So, that's the result, and

the algorithm we use here is a standard finite element simulation.

So finite element simulation is to divide the domain, shape into small regions.

In this case triangle regions.

And then compute physical equations on this matrix on these systems.

And then internally, this is a kind of many,

many it's internally essentially it solves

Huge linear equations, and actually handling matrices.

And in order to accelerate this computation in this kind of

direct manipulation editing, what we use, what we use is here.

Reusing of intermediate computation results.

So, traditionally it's too slow to hm-

run this kind of physical simulation from scratch each, each frame.

But in this example, in this modeling task, you know,

you have the previous step for simulation result.

And compared to the previous simulation result, current suffers only a slight change,

you know? User is

Dragging single vertex, the change is very small.

So you can reuse most of the previous computation.

So that's a topic trick we use, we use.

Now, this is a little bit more details.

So, of course it's not possible to explain everything,

because we skipped the explanation of finite element method.

It's a little bit complicated.

But still, you can get the general idea.

So left hand side uses a coefficient matrix a, pre-conditioned matrix x.

So, we do not describe details about these other mesh-

matrix structure we use in the computation of this simulation.

And also, matrix has a value list and then structure, and the value list,

and then structure.

So these information are heavily used in the system.

And construction, of this information is time consuming.

So in the idle time, nothing happened, so we can reuse old intermediate structure.