Follow Curve, with Squash an Stretch

[Jason]

Hi all,

I started to dabble with some stuff - anyone have better suggestions for this?

[edward]

Not really. But recently, we discovered a caveat with that method. Since we're trying to approximate the curve via straight-line segments (ie. the bone chain), the expression based on the arclength is not actually correct. If you look at the portion of your curve touching the endpoints of a bone, you will note that the arc length of the curve is in fact longer than the length of the bone.

So what happens is that if you bend the curve a lot, it's likely that the bone chain will then become longer than the arc length of the whole curve which can cause unexpected results. I don't really have a good solution for this other than perhaps fudging the length assigned to the bones by some scaling factor to make it shorter. The other solution is to have a proper spine solver which matches the end points at the expense of not necessarily touch the curve at the inner joints of the bone chain. Alas, a spine solver is not near the top of the priority list these days.

[Jason]

Not really. But recently, we discovered a caveat with that method. Since we're trying to approximate the curve via straight-line segments (ie. the bone chain), the expression based on the arclength is not actually correct. If you look at the portion of your curve touching the endpoints of a bone, you will note that the arc length of the curve is in fact longer than the length of the bone.

So what happens is that if you bend the curve a lot, it's likely that the bone chain will then become longer than the arc length of the whole curve which can cause unexpected results. I don't really have a good solution for this other than perhaps fudging the length assigned to the bones by some scaling factor to make it shorter. The other solution is to have a proper spine solver which matches the end points at the expense of not necessarily touch the curve at the inner joints of the bone chain. Alas, a spine solver is not near the top of the priority list these days.

14163[/snapback]

Yeah, this is exactly what I was finding too. I wrote in the obscure "disscusion" on the odwiki page: here it is..

[meshsmooth]

well this is what i have been working on. hence my interest in cyclic quadrilaterals and the like. i have put it on the shelf for now but will come back to it later when i have done some more thinking on the subject with my unconscious brain.

the idea is basicly is to boil down the spine into:

1. A point at each end with a vector at each of those points. then create a quadrennial using the length from the start point to the finish point as one side length and the other 3 sides to be one third of the spline length.

2. Then distort the quadrennial so the sides ether side of the long side to point in the direction of the vectors.

3. Then create a fit curve to pass through the 4 points.

4. then if that was fast enough test the length of the spline in comparison to the length of the spine and shrink or grow the 3 side lengths to maintain the correct length. Then do steps 1 and 2 again.

5.Then stick the bones to it with spline ik.

6. Apply twist after the spline ik chop to the bones.

the benefits are

1. the spine is always reaching from the start point to the end point

2. the vectors effect ether end of the spine in equal amounts

3. it should feel good to use

the catches

1. I haven't solved the step 2 yet. it is like a new IK solver, so this is a non trivial task.

2. I do have a theory on one solution but it is a hack, and only half working

3. it may be slow but i would have to finish it to know for shore, but so far it is ok.