Minor thesis of Daniel Höhne

A framework for modal analysis in the field of computer graphics

Student: Daniel Höhne (alternativ: dh [at] zesem.de)
Betreuer: Prof. Dr. rer. nat. Stefan Gumhold
Verantwortlicher Hochschullehrer: Prof. Dr. rer. nat. Stefan Gumhold

Motivation

Nowadays, softbody objects are simulated using the mass-spring-damper approach. This is true for real-time graphics, where simplicity and speed are trade off for accuracy and physical foundation. Special care must be taken in choosing the right integration schema since stability is crucial in unforeseen environments.
Although modal analysis is not the swiss army knife that will solve all problems it can be used to combine the best of both worlds. But this comes at the cost much more complexity in data preparation. A finite element analysis has to be done. But the resulting 2nd order ODE can be solved without the help of numerical integration, fast and stable.
To overcome the more involved FEM data preparation, a framework has been developed. A GUI tool assists you in every step necessary to do modal analysis of your (triangulated surface) data.

Description

At first a FEM-Maple library was developed, capable of generating mass (M), damping (C), stiffness (K) and modal matrix out of a tetrahedra model and material parameters. These are saved using a xml project file and can be used in one of the provided simulation programs immediately. What's more, the developed c++ framework provides...

materials: an editor/db for isotropic materials
mesh generation: a Tetgen-plugin, exposing most important parameters
models: visualization at the stage of import, mesh generation and modal simulation
FEM: FEM preprocessor for the linear tetrahedra
math data: visualization of the produced matrices and vectors (math data)
solver: modes (eigenvalues) abd eigenvetors are computed using LAPACK
modal analysis: visualization of mode influence on the 3d object, phase portrait, oscillograph curve

all made available through a graphical user interface for easy access. Extending the gui/framework is straightforward. One only needs to write a new plugins for one of the main parts of the frameworks (see above).
Furthermore, modal simulation has been combined with a regular rigid body physics engine Open Dynamics Engine (ODE). This is demonstrated by two (simple) samples programs.

Results

The first pictures show the main application with the gui-windows for the individual modules. Namely the material editor, mesh generator, fem preprocessor, eigenproblem solver and modal stimulation.

material editor	create material
tetgen plugin	surface model	meshed cube
FEM preprocessor	assign materials	vis. mass matrix	vis. stiffness matrix
eigen-solver	xt-portait mode 7	phase-portait mode 7	mode assembly
simulation ctrls	sim. of mode 6+9+12	OpenDE (static)	OpenDE (dynamic)

mode (de)composition

Videos

Some example videos of the gui and the sample applications. To watch them you can use VideoLanClient.
OpenDE (static) means, that the object is treated as static geometry in OpenDE. In contrast, OpenDE (dynamic) is modeled using a dynamic, tri-meshed, rigid object.

Mode 6	Mode 7	Mode 8
Mode 9	Mode 10	Mode 11
Mode 9	OpenDE (static)	OpenDE (dynamic)

Perspective

The most improvements are to be expected from implementing state-ot-the-art in modal simulation - constraints and modal-warping which will greatly enhence the useability and visual quality of the simluation.
More frames per second can be achieved if the matrix-vector computations are ported to dedicated hardware e.g. the gpu.

TUD

Computer Graphics