Final Project Presentation& Demo Zhi Dong Real Time FEM of Elasto-Plastic Simulation

Presentation Summary  Background of real time FEM  State of Art  New Challenges  Techniques/approaches  What have actually been accomplished  Demo Video  Summary of the course project contributions

Background  Computer games or simulators, demand a continuously growing degree of visual realism and technical sophistication.  Movie Industry…. Is that true?

State-of-Art  Linear FEM  Warped Stiffness FEM  Remesh Method

New Challenges Accuracy (Physically Valid) Simulation Frame Rate Stability

Techniques/approaches The basic idea is First Build a Tetrahedral Mesh Get the Stiffness Matrix for each element: Here is the trick: we can first get a matrix which is 12X12 where M[i][i]=1, and M[i][9-i]= M[i][6+i],M[i][3+i], M[i][9+i] is between 0 to which means we move one point and The adjacent point move following it, which is d=Mf, if we want to know the f we should use f=Kd where K is inverse of M, and also the element stiffness matrix. Get the Stiffness Matrix for the mesh using element stiffness matrix(Some vertices are shared by multiple tetrahedrons) (Assembling Method)

Techniques/approaches Basic Idea Mx ¨ + Cx ˙ + K ( x − x 0) = f ext (1) For each element with 4 vertices f= Kd (2) Simulation Procedural Actually, it is pretty simple, first we calculate force then we get the force by (2), then Update the displacement of each vertex by(1), Then we make it as a loop.

Techniques/approaches Triangle Mesh Deformation( Creavity) Now we have the tetrahedron mesh deformation, but we haven’t got the triangle mesh deformation. We should firstly let the tetrahedron mesh totally cover the triangle mesh, then we map the triangle into the nearest vertex in the tetrahedron mesh. If there exists displacement on the vertex, we simply apply: triangle vertex displacement = tetrahedron vertex displacement / (distance to the nearest tetrahedron vertex)

Techniques/approaches Fragile Effect  We firstly predefine some points which are more easily to tear apart, then at each simulation step, we check the displacement of the points, if one exceeds threshold, we should make all crack points tore apart. Pro: Easily to implement Con: Hard to mark the predefine crack points.

What have actually been accomplished Tools Used which part is borrowed, which part is written by myself. Borrowed: SlimDX: API for DirectX11 in C# Written by myself:  Render Engine: Just reuse the code when I complete the previous HWs of COMP 768  Physics Simulation Module: all written by myself, partially because all libs don’t support C#, including high rank matrix multiplication, inverse of matrix, and other trivial stuffs.  Collision Detection: Written by myself. Reuse some code from previous HWs. Bullet seems not work very well because it is a little complex and a little bit harder to integrate.

What have actually been accomplished Architecture of System Single Tetrahedron Simulation : Element Stiffness Matrix : Positions For 4 nodes in the Element Tetrahedron Mesh : Nodes, : Tetrahedrons : Stiffness Matrix FEM Method : Update the forces for each node : Update the displacement of each node : Get the inverse of Stiffness Matrix Mesh Mapping Update triangle position based on tetrahedron positions Contains Uses Following

What have actually been accomplished Actually create Physics Engine  After all is done, in the demo we will see that we actually build a whole physics engine, including collision between soft-body to rigid body and rigid body to rigid body.  What can be improved is creating some low level math libs.

What have actually been accomplished Demos After Implementing all the features of FEM, I also have done some demos to show the correctness and efficiency for my method: Two Demos:  Stretch Bunny Pull the tail of the bunny to stretch down and see what happens.  Balls Hitting Deformable Body Show the interaction with rigid body and fragile effect.

Demo Video Let’s Watch it! URL:

Demo Video Correctness  In the first demo, the bunny is stretched down, all adjacent parts in around the tail are moving following the tail, but it does not exceed the movement of tail.  The head of bunny moves down with the greatest “latency” which means the tetrahedrons movement are damping to the head.

Demo Video Correctness  In the second demo, the soft body is hit by several balls, I predefined the upside of the deformable body having a line of crack points. So it is obvious that if they are colliding, there exists a big crack.  It is visual convincing and shows a nice deformation intuitively.

Results: comparison, analysis Efficiency  In the whole simulation procedural, the mesh has been preprocessed, and once it has been processed, it has no updating. So the main part which affects the simulation is calculating the forces and displacement.  In our method, the displacement and forced computing is done in linear time complexity. See the previous slides…

Results: comparison, analysis Efficiency In our demos, our laptop is using Nvidia GF170M with 2 GB memory and Pentium 4 processor. The triangle consists of 1K vertices. In our demos, it can reach 62 FPS.

Summary of the course project contribution(s)  Implement real time FEM with fragile effect.  Triangle Mesh displacement Computing Method is novel and easy to implement.  Integrate FEM with rigid body dynamics which makes the system like a physics engine.  Write all stuff from scratch, without using any physics tools or libs. Just leverage DirectX11. Best way to avoid some illegal infringement.

Possible future work  Using CUDA to accelerate calculation  Release or modify some parts of Bullet Engine, because it is open source engine, but Softbody module solves it using spring mass model. Adding FEM will add more fantastic effect

Thanks and Have a Nice Holiday !