2D& b, float t){   return (1 - t) * a + t * b;}Vector2D slerp(const Vector2D& a, const Vector2D& b, float t){   // precondition: a and b are on a circle of radius r   float s = acos(a.Dot(b) / (a.Length() * b.Length()));    return a*sin((1-t)*s)/sin(s) + b*sin(t*s)/sin(s);}// ... // inside Update(...)SteeringForce = m_pSteering->Calculate();Vector2D acceleration = SteeringForce / m_dMass;Vector2D NewVelocity = m_vVelocity + acceleration; float angle = acos(m_vVelocity.Dot(NewVelocity) / (m_vVelocity.Length() * NewVelocity.Length())); // Check against max turn rate (in radians/sec)if(angle > MaxTurnRate){  // Perform some clever interpolations to get an acceleration that satisfies  // the maximum turn rate  Vector2D OldV2 = Vec2DNormalize(NewVelocity) * m_vVelocity.Length();  Vector2D NewV1 = Vec2DNormalize(m_vVelocity) * NewVelocity.Length();  float t = MaxTurnRate / angle;   Vector2D MaxV1 = slerp(m_vVelocity, OldV2, t);  Vector2D MaxV2 = slerp(NewV1, NewVelocity, t);  acceleration = lerp(MaxV1, MaxV2, t) - m_vVelocity;} m_vVelocity += acceleration * time_elapsed; // continue as before

Quote:
the velocity vector of the vehicle in this timestep (vNow) and the the velocity in the previous (vPrev) can be thought of as two hands on a watch. To constrain the angle between the vectors by maxTurnRate follow these steps:

speed = the length of vNow

normPrev = Normilize(vPrev)

amountOfTurn = calculate angle between VNow and vPrev

Rotate normPrev about the origin by the smaller of maxTurnRate or amountOfTurn

multiply normPrev by speed

However, some of the steering behaviors may then perform less well since they are not taking maxTurnRate into consideration. Arrive, in particular, may have difficulty stopping.

Quote: Original post by Zipster
These constants can be modified to change the locomotion behavior, but right now they're calibrated for a 0.5 transient response time and no heading oscillation or overshoot.