Dynamic Stiffness/damping Expression Via Mel?

[puppetsoul]

Some one have a comprehensive site/algo/mel about a stiffness/dammping based expression?

I want to do it by mel who create an expression, but I didnt found the math formula on internet (and Im not mathematician!)

The way of my mel is that there is a goal (locator on other, and a dynamic object with stiffness/damping channel to control how it follow the goal.
I know there is the jiggle dimension, but I found the expression really big, and Im sure that there is a little!

Thanks in advance.

(sorry for the double post, I have see it too late!)

[joojaa]

I think the main problem is that ist invariably a simulation.based on velocity change/ movement.

So the expression would make little or no sense if you scrub back and forth. THere are many ways you coould do this tough. one of the easiest is touse particle goals for this. tha basic dea is that the object that follows has a bit of innertia behind it.

At simplest it could be expressed like this (its wee bit fof pseoudocode)

CODE

deltaPos=(targetObject.position-ladObject.Position);
ltargeObject.position=targetObject.position+somefunc(deltaPos);

Now for the func. wich traditionaly speaking is just the formula for a spring wich is mathematicaly expressed as f=-kx in thiscase the x is a vector pointing at taget so -k is defined as +k

so

CODE

deltaPos=(targetObject.position-ladObject.Position);
ltargeObject.position=targetObject.position+deltaPos*k;

where k is a constant from 0 to 1

Now in reality the force might not be totaly harmonical so you might want to use

CODE

deltaPos=(targetObject.position-ladObject.Position);
ltargeObject.position=targetObject.position+pow(mag(deltaPos),Exp)kunit(deltaPos);

This can create a more subtle or exagarated movemenet pow is just on fuction. you could use smoothstep or something esle instead as the function

now to make this look good it needs to be added with last turns velocity fro the inertia now multiply this with damping factor like above... sdame strategies apply
heres some tested code.

CODE
global float $moveX,$moveY,$moveZ;
if (time==0){
nurbsSphere1.translateX=0;
nurbsSphere1.translateY=0;
nurbsSphere1.translateZ=0;
$moveX=0;
$moveY=0;
$moveZ=0;
}
$moveXlast=nurbsSphere1.translateX;
$moveYlast=nurbsSphere1.translateY;
$moveZlast=nurbsSphere1.translateZ;

//0.3 is k
nurbsSphere1.translateX=nurbsSphere1.translateX+
                                  $moveX+(locator1.translateX-nurbsSphere1.translateX)*0.3;
nurbsSphere1.translateY=nurbsSphere1.translateY+
                                   $moveY+(locator1.translateY-nurbsSphere1.translateY)*0.3;
nurbsSphere1.translateZ=nurbsSphere1.translateZ+
                                  $moveZ+(locator1.translateZ-nurbsSphere1.translateZ)*0.3;
$moveX=(nurbsSphere1.translateX-$moveXlast)*0.85//0.85 is the damping factor;
$moveY=(nurbsSphere1.translateY-$moveYlast)*0.85;
$moveZ=(nurbsSphere1.translateZ-$moveZlast)*0.85;

[joojaa]

oh and dont doublepost

[puppetsoul]

Ok, sorry for the double post....

So damping is 0.85 and k is stiffness value?

I will test it on my script this week end, thank you very much

QUOTE(Joojaa @ 08/19/05, 03:13 AM)
I think the main problem is that ist invariably a simulation.based on velocity change/ movement.

So the expression would make little or no sense if you scrub back and forth. THere are many ways you coould do this tough. one of the easiest is touse particle goals for this. tha basic dea is that the object that follows has a bit of innertia behind it.

At simplest it could be expressed like this (its  wee bit fof pseoudocode)

CODE

deltaPos=(targetObject.position-ladObject.Position);
ltargeObject.position=targetObject.position+somefunc(deltaPos);

Now for the func.  wich traditionaly speaking is just the formula for a spring wich is mathematicaly expressed as f=-kx in thiscase the x is a vector pointing at taget so -k is defined as +k

so

CODE

deltaPos=(targetObject.position-ladObject.Position);
ltargeObject.position=targetObject.position+deltaPos*k;

where k is a constant from 0 to 1

Now in reality the force might not be totaly harmonical so you might want to use

CODE

deltaPos=(targetObject.position-ladObject.Position);
ltargeObject.position=targetObject.position+pow(mag(deltaPos),Exp)kunit(deltaPos);

This can create a more subtle or exagarated movemenet pow is just on fuction. you could use smoothstep or something esle instead as the function

now to make this look good it needs to be added with last turns velocity fro the inertia now multiply this with damping factor like above... sdame strategies apply
heres some tested code.

CODE
global float $moveX,$moveY,$moveZ;
if (time==0){
nurbsSphere1.translateX=0;
nurbsSphere1.translateY=0;
nurbsSphere1.translateZ=0;
$moveX=0;
$moveY=0;
$moveZ=0;
}
$moveXlast=nurbsSphere1.translateX;
$moveYlast=nurbsSphere1.translateY;
$moveZlast=nurbsSphere1.translateZ;

//0.3 is k
nurbsSphere1.translateX=nurbsSphere1.translateX+
                                  $moveX+(locator1.translateX-nurbsSphere1.translateX)*0.3;
nurbsSphere1.translateY=nurbsSphere1.translateY+
                                   $moveY+(locator1.translateY-nurbsSphere1.translateY)*0.3;
nurbsSphere1.translateZ=nurbsSphere1.translateZ+
                                  $moveZ+(locator1.translateZ-nurbsSphere1.translateZ)*0.3;
$moveX=(nurbsSphere1.translateX-$moveXlast)*0.85//0.85 is the damping factor;
$moveY=(nurbsSphere1.translateY-$moveYlast)*0.85;
$moveZ=(nurbsSphere1.translateZ-$moveZlast)*0.85;

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[joojaa]

yes it makes for a linear stiffness... Actualy what you proably want is a stiffless thats very low at small distances and 1 at big ones.

[puppetsoul]

Hello....

again one little question, but first, thanks you very much, you algo works really good!!!, thansk a lot

Ok, I have put the pow on the stiffnes and damping (and only that), but I cant understand your smoothstep point, because if I put a smoothstep on :

ltargeObject.position=targetObject.position+pow(mag(deltaPos),Exp)kunit(deltaPos);

where there is the pow func, the smoothstep will return a value bteween 0 and 1.

How do that to have any value smoothed? (I found this really sexy!

thanks a lot

sorry for my math level..