Name 

Office 
ACES 2.324 


Phone 
5124718870 
Office hours 
Tue 1:30  3:00p Wed 2:30 pm  3:30 pm or by appt. via suzanne@ices.utexas.edu 
CS384R, CAM395T 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. Biomedical 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, ionchannels, neurotransmitters), and their interactions (molecular energetics
and force fields, molecular flexibility, synaptic transmission, synaptic spillover).
Lecture Topics
Grading
You will be graded on weekly homework assignments (70%) and a final exam (30%).
Lectures
DATE 
LECTURES 
August 28 
Preliminaries of Multiscale geometry; Multiscale imaging; Applications from Modeling Biology

September 2 

September 4 

September 9,11 

September 16,18 
Models/Maps: Extraction of affine invariant PCS from 3D Images (Geometry Elucidation)

September 23,25 

September 30 
Generation of Curves and Surface Splines from Scattered Points III: Contouring Scalar Functions

October 7,9 
Generation of Surface Splines from Curves I: Sweeping with Applications
to Cellular Organelles, Vasculature modeling 
October 14,16 
Generation of Surface Splines from Curves II: Lofting with Applications
in Neuronal Cell Modeling 
October 9 
Generation of Surface Splines from Curvilinear Complex III: Patch Fitting
with Applications to Organ modeling 
October 14 
Generation of Surface Splines from Curvilinear Complex IV: Subdivision
Schemes with Applications to Cell, Organs, Vessel modeling 
October 16 
Generation of Surface Splines from Curvilinear Complex V: Geometric
Flow with Applications to Hole Filling 
October 21 
Generation of Skeletons from Surface Models with Applications to Secondary/Tertiary
Protein Structure Elucidation 
October 23 
Generation of Complementary Surface Features with Applications to Shape
Matching 
October 28 
Construction of Adaptive Grids of Volumetric Domains with Boundaries

October 30 
Construction of Adaptive Triangulations of Volumetric Domains with Boundaries

November 4 
Construction of Adaptive Hexahedral Decompositions of Volumetric Domains
with Boundaries 
November 6 
Geometric Matching and Docking I: Complementary Space Docking 
November 11 
Geometric Matching and Docking II: Flexible Docking 
November 13 
Geometric Matching and Docking III: Matching Geometry with Imaging 
November 18 
Multiscale Function Modeling I: Molecular Energetics, Solvation, Force
Fields 
November 20 
Multiscale Function Modeling II: Generalized Born and Poisson Boltzmann

November 11 
Multiscale Function Modeling III: Random Walks, Diffusion and Drift

November 18 
Multiscale Function Modeling IV: Diffusion and Reaction 
November 20 
Multiscale Function Modeling V: Branching Processes 
November 25 
Multiscale Function Modeling V: Branching Processes
Actin Polymerization, Vascular Networks

Decemeber 2 
Multiscale Function Modeling VI: Interfacial Dynamics 
December 4 
Multiscale Function Modeling VII: Acoustic , Light, EM Scattering 
December 4 
Multiscale Visualization, Informatics I : Model and Map Resolutions,
Errors and Uncertainity 
December 6 
Multiscale Visualization, Informatics II: 
Exercises:
1 
Exercise 1 Algebraic Curve, Surface Splines  I Solution 1 
2 
Exercise 2 Algebraic Curve, Surface Splines  II Solution 2 
3 
Exercise 3 Algebraic Curve, Surface Splines  III Solution 3 
4 
Exercise 4 Algebraic Curve, Surface Splines  IV: Molecular Models Solution 4 
5 
Exercise 5 Finite Element Meshing  I: Linear Elemen Solution 5 
6 
Exercise 6 Finite Element Meshing II  NonLinear Elements Solution 6 
7 
Exercise 7 Geometric Modeling and Visualization Final Solution 7 
Pictures and Animations
Suggested Reading
Links