---

<!-- Event Graph ROUTE Table shows event connections -->
 
<!-- Index for DEF nodes: EFFS, LastNode, ScreenPositionDamper_OrientationChaser, ScreenPositionDamper_PlacementChaser, ScreenPositionDamper_Position2fChaser, ScreenPositionDamper_PositionChaser, Timer_PositionDamper, Tmer_OrientationChaser, Tmer_PlacementChaser, Tmer_Position2fChaser, Tmer_PositionChaser, Worker

---

Index for ProtoDeclare definitions: EFFS, OrientationChaser, PlacementChaser, Position2fChaser, PositionChaser, PositionDamper

---

          
ecmascript:

function initialize()
{
    CheckInit();
}

function CheckInit()
{
    if(!bInitialized)
    {
        bInitialized= true;  // Init() may call other functions that call CheckInit(). In that case it's better the flag is already set, otherwise an endless loop would occur.
        Init();
    }
}

function Init()
{
    destination= initial_destination;

    Buffer.length= cNumSupports;

    Buffer[0]= initial_destination;
    for(var C= 1; C<Buffer.length; C++ )
        Buffer[C]= initial_value;

    previousValue= initial_value;

    cStepTime= duration / cNumSupports;
}

function set_destination(Dest, Now)
{
    CheckInit();

    destination= Dest;
    // Somehow we assign to Buffer[-1] and wait untill this gets shifted into the real buffer.
    // Would we assign to Buffer[0] instead, we'd have no delay, but this would create a jump in the
    // output because Buffer[0] is associated with a value in the past.

    UpdateBuffer(Now);
}

function Tick(Now)
{
    CheckInit();

    if(!BufferEndTime)
    {
        BufferEndTime= Now; // first event we received, so we are in the initialization phase.

        value_changed= initial_value;
        return;
    }

    var Frac= UpdateBuffer(Now);
    // Frac is a value in   0 <= Frac < 1.

    // Now we can calculate the output.
    // This means we calculate the delta between each entry in Buffer and its previous
    // entries, calculate the step response of each such step and add it to form the output.

    // The oldest vaule Buffer[Buffer.length - 1] needs some extra thought, because it has
    // no previous value. More exactly, we haven't stored a previous value anymore.
    // However, the step response of that missing previous value has already reached its
    // destination, so we can - would we have that previous value - use this as a start point
    // for adding the step responses.
    // Actually UpdateBuffer(.) maintains this value in

    var Output= previousValue;

    var DeltaIn= Buffer[Buffer.length - 1].subtract(previousValue);

    var DeltaOut= DeltaIn.multiply(StepResponse((Buffer.length - 1 + Frac) * cStepTime));

    Output= Output.add(DeltaOut);

    for(var C= Buffer.length - 2; C>=0; C-- )
    {
        var DeltaIn= Buffer[C].subtract(Buffer[C + 1]);

        var DeltaOut= DeltaIn.multiply(StepResponse((C + Frac) * cStepTime));

        Output= Output.add(DeltaOut);
    }
    if(Output != value_changed)
        value_changed= Output;
}

function UpdateBuffer(Now)
{
    var Frac= (Now - BufferEndTime) / cStepTime;
    // is normally < 1. When it has grown to be larger than 1, we have to shift the array because the step response
    // of the oldest entry has already reached its destination, and it's time for a newer entry.
    // has already reached it
    // In the case of a very low frame rate, or a very short cStepTime we may need to shift by more than one entry.

    if(Frac >= 1)
    {
        var NumToShift= Math.floor(Frac);
        Frac-= NumToShift;

        if(NumToShift < Buffer.length)
        {   // normal case.

            previousValue= Buffer[Buffer.length - NumToShift];

            for(var C= Buffer.length - 1; C>=NumToShift; C-- )
                Buffer[C]= Buffer[C - NumToShift];

            for(var C= 0; C<NumToShift; C++ )
            {
                // Hmm, we have a destination value, but don't know how it has
                // reached the current state.
                // Therefore we do a linear interpolation from the latest value in the buffer to destination.

                var Alpha= C / NumToShift;

                Buffer[C]= Buffer[NumToShift].multiply(Alpha).add(destination.multiply((1 - Alpha)));
            }
        }else
        {
            // degenerated case:
            //
            // We have a _VERY_ low frame rate...
            // we can only guess how we should fill the array.
            // Maybe we could write part of a linear interpolation
            // from Buffer[0] to destination, that goes from BufferEndTime to Now
            // (possibly only the end of the interpolation is to be written),
            // but if we rech here we are in a very degenerate case...
            // Thus we just write destination to the buffer.

            previousValue= NumToShift == Buffer.length? Buffer[0] : destination;

            for(var C= 0; C<Buffer.length; C++ )
                Buffer[C]= destination;
        }

        BufferEndTime+= NumToShift * cStepTime;
    }
    return Frac;
}

function StepResponse(t)
{
    if(t < 0)
        return 0;

    if(t > duration)
        return 1;

    // When optimizing for speed, the above two if(.) cases can be omitted,
    // as this funciton will not be called for values outside of 0..duration.

    return StepResponseCore(t / duration);
}

// This function defines the shape of how the output responds to the input.
// It must accept values for T in the range 0 <= T <= 1.
// In order to create a smooth animation, it should return 0 for T == 0,
// 1 for T == 1 and be sufficient smooth in the range 0 <= T <= 1.

// It should be optimized for speed, in order for high performance. It's
// executed Buffer.length + 1 times each simulation tick.

function StepResponseCore(T)
{
    return .5 - .5 * Math.cos(T * Math.PI);
}

// The following functions are not used. They provide other responses (for fun).
function StepResponseCoreF(T)
{
    var cTau= .3;
    var cFrequency= 2.5;
    return 1 - Math.cos(T * 2 * Math.PI * cFrequency) * Math.exp(-T / cTau) * (1 - T);
//      return 1 - Math.cos(T * 2 * Math.PI * cFrequency) * Math.exp(-T / cTau) * (1 - T) * (1 - T);
//      return 1 - Math.cos(T * 2 * Math.PI * cFrequency) * Math.exp(-T / cTau) * (.5 + .5 * Math.cos(T * Math.PI));
//      return 1 - Math.cos(T * 2 * Math.PI * cFrequency) * Math.exp(-T / cTau) * (.5 + .5 * Math.cos(T * Math.PI))* (.5 + .5 * Math.cos(T * Math.PI));
}


function StepResponseCoreE(T)
{
    var A= .5 - .5 * Math.cos(T * Math.PI);

    var cFrequency= 2.5;
    var B= 1 - Math.cos(T * 2 * Math.PI * cFrequency) * Math.sin(Math.sqrt(1 - T) * Math.PI/2);

    return A * .8 + B * .2;
}


function StepResponseCoreD(T)
{
    var A= .5 - .5 * Math.cos(T * Math.PI);

    var cFrequency= 2.5;
    var B= 1 - Math.cos(T * 2 * Math.PI * cFrequency) * Math.sin((1 - T) * Math.PI/2);

    return A * .8 + B * .2;
}

function StepResponseCoreC(T)
{
    var A= .5 - .5 * Math.cos(T * Math.PI);

    var cTau= .3;
    var cFrequency= 5;
    var B= 1 - Math.cos(T * 2 * Math.PI * cFrequency) * Math.exp(-T / cTau) * (1 - T);

    return A * .8 + B * .2;
}

function StepResponseCoreB(T)
{
    var A= .5 - .5 * Math.cos(T * Math.PI);

    var cTau= .3;
    var cFrequency= 5;
    var B= 1 - Math.cos(T * 2 * Math.PI * cFrequency) /** Math.exp(-T / cTau)*/ * (1 - T);

    return A * .8 + B * .2;
}
function StepResponseCoreA(T)
{
    var A= .5 - .5 * Math.cos(T * Math.PI);

    var cTau= .3;
    var cFrequency= 5;
    var B= 1 - Math.cos(T * 2 * Math.PI * cFrequency) /** Math.exp(-T / cTau)*/ * (1 - T);

    var Alpha= .2 * T;
    return A * (1 - Alpha) + B * Alpha;
}

        

          
ecmascript:

function initialize()
{
    CheckInit();
}

function CheckInit()
{
    if(!bInitialized)
    {
        bInitialized= true;  // Init() may call other functions that call CheckInit(). In that case it's better the flag is already set, otherwise an endless loop would occur.
        Init();
    }
}

function Init()
{
    destination= initial_destination;

    Buffer.length= cNumSupports;

    Buffer[0]= initial_destination;
    for(var C= 1; C<Buffer.length; C++ )
        Buffer[C]= initial_value;

    previousValue= initial_value;

    cStepTime= duration / cNumSupports;
}

function set_destination(Dest, Now)
{
    CheckInit();

    destination= Dest;
    // Somehow we assign to Buffer[-1] and wait untill this gets shifted into the real buffer.
    // Would we assign to Buffer[0] instead, we'd have no delay, but this would create a jump in the
    // output because Buffer[0] is associated with a value in the past.

    UpdateBuffer(Now);
}

function Tick(Now)
{
    CheckInit();

    if(!BufferEndTime)
    {
        BufferEndTime= Now; // first event we received, so we are in the initialization phase.

        value_changed= initial_value;
        return;
    }

    var Frac= UpdateBuffer(Now);
    // Frac is a value in   0 <= Frac < 1.

    // Now we can calculate the output.
    // This means we calculate the delta between each entry in Buffer and its previous
    // entries, calculate the step response of each such step and add it to form the output.

    // The oldest vaule Buffer[Buffer.length - 1] needs some extra thought, because it has
    // no previous value. More exactly, we haven't stored a previous value anymore.
    // However, the step response of that missing previous value has already reached its
    // destination, so we can - would we have that previous value - use this as a start point
    // for adding the step responses.
    // Actually UpdateBuffer(.) maintains this value in

    var Output= previousValue;

    var DeltaIn= previousValue.inverse().multiply(Buffer[Buffer.length - 1]);

    Output= Output.slerp(Output.multiply(DeltaIn), StepResponse((Buffer.length - 1 + Frac) * cStepTime));

    for(var C= Buffer.length - 2; C>=0; C-- )
    {
        var DeltaIn= Buffer[C + 1].inverse().multiply(Buffer[C]);

        Output= Output.slerp(Output.multiply(DeltaIn), StepResponse((C + Frac) * cStepTime));
    }


    if(Output != value_changed)
        value_changed= Output;
}

function UpdateBuffer(Now)
{
    var Frac= (Now - BufferEndTime) / cStepTime;
    // is normally < 1. When it has grown to be larger than 1, we have to shift the array because the step response
    // of the oldest entry has already reached its destination, and it's time for a newer entry.
    // has already reached it
    // In the case of a very low frame rate, or a very short cStepTime we may need to shift by more than one entry.

    if(Frac >= 1)
    {
        var NumToShift= Math.floor(Frac);
        Frac-= NumToShift;

        if(NumToShift < Buffer.length)
        {   // normal case.

            previousValue= Buffer[Buffer.length - NumToShift];

            for(var C= Buffer.length - 1; C>=NumToShift; C-- )
                Buffer[C]= Buffer[C - NumToShift];

            for(var C= 0; C<NumToShift; C++ )
            {
                // Hmm, we have a destination value, but don't know how it has
                // reached the current state.
                // Therefore we do a linear interpolation from the latest value in the buffer to destination.

                Buffer[C]= destination.slerp(Buffer[NumToShift], C / NumToShift);
            }
        }else
        {
            // degenerated case:
            //
            // We have a _VERY_ low frame rate...
            // we can only guess how we should fill the array.
            // Maybe we could write part of a linear interpolation
            // from Buffer[0] to destination, that goes from BufferEndTime to Now
            // (possibly only the end of the interpolation is to be written),
            // but if we rech here we are in a very degenerate case...
            // Thus we just write destination to the buffer.

            previousValue= NumToShift == Buffer.length? Buffer[0] : destination;

            for(var C= 0; C<Buffer.length; C++ )
                Buffer[C]= destination;
        }
        BufferEndTime+= NumToShift * cStepTime;
    }

return Frac;
}

function StepResponse(t)
{
    if(t < 0)
        return 0;

    if(t > duration)
        return 1;

    // When optimizing for speed, the above two if(.) cases can be omitted,
    // as this funciton will not be called for values outside of 0..duration.

     return StepResponseCore(t / duration);
}

// This function defines the shape of how the output responds to the input.
// It must accept values for T in the range 0 <= T <= 1.
// In order to create a smooth animation, it should return 0 for T == 0,
// 1 for T == 1 and be sufficient smooth in the range 0 <= T <= 1.

// It should be optimized for speed, in order for high performance. It's
// executed Buffer.length + 1 times each simulation tick.

function StepResponseCore(T)
{
    return .5 - .5 * Math.cos(T * Math.PI);
}

// The following functions are not used. They provide other responses (for fun).

function StepResponseCoreG(T)
{
    var cTau= .3;
    var cFrequency= 5;
    return 1 - Math.cos(T * 2 * Math.PI * cFrequency) * Math.exp(-T / cTau) * (.5 + .5 * Math.cos(T * Math.PI));
}

function StepResponseCoreF(T)
{
    var cTau= .3;
    var cFrequency= 2.5;
//      return 1 - Math.cos(T * 2 * Math.PI * cFrequency) * Math.exp(-T / cTau) * (1 - T);
//      return 1 - Math.cos(T * 2 * Math.PI * cFrequency) * Math.exp(-T / cTau) * (1 - T) * (1 - T);
//      return 1 - Math.cos(T * 2 * Math.PI * cFrequency) * Math.exp(-T / cTau) * (.5 + .5 * Math.cos(T * Math.PI));
//      return 1 - Math.cos(T * 2 * Math.PI * cFrequency) * Math.exp(-T / cTau) * (.5 + .5 * Math.cos(T * Math.PI))* (.5 + .5 * Math.cos(T * Math.PI));
}

function StepResponseCoreE(T)
{
    var A= .5 - .5 * Math.cos(T * Math.PI);

    var cFrequency= 2.5;
    var B= 1 - Math.cos(T * 2 * Math.PI * cFrequency) * Math.sin(Math.sqrt(1 - T) * Math.PI/2);

    return A * .8 + B * .2;
}

function StepResponseCoreD(T)
{
    var A= .5 - .5 * Math.cos(T * Math.PI);

    var cFrequency= 2.5;
    var B= 1 - Math.cos(T * 2 * Math.PI * cFrequency) * Math.sin((1 - T) * Math.PI/2);

    return A * .8 + B * .2;
}

function StepResponseCoreC(T)
{
    var A= .5 - .5 * Math.cos(T * Math.PI);

    var cTau= .3;
    var cFrequency= 5;
    var B= 1 - Math.cos(T * 2 * Math.PI * cFrequency) * Math.exp(-T / cTau) * (1 - T);

    return A * .8 + B * .2;
}

function StepResponseCoreB(T)
{
    var A= .5 - .5 * Math.cos(T * Math.PI);

    var cTau= .3;
    var cFrequency= 5;
    var B= 1 - Math.cos(T * 2 * Math.PI * cFrequency) /** Math.exp(-T / cTau)*/ * (1 - T);

    return A * .8 + B * .2;
}

function StepResponseCoreA(T)
{
    var A= .5 - .5 * Math.cos(T * Math.PI);
    var cTau= .3;
    var cFrequency= 5;
    var B= 1 - Math.cos(T * 2 * Math.PI * cFrequency) /** Math.exp(-T / cTau)*/ * (1 - T);
    var Alpha= .2 * T;
    return A * (1 - Alpha) + B * Alpha;
}

        

          
ecmascript:

function initialize()
{
    CheckInit();
}

function CheckInit()
{
    if(!bInitialized)
    {
        bInitialized= true;  // Init() may call other functions that call CheckInit(). In that case it's better the flag is already set, otherwise an endless loop would occur.
        Init();
    }
}

function Init()
{
    destination= initial_destination;

    Buffer.length= cNumSupports;

    Buffer[0]= initial_destination;
    for(var C= 1; C<Buffer.length; C++ )
        Buffer[C]= initial_value;

    previousValue= initial_value;

    cStepTime= duration / cNumSupports;
}

function set_destination(Dest, Now)
{
    CheckInit();

    destination= Dest;
    // Somehow we assign to Buffer[-1] and wait untill this gets shifted into the real buffer.
    // Would we assign to Buffer[0] instead, we'd have no delay, but this would create a jump in the
    // output because Buffer[0] is associated with a value in the past.

    UpdateBuffer(Now);
}

function Tick(Now)
{
    CheckInit();

    if(!BufferEndTime)
    {
        BufferEndTime= Now; // first event we received, so we are in the initialization phase.

        value_changed= initial_value;
        return;
    }

    var Frac= UpdateBuffer(Now);
    // Frac is a value in   0 <= Frac < 1.

    // Now we can calculate the output.
    // This means we calculate the delta between each entry in Buffer and its previous
    // entries, calculate the step response of each such step and add it to form the output.

    // The oldest vaule Buffer[Buffer.length - 1] needs some extra thought, because it has
    // no previous value. More exactly, we haven't stored a previous value anymore.
    // However, the step response of that missing previous value has already reached its
    // destination, so we can - would we have that previous value - use this as a start point
    // for adding the step responses.
    // Actually UpdateBuffer(.) maintains this value in

    var Output= previousValue;

    var DeltaIn= Buffer[Buffer.length - 1].subtract(previousValue);

    var DeltaOut= DeltaIn.multiply(StepResponse((Buffer.length - 1 + Frac) * cStepTime));

    Output= Output.add(DeltaOut);

    for(var C= Buffer.length - 2; C>=0; C-- )
    {
        var DeltaIn= Buffer[C].subtract(Buffer[C + 1]);

        var DeltaOut= DeltaIn.multiply(StepResponse((C + Frac) * cStepTime));

        Output= Output.add(DeltaOut);
    }


    if(Output != value_changed)
        value_changed= Output;
}

function UpdateBuffer(Now)
{
    var Frac= (Now - BufferEndTime) / cStepTime;
    // is normally < 1. When it has grown to be larger than 1, we have to shift the array because the step response
    // of the oldest entry has already reached its destination, and it's time for a newer entry.
    // has already reached it
    // In the case of a very low frame rate, or a very short cStepTime we may need to shift by more than one entry.

    if(Frac >= 1)
    {
        var NumToShift= Math.floor(Frac);
        Frac-= NumToShift;

        if(NumToShift < Buffer.length)
        {   // normal case.

            previousValue= Buffer[Buffer.length - NumToShift];

            for(var C= Buffer.length - 1; C>=NumToShift; C-- )
                Buffer[C]= Buffer[C - NumToShift];

            for(var C= 0; C<NumToShift; C++ )
            {
                // Hmm, we have a destination value, but don't know how it has
                // reached the current state.
                // Therefore we do a linear interpolation from the latest value in the buffer to destination.

                var Alpha= C / NumToShift;

                Buffer[C]= Buffer[NumToShift].multiply(Alpha).add(destination.multiply((1 - Alpha)));
            }
        }else
        {
            // degenerated case:
            //
            // We have a _VERY_ low frame rate...
            // we can only guess how we should fill the array.
            // Maybe we could write part of a linear interpolation
            // from Buffer[0] to destination, that goes from BufferEndTime to Now
            // (possibly only the end of the interpolation is to be written),
            // but if we rech here we are in a very degenerate case...
            // Thus we just write destination to the buffer.

            previousValue= NumToShift == Buffer.length? Buffer[0] : destination;

            for(var C= 0; C<Buffer.length; C++ )
                Buffer[C]= destination;
        }

        BufferEndTime+= NumToShift * cStepTime;
    }

return Frac;
}



function StepResponse(t)
{
    if(t < 0)
return 0;

    if(t > duration)
return 1;

    // When optimizing for speed, the above two if(.) cases can be omitted,
    // as this funciton will not be called for values outside of 0..duration.

return StepResponseCore(t / duration);
}


// This function defines the shape of how the output responds to the input.
// It must accept values for T in the range 0 <= T <= 1.
// In order to create a smooth animation, it should return 0 for T == 0,
// 1 for T == 1 and be sufficient smooth in the range 0 <= T <= 1.

// It should be optimized for speed, in order for high performance. It's
// executed Buffer.length + 1 times each simulation tick.
function StepResponseCore(T)
{
return .5 - .5 * Math.cos(T * Math.PI);
}


// The following functions are not used. They provide other responses (for fun).
function StepResponseCoreF(T)
{
    var cTau= .3;
    var cFrequency= 2.5;
return 1 - Math.cos(T * 2 * Math.PI * cFrequency) * Math.exp(-T / cTau) * (1 - T);
//      return 1 - Math.cos(T * 2 * Math.PI * cFrequency) * Math.exp(-T / cTau) * (1 - T) * (1 - T);
//      return 1 - Math.cos(T * 2 * Math.PI * cFrequency) * Math.exp(-T / cTau) * (.5 + .5 * Math.cos(T * Math.PI));
//      return 1 - Math.cos(T * 2 * Math.PI * cFrequency) * Math.exp(-T / cTau) * (.5 + .5 * Math.cos(T * Math.PI))* (.5 + .5 * Math.cos(T * Math.PI));
}

function StepResponseCoreE(T)
{
    var A= .5 - .5 * Math.cos(T * Math.PI);

  var cFrequency= 2.5;
    var B= 1 - Math.cos(T * 2 * Math.PI * cFrequency) * Math.sin(Math.sqrt(1 - T) * Math.PI/2);

return A * .8 + B * .2;
}

function StepResponseCoreD(T)
{
    var A= .5 - .5 * Math.cos(T * Math.PI);

  var cFrequency= 2.5;
    var B= 1 - Math.cos(T * 2 * Math.PI * cFrequency) * Math.sin((1 - T) * Math.PI/2);

return A * .8 + B * .2;
}

function StepResponseCoreC(T)
{
    var A= .5 - .5 * Math.cos(T * Math.PI);

  var cTau= .3;
  var cFrequency= 5;
    var B= 1 - Math.cos(T * 2 * Math.PI * cFrequency) * Math.exp(-T / cTau) * (1 - T);

return A * .8 + B * .2;
}

function StepResponseCoreB(T)
{
    var A= .5 - .5 * Math.cos(T * Math.PI);

  var cTau= .3;
  var cFrequency= 5;
    var B= 1 - Math.cos(T * 2 * Math.PI * cFrequency) /** Math.exp(-T / cTau)*/ * (1 - T);

return A * .8 + B * .2;
}

function StepResponseCoreA(T)
{
    var A= .5 - .5 * Math.cos(T * Math.PI);

  var cTau= .3;
  var cFrequency= 5;
    var B= 1 - Math.cos(T * 2 * Math.PI * cFrequency) /** Math.exp(-T / cTau)*/ * (1 - T);

    var Alpha= .2 * T;
return A * (1 - Alpha) + B * Alpha;
}

        

          
ecmascript:

function initialize()
{
    CheckInit();
}

function CheckInit()
{
    if(!bInitialized)
    {
        bInitialized= true;  // Init() may call other functions that call CheckInit(). In that case it's better the flag is already set, otherwise an endless loop would occur.
        Init();
    }
}
function Init()
{
    destinationPos= initial_destinationPos;
    destinationOri= initial_destinationOri;

    BufferPos.length=
    BufferOri.length= cNumSupports;

    BufferPos[0]= initial_destinationPos;
    BufferOri[0]= initial_destinationOri;
    for(var C= 1; C<BufferPos.length; C++ )
    {
        BufferPos[C]= initial_valuePos;
        BufferOri[C]= initial_valueOri;
    }

    previousValuePos= initial_valuePos;
    previousValueOri= initial_valueOri;

    cStepTime= duration / cNumSupports;
}
function set_destinationPos(Dest, Now)
{
    CheckInit();

    destinationPos= Dest;
    // Somehow we assign to Buffer[-1] and wait untill this gets shifted into the real buffer.
    // Would we assign to Buffer[0] instead, we'd have no delay, but this would create a jump in the
    // output because Buffer[0] is associated with a value in the past.

    //UpdateBuffer(Now);
}

function set_destinationOri(Dest, Now)
{
    CheckInit();

    destinationOri= Dest;
    // Somehow we assign to Buffer[-1] and wait untill this gets shifted into the real buffer.
    // Would we assign to Buffer[0] instead, we'd have no delay, but this would create a jump in the
    // output because Buffer[0] is associated with a value in the past.

    //UpdateBuffer(Now);
}
function Tick(Now)
{
    CheckInit();

    if(!BufferEndTime)
    {
        BufferEndTime= Now; // first event we received, so we are in the initialization phase.

        valuePos_changed= initial_valuePos;
        valueOri_changed= initial_valueOri;
        return;
    }

    var Frac= UpdateBuffer(Now);
    // Frac is a value in   0 <= Frac < 1.

    // Now we can calculate the output.
    // This means we calculate the delta between each entry in Buffer and its previous
    // entries, calculate the step response of each such step and add it to form the output.

    // The oldest vaule Buffer[Buffer.length - 1] needs some extra thought, because it has
    // no previous value. More exactly, we haven't stored a previous value anymore.
    // However, the step response of that missing previous value has already reached its
    // destination, so we can - would we have that previous value - use this as a start point
    // for adding the step responses.
    // Actually UpdateBuffer(.) maintains this value in

    var OutputPos= previousValuePos;
    var OutputOri= previousValueOri;

    var DeltaInPos= BufferPos[BufferPos.length - 1].subtract(previousValuePos);
    var DeltaInOri= previousValueOri.inverse().multiply(BufferOri[BufferOri.length - 1]);

    var DeltaOutPos= DeltaInPos.multiply(StepResponse((BufferPos.length - 1 + Frac) * cStepTime));

    OutputPos= OutputPos.add(DeltaOutPos);
    OutputOri= OutputOri.slerp(OutputOri.multiply(DeltaInOri), StepResponse((BufferOri.length - 1 + Frac) * cStepTime));

    for(var C= BufferPos.length - 2; C>=0; C-- )
    {
        var DeltaInPos= BufferPos[C].subtract(BufferPos[C + 1]);
        var DeltaInOri= BufferOri[C + 1].inverse().multiply(BufferOri[C]);

        var DeltaOutPos= DeltaInPos.multiply(StepResponse((C + Frac) * cStepTime));

        OutputPos= OutputPos.add(DeltaOutPos);
        OutputOri= OutputOri.slerp(OutputOri.multiply(DeltaInOri), StepResponse((C + Frac) * cStepTime));
    }
    if(OutputPos != valuePos_changed)
        valuePos_changed= OutputPos;

    if(OutputOri != valueOri_changed)
        valueOri_changed= OutputOri;
}
function UpdateBuffer(Now)
{
    var Frac= (Now - BufferEndTime) / cStepTime;
    // is normally < 1. When it has grown to be larger than 1, we have to shift the array because the step response
    // of the oldest entry has already reached its destination, and it's time for a newer entry.
    // has already reached it
    // In the case of a very low frame rate, or a very short cStepTime we may need to shift by more than one entry.

    if(Frac >= 1)
    {
        var NumToShift= Math.floor(Frac);
        Frac-= NumToShift;

        if(NumToShift < BufferPos.length)
        {   // normal case.

            previousValuePos= BufferPos[BufferPos.length - NumToShift];
            previousValueOri= BufferOri[BufferOri.length - NumToShift];

            for(var C= BufferPos.length - 1; C>=NumToShift; C-- )
            {
                BufferPos[C]= BufferPos[C - NumToShift];
                BufferOri[C]= BufferOri[C - NumToShift];
            }

            for(var C= 0; C<NumToShift; C++ )
            {
                // Hmm, we have a destination value, but don't know how it has
                // reached the current state.
                // Therefore we do a linear interpolation from the latest value in the buffer to destination.

                var Alpha= C / NumToShift;

                BufferPos[C]= BufferPos[NumToShift].multiply(Alpha).add(destinationPos.multiply((1 - Alpha)));
                BufferOri[C]= destinationOri.slerp(BufferOri[NumToShift], Alpha);
            }
        }else
        {
            // degenerated case:
            //
            // We have a _VERY_ low frame rate...
            // we can only guess how we should fill the array.
            // Maybe we could write part of a linear interpolation
            // from Buffer[0] to destination, that goes from BufferEndTime to Now
            // (possibly only the end of the interpolation is to be written),
            // but if we rech here we are in a very degenerate case...
            // Thus we just write destination to the buffer.

            previousValuePos= NumToShift == BufferPos.length? BufferPos[0] : destinationPos;
            previousValueOri= NumToShift == BufferOri.length? BufferOri[0] : destinationOri;

            for(var C= 0; C<BufferPos.length; C++ )
            {
                BufferPos[C]= destinationPos;
                BufferOri[C]= destinationOri;
            }
        }
        BufferEndTime+= NumToShift * cStepTime;
    }
    return Frac;
}
function StepResponse(t)
{
    if(t < 0)
        return 0;

    if(t > duration)
        return 1;

    // When optimizing for speed, the above two if(.) cases can be omitted,
    // as this funciton will not be called for values outside of 0..duration.

    return StepResponseCore(t / duration);
}


// This function defines the shape of how the output responds to the input.
// It must accept values for T in the range 0 <= T <= 1.
// In order to create a smooth animation, it should return 0 for T == 0,
// 1 for T == 1 and be sufficient smooth in the range 0 <= T <= 1.

// It should be optimized for speed, in order for high performance. It's
// executed Buffer.length + 1 times each simulation tick.
function StepResponseCore(T)
{
    return .5 - .5 * Math.cos(T * Math.PI);
}

// The following functions are not used. They provide other responses (for fun).
function StepResponseCoreF(T)
{
    var cTau= .3;
    var cFrequency= 2.5;
    return 1 - Math.cos(T * 2 * Math.PI * cFrequency) * Math.exp(-T / cTau) * (1 - T);
//      return 1 - Math.cos(T * 2 * Math.PI * cFrequency) * Math.exp(-T / cTau) * (1 - T) * (1 - T);
//      return 1 - Math.cos(T * 2 * Math.PI * cFrequency) * Math.exp(-T / cTau) * (.5 + .5 * Math.cos(T * Math.PI));
//      return 1 - Math.cos(T * 2 * Math.PI * cFrequency) * Math.exp(-T / cTau) * (.5 + .5 * Math.cos(T * Math.PI))* (.5 + .5 * Math.cos(T * Math.PI));
}
function StepResponseCoreE(T)
{
    var A= .5 - .5 * Math.cos(T * Math.PI);

    var cFrequency= 2.5;
    var B= 1 - Math.cos(T * 2 * Math.PI * cFrequency) * Math.sin(Math.sqrt(1 - T) * Math.PI/2);

    return A * .8 + B * .2;
}
function StepResponseCoreD(T)
{
    var A= .5 - .5 * Math.cos(T * Math.PI);

    var cFrequency= 2.5;
    var B= 1 - Math.cos(T * 2 * Math.PI * cFrequency) * Math.sin((1 - T) * Math.PI/2);

    return A * .8 + B * .2;
}
function StepResponseCoreC(T)
{
    var A= .5 - .5 * Math.cos(T * Math.PI);

    var cTau= .3;
    var cFrequency= 5;
    var B= 1 - Math.cos(T * 2 * Math.PI * cFrequency) * Math.exp(-T / cTau) * (1 - T);

    return A * .8 + B * .2;
}


function StepResponseCoreB(T)
{
    var A= .5 - .5 * Math.cos(T * Math.PI);

    var cTau= .3;
    var cFrequency= 5;
    var B= 1 - Math.cos(T * 2 * Math.PI * cFrequency) /** Math.exp(-T / cTau)*/ * (1 - T);

    return A * .8 + B * .2;
}
function StepResponseCoreA(T)
{
    var A= .5 - .5 * Math.cos(T * Math.PI);

    var cTau= .3;
    var cFrequency= 5;
    var B= 1 - Math.cos(T * 2 * Math.PI * cFrequency) /** Math.exp(-T / cTau)*/ * (1 - T);

    var Alpha= .2 * T;
    return A * (1 - Alpha) + B * Alpha;
}

        

          
ecmascript:

function initialize()
{
    isLoaded= true;
}

        

          
ecmascript:

function StartTimer()
{
    if(IsCortona)
        return;

    if(!needTimer)
    {
        lastTick= 0;
        needTimer= true;
    }
}

function StopTimer()
{
    if(IsCortona)
        return;

    if(needTimer)
    {
        needTimer= false;
    }
}

function initialize()
{
    CheckInit();
}

function CheckInit()
{
    if(!bInitialized)
    {
        bInitialized= true;
        Init();
    }

}

function Init()
{
    IsCortona= false && Browser.getName().indexOf('Cortona') != -1;

    bNeedToTakeFirstInput= takeFirstInput;

    tau= effs.tau;
    set_value(initial_value);
    if(IsCortona)
        needTimer= true;
    else
        needTimer=    input.x != initial_value.x
                   || input.y != initial_value.y
                   || input.z != initial_value.z
                   ;
}

function set_tau(t)
{
    CheckInit();

    tau= t;
}

function set_destination(i)
{
    CheckInit();

    if(bNeedToTakeFirstInput)
    {
        bNeedToTakeFirstInput= false;
        set_value(i);
    }


    if(i != input)
    {
        input= i;
        StartTimer();
    }
}

function set_value(o)
{
    CheckInit();

    bNeedToTakeFirstInput= false;

    value1= value2= value3= value4= value5= o;
    value_changed= o;
    UpdateReached();
    StartTimer();
}

function tick(now)
{
    CheckInit();

    if(!lastTick)
    {
        lastTick= now;
        return;
    }

    var delta= now - lastTick;
    lastTick= now;

    var alpha= Math.exp(-delta / tau);


    if(bNeedToTakeFirstInput)  // then don't do any processing.
        return;

    value1= order > 0 && tau
               ? input  .add(value1.subtract(input  ).multiply(alpha))
               : input;

    value2= order > 1 && tau
               ? value1.add(value2.subtract(value1).multiply(alpha))
               : value1;

    value3= order > 2 && tau
               ? value2.add(value3.subtract(value2).multiply(alpha))
               : value2;

    value4= order > 3 && tau
               ? value3.add(value4.subtract(value3).multiply(alpha))
               : value3;

    value5= order > 4 && tau
               ? value4.add(value5.subtract(value4).multiply(alpha))
               : value4;

    var dist= GetDist();

    if(dist < eps)
    {
        value1= value2= value3= value4= value5= input;

        value_changed= input;
        UpdateReached2(dist);

        StopTimer();
        return;
    }
    value_changed= value5;
    UpdateReached2(dist);

}

function GetDist()
{
    var dist= value1.subtract(input).length();
    if(order > 1)
    {
        var dist2= value2.subtract(value1).length();
        if( dist2 > dist)  dist= dist2;
    }
    if(order > 2)
    {
        var dist3= value3.subtract(value2).length();
        if( dist3 > dist)  dist= dist3;
    }
    if(order > 3)
    {
        var dist4= value4.subtract(value3).length();
        if( dist4 > dist)  dist= dist4;
    }
    if(order > 4)
    {
        var dist5= value5.subtract(value4).length();
        if( dist5 > dist)  dist= dist5;
    }
    return dist;
}

function UpdateReached()
{
    return UpdateReached2(GetDist());
}

function UpdateReached2(Dist)
{
    if(reached)
    {
        if(Dist > reachThreshold)
            reached= false;
    }else
    {
        if(Dist <= reachThreshold)
            reached= true;
    }
}