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Slerping the Kool Aid - Help!


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#1 Nick Joseph   Members   -  Reputation: 116

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Posted 25 January 2013 - 08:13 PM

After 16 hours I have nowhere to turn and have become desperate to so I'm going to be posting quite a bit of code here, just warning ya.  I can't seem to wrap my head around slerping an object...

 

The following code allows me to immediately rotate my AI actor to face his next patrol point...

 

 

TransformComponent transformComponent = _actor.GetComponent<TransformComponent>();
 
            Vector3 position = transformComponent.Transform.Translation;
 
            Vector3 currentPatrolPoint = _patrolPoints.ElementAt(_currentPatrolPoint);
 
            Vector3 difference = (currentPatrolPoint - position);
 
            if (_hasFinishedRotating == false)
            {
                Vector3 lookAtDirection = Vector3.Normalize(difference);
                
                Vector3 forward = Vector3.Normalize(transformComponent.Transform.Forward);
 
                float forwardDot = (float)Math.Round(
                    Vector3.Dot(
                        forward,
                        lookAtDirection),
                    DOT_PRECISION);
 
                if (forwardDot != 1)
                {
                    Vector3 rotationAxis = Vector3.Cross(lookAtDirection, forward);
                        
                    float rotationAngle = MathUtilities.GetUnsignedAngle(
                        forward,
                        lookAtDirection);
 
                    Vector3 right = Vector3.Normalize(transformComponent.Transform.Right);
 
                    float rightDot = (float)Math.Round(
                        Vector3.Dot(
                            right,
                            lookAtDirection),
                        DOT_PRECISION);
 
                    if (rightDot > 0)
                    {
                        rotationAngle *= -1;
                    }
 
                    Matrix rotation = transformComponent.Transform;
 
                    rotation *= Matrix.CreateFromAxisAngle(
                        rotationAxis,
                        rotationAngle);
 
                    rotation.Translation = position;
 
                    PhysicsComponent physicsComponent = _actor.GetComponent<PhysicsComponent>();
 
                    physicsComponent.KinematicMove(rotation);
                }
                else
                {
                    _hasFinishedRotating = true;
                }
            }

 

...but now I want him to SLERP his rotation to make it more realistic.  I'm definitely not an expert but from what I understand and read the following should get me there (NOTE: I do know that SLERP won't get me 100% there so I need some type of threshold but even after trying that I still see whacky results so the piece I'm not understanding has to be here somewhere...)

 

 

TransformComponent transformComponent = _actor.GetComponent<TransformComponent>();
 
            Vector3 position = transformComponent.Transform.Translation;
 
            Vector3 currentPatrolPoint = _patrolPoints.ElementAt(_currentPatrolPoint);
 
            Vector3 difference = (currentPatrolPoint - position);
 
            if (_hasFinishedRotating == false)
            {
                Vector3 lookAtDirection = Vector3.Normalize(difference);
                
                Vector3 forward = Vector3.Normalize(transformComponent.Transform.Forward);
 
                float forwardDot = (float)Math.Round(
                    Vector3.Dot(
                        forward,
                        lookAtDirection),
                    DOT_PRECISION);
 
                if (forwardDot != 1)
                {
                    Vector3 rotationAxis = Vector3.Cross(lookAtDirection, forward);
 
                    float rotationAngle = MathUtilities.GetUnsignedAngle(
                        forward,
                        lookAtDirection);
 
                    Vector3 right = Vector3.Normalize(transformComponent.Transform.Right);
 
                    float rightDot = (float)Math.Round(
                        Vector3.Dot(
                            right,
                            lookAtDirection),
                        DOT_PRECISION);
 
                    if (rightDot > 0)
                    {
                        rotationAngle *= -1;
                    }
 
                    Quaternion qStart = Quaternion.CreateFromRotationMatrix(transformComponent.Transform);
 
                    Quaternion qEnd = Quaternion.CreateFromAxisAngle(rotationAxis, rotationAngle);
 
                    Quaternion qSlerp = Quaternion.Slerp(
                        qStart,
                        qEnd,
                        (float)gameTime.ElapsedGameTime.Milliseconds / 1000f);
 
                    Matrix rotation = Matrix.CreateFromQuaternion(qSlerp);
 
                    rotation.Translation = position;
 
                    PhysicsComponent physicsComponent = _actor.GetComponent<PhysicsComponent>();
 
                    physicsComponent.KinematicMove(rotation);
                }
                else
                {
                    _hasFinishedRotating = true;
                }
            }
 
...but it looks like my actor only rotates maybe a little more than half way than hangs.  If anyone has any ideas, suggestions, etc on how I can make this code better or if you happen to spot the problem (gold star!) I'd really appreciate it.
 
Thanks!


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#2 eppo   Crossbones+   -  Reputation: 2298

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Posted 26 January 2013 - 04:53 AM

Quaternion.CreateFromAxisAngle(rotationAxis, rotationAngle) calculates the difference in orientation between forward and lookAt, but when slerping you treat is as an absolute orientation.

Quaternion qSlerp = Quaternion.Slerp(qStart, qEnd, (float)gameTime.ElapsedGameTime.Milliseconds / 1000f);

should be:

Quaternion qSlerp = Quaternion.Slerp(qStart, qStart * qEnd, (float)gameTime.ElapsedGameTime.Milliseconds / 1000f);

I don't know the exact implementation of these math functions, but you should check whether CreateFromAxisAngle() requires a normalized vector as input (which rotationAxis = Vector3.Cross(lookAtDirection, forward) likely isn't).

MathUtilities.GetUnsignedAngle() seems to throw out the sign of the angle, but in the code that follows you recalculate it:

Vector3 right = Vector3.Normalize(transformComponent.Transform.Right);

float rightDot = (float)Math.Round()...
if (rightDot > 0){ rotationAngle *= -1; }

So, you should either use GetSignedAngle() (if it exists) or use angle = acos(forwardDot).

Edited by eppo, 26 January 2013 - 04:55 AM.


#3 Nick Joseph   Members   -  Reputation: 116

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Posted 26 January 2013 - 11:14 AM

I don't even know what to say, every point you made was valid.  Thank you so much!  To anyone interested here's the updated code (though it's not perfect, the rotation slows down as the actor gets closer to his desired rotation on account of the SLERP calculations so that'll be the next thing I look into)...

 

 

TransformComponent transformComponent = _actor.GetComponent<TransformComponent>();
 
            Vector3 position = transformComponent.Transform.Translation;
 
            Vector3 currentPatrolPoint = _patrolPoints.ElementAt(_currentPatrolPoint);
 
            Vector3 difference = (currentPatrolPoint - position);
 
            if (_hasFinishedRotating == false)
            {
                Vector3 lookAtDirection = Vector3.Normalize(difference);
                
                Vector3 forward = Vector3.Normalize(transformComponent.Transform.Forward);
 
                float forwardDot = (float)Math.Round(
                    Vector3.Dot(
                        forward,
                        lookAtDirection),
                    DOT_PRECISION);
 
                if (forwardDot != 1)
                {
                    Vector3 rotationAxis = Vector3.Normalize(
                        Vector3.Cross(
                            lookAtDirection, 
                            forward));
 
                    float rotationAngle = MathUtilities.GetUnsignedAngle(
                        forward,
                        lookAtDirection);
 
                    Vector3 right = Vector3.Normalize(transformComponent.Transform.Right);
 
                    float rightDot = (float)Math.Round(
                        Vector3.Dot(
                            right,
                            lookAtDirection),
                        DOT_PRECISION);
 
                    if (rightDot > 0)
                    {
                        rotationAngle *= -1;
                    }
 
                    float slerpAmount = (float)gameTime.ElapsedGameTime.Milliseconds / 1000f;
 
                    if (forwardDot > .98f)
                    {
                        slerpAmount = 1.0f;
                    }
 
                    Quaternion qStart = Quaternion.CreateFromRotationMatrix(transformComponent.Transform);
 
                    Quaternion qEnd = Quaternion.CreateFromAxisAngle(rotationAxis, rotationAngle);
 
                    Quaternion qSlerp = Quaternion.Slerp(
                        qStart,
                        qStart * qEnd,
                        slerpAmount);
 
                    Matrix rotation = Matrix.CreateFromQuaternion(qSlerp);
 
                    rotation.Translation = position;
 
                    PhysicsComponent physicsComponent = _actor.GetComponent<PhysicsComponent>();
 
                    physicsComponent.KinematicMove(rotation);
                }
                else
                {
                    _hasFinishedRotating = true;
                }
            }


#4 Nick Joseph   Members   -  Reputation: 116

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Posted 26 January 2013 - 11:56 AM

I fixed the "slow down" by keeping track of the slerp amount in a private variable and incrementing it...

 

 

_slerpAmount += (float)gameTime.ElapsedGameTime.Milliseconds / 3000f;
 
                    Quaternion qStart = Quaternion.CreateFromRotationMatrix(transformComponent.Transform);
 
                    Quaternion qEnd = Quaternion.CreateFromAxisAngle(rotationAxis, rotationAngle);
 
                    Quaternion qSlerp = Quaternion.Slerp(
                        qStart,
                        qStart * qEnd,
                        _slerpAmount);





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