0:18

So, computer-aided design is a process of designing products using computers.

Â And today, almost all products are designed using computers.

Â Starting from home electronics or garments, or cars, and houses.

Â Everything is designed using a computer.

Â And physics, plays an important role in here, and

Â physics simulation is already heavily used in the design.

Â However, in most cases currently, physics analysis is done after modeling.

Â So a user or designers design a model and the modelers calibrate model.

Â And only after that, the model is transported into the physical simulation

Â system, and then, so people will analyze the property like collision, friction,

Â material property, gravity and so on.

Â And if there's a problem, go back to the design.

Â So, but this is useful for testing the validity afterwards, but

Â this is not very good for actively use physics into the design process.

Â 1:24

So what we try to do here, is to integrate real-time physics into modeling.

Â So, so currently 3D model ignore physics.

Â Just specify x, y, z coordinates and

Â shapes, but here in the system we introduce here.

Â Are all integrates, 3D of physical assimilation into the modeling process, so

Â as user generates a model, of physical assimilation automatically checks

Â validity and then provides feedbacks.

Â So that's the basic idea.

Â And then we will show a couple of example systems here.

Â So, this is a list of topics we're discussing this week.

Â So one is cantilever design for architecture.

Â And design with music [INAUDIBLE] noble musical instruments and

Â garment design, furniture design and finally hobby glider design.

Â 2:17

So this one is called responsive FEM, Finite Element Method, for

Â aiding interactive geometric modeling.

Â So the program we want today,

Â discuss here is design of a, physical with physical constraint.

Â Here, as an example is a cantilever design.

Â Suppose you have a vertical wall here.

Â And they have a horizontal steel bar attached to the wall.

Â 2:44

So originally, the steel bar is connected vertically com,

Â completely horizontally, perpendicular to the wall.

Â But after construction, if you release your hand,

Â support material, gravity pulls the steel downwards.

Â So, this is of course exaggerated.

Â But in reality, there's always a deformation.

Â So the goal is to find the shape that di,

Â ended in a completely flat horizontal shape, after applying gravity.

Â So this is kind of difficult inverse problem.

Â 3:18

A traditional approach is to run physical simulation after modeling.

Â So, use a space for the rest shape and

Â then physical simulation predicts what happens.

Â Looking at the result, user go back to the design phrase, and adjusts the shape and

Â they go to a simulation.

Â Now this kind of back and forth interaction is not very efficient.

Â 3:36

So what we propose is to run physical simulation during modeling, specifically,

Â while the user is dragging one by one.

Â System should continuously provides feedback.

Â This way, you can just know when to release dragging.

Â So let me show you a demonstration.

Â 4:04

So here is a demonstration.

Â So left side is original rest shape.

Â Then right side is after the gravity, is applied.

Â And here, the simulation is continuous, as a user.

Â So this is so natural, so smooth, it's very hard to see, but hard to appreciate.

Â But, as a user drags a system continuously physical simulation and continuously

Â presenting the deformed shape, after physical simulation, it's very, very fast.

Â So as a user change, the position system continuously updates lines many,

Â many simulations.

Â And the it shows a simulation result.

Â So it's so fast and

Â so smooth, so user actually looking at this simulation result, while dragging.

Â So simulation result is satisfactory, these are just stop dragging, and

Â you'll get the desired result.

Â 5:02

So, that's the result, and

Â the other one that we use here is a standard finite element simulation.

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

Â In this case triangle regions.

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

Â On the internally, this is a kind of many,

Â many it's internally essentially it solves.

Â Huge linear equations, and actually handling matrices.

Â And in order to accelerate this computation in this kind of

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

Â Reusing of intermediate computation results.

Â So, traditionally it's too slow to hm,

Â run this kind of physi, simulation from scratch each, each frame.

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

Â you have the previous step for simulation result.

Â And compared to the previous simulation result, [INAUDIBLE] only a slight change,

Â you know?

Â Dragging single bar this, the change is very small.

Â So you can reuse most of the previous computation.

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

Â Now, this is a little bit more details.

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

Â because we skipped the exponential finite element measure.

Â It's a little bit complicated.

Â But still, you can get the general idea.

Â So left hand side uses a coefficient matrix a, reconditioned matrix x.

Â So, we do not describe details about these other ma,

Â matrix structure we use in the computation of this simulation.

Â And also, matrix has a value list and their structure, and the body list,

Â and structure.

Â So these information are heavily used in the system.

Â And construction, of this information is time consuming.

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

Â 7:04

And in the during dragging, we divided the dragging depending with the distance.

Â When the dragging operation is very small, very small relocation,

Â then what's the system is do just updates the mash-mish vertices.

Â And almost all information will be used.

Â As a user drags more and more, then, simple vertex relocation doesn't work, so

Â system tries the update, while it finds a topology.

Â But after a while, if the deformation still rise, then simple relocation and

Â simple topology changes nothing there, so system re,

Â reconstructs So this is what is happening, behind the scene, in this example.

Â And internally, if the relocation is very small.

Â Then only, system only, recomputes a value list of its matrix A.

Â And if you change the topology, you have to refresh all the coe,

Â coef, coefficient matrix A.

Â But you can reuse the pre-condition matrix B.

Â But after the reconstruction everything is re-computed.

Â So this is equivalent to [INAUDIBLE] simulation from scratch.

Â But this happens very rarely.

Â So this is a very short section, but

Â summary is to introduce cantilever design with concurrent physical simulation.

Â So you can change the shape while watching a simulation result.

Â And internally, most important point is that we apply multi-level reuse,

Â of intermediate computation result.

Â More specifically internal large matrixes, matrices.

Â For efficient computation.

Â 8:40

So original paper is available as Responsive FEM for

Â Aiding Interactive Geometric Modeling.

Â We discussed many other examples too there.

Â And finite element method is an est, established method and

Â there are many textbooks.

Â One example is this one, the finite element method.

Â It's basis on the fundamentals.

Â 8:59

And structural optimization is often discussed in computer graphics.

Â One example is this one.

Â A procedure modeling of structurally sound masonry buildings.

Â So this one is the kind of physics aware 3D modeling.

Â However, there is also just automatic optimization, and

Â did not discuss interme not bring the feedback to end user manipulation.

Â Thank you.

Â