CS 384R (#52590), CAM 395T (#65115), BME 383J (#52590)

FALL 2010     MW 9:30 – 11:00am    WEL 4.224

Geometric (Bio-) Modeling and Visualization


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



Chandrajit Bajaj


ACES 2.324





Office hours

Mon,Wed 3:00 - 4:00p or by appt. via suzanne@ices.utexas.edu

CS384R, CAM395T, BME383J 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: algebraic curves, surfaces, splines, parametrization, intersection manifolds, singularities, topology,

Maps: x-ray diffraction, electron microscopy, CT/MRI imaging, reconstruction

Maps2Models: filtering, contrast enhancement, classification, symmetry detection, segmentation, skeletonization,  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 molecular energetics, forces, numerical quadrature, cubature, fast multiple methods, discrete differential operators, de-Rham diagrams, integral equations

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


Case Studies: molecular recognition, electrical signaling amongst neurons, cardio electrophysiology



You will be graded on bi-weekly homework assignments (50%), a semester programming project (30%), and a final exam (20%).





August 25

Preliminaries of Multiscale geometry; Multiscale imaging and Physiology; Applications in Modeling Biology Interpretive Bio-Animations

August 30

Models I: Shape Representations - Algebraic Curves, Surfaces Ganith

September 1

Models II: Shape Representations - Rational Parameterization I  Ganith

September 8

Models III: Shape Representations - Rational Parameterization II Ganith

September 13

Models IV: Shape Representations Regular Triangulations, Power Diagrams, Molecular Models Ganith

September 15

Models V: Algebraic Finite Elements - Curve-segments, Surface-patches Prism

September 20

Models VI: Algebraic Finite Elements - Barycentric Coordinates, Bernstein-Bezier Polynomial Interpolants Prism

September 22

Models VII: Algebraic Finite Elements - A-Splines and A-Patches Prism

September 27

Models VIII: Modeling with Algebraic Spline Finite Elements I (A-splines) Prism

September 29

Models IX: Modeling with Algebraic Spline Finite Elements II (A-patches) Prism

October 4

Models X: Modeling with Algebraic Spline Finite Elements III (Blending, Hermite Approximants) Prism

October 11

Models Xa: Modeling with Algebraic Spline Finite Elements IV (Reduction to SVD, QR Factorization)

October 13

Models XI: Modeling with Algebraic Spline Finite Element V (Trimmed Blending, Lofted Surfaces) 

October 18

Finite Element Meshing I - Quality Triangulations from Cross-Sections, Quadrangulations   LBIE

October 20

Finie Element Meshing II - Contouring/Dual Contouring LBIE


October 25

Finite Element Meshing III: Quality Improvement Techniques LBIE


October 27

Molecular Modeling I: Dynamic Packing Grids Algebraic Spline Molecular SurfacesLBIE


November 1

Molecular Modeling II: Energetics, Forces TexMol

November 3

Molecular Modeling III: Docking, Similarity TexMol

November 8

Maps I : B-spline Representations of ImagesVisTool

November 10

Maps IIa: Image Contrast Enhancement VisTool

November 15

Maps IIb: Image/Surface Anisotropic FilteringVisTool

November 17

Maps IIIa: Image/Maps Segmentation, Structure Elucidation VisTool

November 22

Maps IIIb: Molecular Modeling from Imaging: Match and FitVolRover

November 29

Maps IV: Shape Reconstruction from Imaging


1 (Sept.  13)

Exercise 1 Algebraic Curve, Surface Splines - I Solution 1

2   (Oct. 7))

Exercise 2 Algebraic Curve, Surface Splines - II Solution 2

3  (Oct. 28)

Exercise 3 Spline Finite Elements Interpolation, Meshing /span> Solution 3

4  (Nov. 19)

Exercise 4 Spline Finite Elements and Image Processing Solution 4

5  (Dec. 3)

Final Exercise Molecular Models and Differential Properties Final Solution


Suggested Projects


I Molecular Forces and Recognition


II Neuronal Structure and Plasticity


III Cardio Deformations and Electrophysiology


Pictures and Animations


Suggested Reading

Papers Reading List


Group Meeting Schedule