The seminar is given at UNIK, room 308, Tuesdays at 13.15-16.00. Start January-18.
Lecturers:
| ?yvind Andreassen | Email: oya@ffi.no |
| Anders Helgeland | Email: ahe@ffi.no |
Background:
The purpose of this seminar is to give the student an
introduction to modern data visualization. It starts with a short
introduction to basic computer graphics, then we discuss visualization
terminology, data representation and algorithms for geometry-generation.
Kinematics is introduced to give the students an undestanding of
the effects of motion in a continuous medium and how to visualize
motion. Lagrangian versus Eulerian expression of motion is presented
as well as the interpretation of vectors and tensors.
Animation is visualization of motion in space and time.
After the discussion of geometry based visualization techniques, methods for
volume visualization is presented. In volume visualization the voxel
(the 3-dimensional analogy to the 2-dimensional pixel) is a key building
brick of the volume. A shading technique called limb darkening is discussed.
We present techniques for vector and tensor field visualization like line
integral convolution, illuminated field lines, anisotropic diffusion and
some primitive techniques for visualilzation of tensors.
The seminar is concluded with a lecture on visualization of
time dependent fields, animation of scalar and vector fields.
Figure illustrating three different visualization applications. Shown upper
left is a super computer, in the middle a seismic exploration ship, and
lower left a magnetic resonance imager (MRI). The data outputs from these
"devices" are processed a on dedicated visualization computer shown in the
center and where the data are converted into a visual form (images)
understandable for humans. The outputs of the visualization computer
are three-dimensional scenes projected on a computer screen.
As examples are shown upper right:
vorticity and temperature structures in simulated stellar convection. Center
right: seismic data, and lower right: MRI output showing a human brain.
Lectures:
Introduction. General presentation, basics of visualization.
What is visualization? Some applications are presented. A brief introduction to computer graphics hardware and software is given. We proceed with an introduction to basic computer graphics, coordinate systems, transformations and the use of color and light models. Color and light models are discussed as well as basic reflection models and rendering techniques.
More about computer graphics and rendering algorithms.
Systems for organizing and storage and porting of large scientific datasets are presented in this lecture. HDF5 and netCDFare shortly presented, with some examples.
Briefly about ODE integration/Introduction to KINEMATICS (pdf: slides)
Various techniques for scalar, vector and tensor data are covered. Use of color tables and "carpet plots" etc... We discuss the "Marching cube algorithm" for generation of contour lines and iso surfaces. Voxel or "volume" visualization techniques are shortly discussed.
Introductory kinematics, Lagrangian (material) versus Eulerian (spatial) description of motion in a continuous medium. Material derivative, stream lines, path lines and streak lines. A introduction to vector and tensor calculus can be found in Simmonds. A basic treatment of kinematics can be found in Kundu's book on fluid mechanics. A more advanced description is given in Aris' book on vector and tensor analysis.
Presentation of visualization techniques is continued.
Kinematics continued. Physical interpretation of vorticity and strain rates. Strain and rotation tensors. Visualization of tensor-fields. Assignments in kinematics.
DEMO, volume rendering of various data sets
Visualization of vector fields using Line Integral Convolution (LIC). LIC is a texture-based technique for visualizing two- and three-dimensional vector fields. It was first introduced by Cabral and Leedom 1993. This algorithm has been improved by several authors. For example, a Fast LIC algorithm was developed by Stalling and Hege in 1995. The principles of line integral convolution is discussed together with examples.
Kinematics continued. Definition of a vortex. Determination of NULL vectors and critical points in numerical data. Classification of critical points.
Two techniques for vector field visualization are presented: Illuminated field line and a technique based on anisotropic diffusion.
Illuminated field lines, examples.
Visualization techniques for time dependent scalar and vector fields are discussed in this lecture.