CS 384R (#56767), CAM 395T (#67597), BME 385J (#14608)

FALL 2007     TTH 9:30 – 11:00am    TAY 3.114

Geometric Modeling and Visualization


Image consists of Ribosome, Virus, Human body, Brain, NMJ(Neuromuscular junction), and Universe



Chandrajit Bajaj


ACES 2.324





Office hours

Wed 9:00 am - 12:00 am or by appt. via suzanne@ices.utexas.edu

CS384R, CAM395T, BME385J Course Outline

The course will teach you the basic algorithms, techniques and tools of geometric modeling and visualization with applications in the biomedical sciences and engineering. Bio-medical modeling (or Biomodeling) and visualization has roots in medical illustration and communication for the health sciences, with branches of application to mathematical modeling and computer simulation of artificial life. In this course we shall emphasize computational image processing, computational topology, computational algebraic and differential geometry, polynomial spline approximations, computer graphics, together with aesthetic choices involved in producing effective scientific animations. The emphasis shall be on spatial realism, and the programmatic use of physiological simulation and visualization to quantitatively depict "how things work" at the molecular, cellular, tissue, and organ level scales.

Exercises on domain and physiological modeling and visualization at multiple scales, shall be drawn from virology (viral envelopes, capsids, proteins, nucleic acids), and neurology (brain, hippocampus, neuropil, axons, dendrites, glial cells, ion-channels, neurotransmitters), and their interactions (molecular energetics and force fields, molecular flexibility, synaptic transmission, synaptic spillover).

Lecture Topics

Models and Maps: algebraic curves, surfaces, splines, parametrization, manifolds, singularities, topology, electron microscopy, CT/MRI imaging, reconstruction.

Maps2Models: filtering, contrast enhancement, classification, symmetry detection, segmentation, skeletonization, subunit identification, clustering, matching, compression, reconstruction

Models2Analytics I: surfaces, finite element meshing, spline representations, feature identification, symmetry detection, shape segmentation, matching & complementary docking, flexibility

Models2Analytics II: bonded and non-bonded energetics, forces, torques, dynamics, cubature, discrete differential operators, integral equations, sparsifiers, preconditioners, solvers.

Analytics2Informatics/Visualization I: differential/integral/topological/combinatorial properties, active sites, pockets, tunnels, regions of interest, contour trees, comparative structural analysis.

Analytics2Informatics/Visualization II: multi-dimensional transfer functions, visible surface and volume rendering, function on surface, capturing uncertainity, VisPortal, MolSignatureDB.


You will be graded on weekly homework assignments (70%) and a final exam (30%).




August 30

Geometric Modeling and Visualization

September 4

Algebraic Splines and Analysis
BEM/FEM Domain Splines

September 6

Geometric and Signal 3D Processing (and some Visualization)

September 18

Molecular Structures (Models) from PDB, VIPER

October 23

Cellular Structure Models from Thin Section EM

October 30

Boundary & Finite Element Meshed Models II: Contouring

November 6

Boundary & Finite Element Meshed Models III: Topologically Accurate Non-Linear Elements

November 12

Finite Elements from Imaging I & II: Active Contouring, Segmentation, Reconstruction

November 27

Geometric Partial Differential Equations: Non-Linear Surface & Volume Diffusion

December 12

Integrals & Integral Equations: Molecular Energetics & Forces



Exercise 1 Algebraic Curve, Surface Splines - I Solution 1


Exercise 2 Algebraic Curve, Surface Splines - II Solution 2


Exercise 3 Algebraic Curve, Surface Splines - III Solution 3


Exercise 4 Algebraic Curve, Surface Splines - IV: Molecular Models Solution 4


Exercise 5 Finite Element Meshing - I: Linear Elemen Solution 5


Exercise 6 Finite Element Meshing II - Non-Linear Elements Solution 6


Exercise 7 Geometric Modeling and Visualization Final Solution 7

Pictures and Animations


Suggested Reading

Papers Reading List


Group Meeting Schedule