2. Molecular Shape Generation
Links
Interactive Visualization of Biomolecules and their Properties
(pdf).
2.1 CPK model, Solvent Accessible and Solvent Excluded surfaces
We consider NURBS based data structures for molecules and their properties, to
support synthetic drug design and structural reasoning applications in molecular chemistry.
The difficulty of modeling and visualization of large molecules derives from the high
combinatorial complexity of the typical molecule considered (e.g. proteins or nucleic
acids). There are two main modeling approaches. The first describes the molecule's
primary structure and the detailed 3D position of each of its atoms. The second groups
some regions of the molecule into simpler shapes to describe the folding of the molecule
into its secondary, tertiary and higher order structures.
We develop a Brep data structure for molecular surfaces that aims to be useful both for
visualization and modeling purposes. This requires the ability (a) to exactly represent
the shape of the molecule, (b) to directly render such a representation, and (c) to perform
modeling operations that correspond to the addition/deletion of residues. The natural
choice to achieve both goals is to use trimmed NURBS (Non Uniform Rational tensorproduct
BSpline with rational BSpline trimming curves). They are an industrywide standard as
a modeling primitive and graphics libraries for NURBS rendering are available (e.g. openGL,
OpenInventor). Moreover, the rational parameterization allows for an exact representation
of a spherical surface. This alone is not sufficient. In order to have an exact
representation of a macromolecular structure we also need to represent for each atom, not
its entire sphere, only that portion of the sphere which belongs to the external molecule
surface. This means that from the sphere which represents one atom we must cut away the
pieces contained in the neighboring atoms. We prove that adopting a certain parameterization
each trimming curve (a circle) in the 3D space is mapped back in the parameter domain to
a curve that can be in turn represented exactly as a NURBS curve. In this way we can
represent the contribution of each atom to the molecule surface with a trimmed NURBS patch
without any approximation.
The main contributions of the approach are:
 the definition of a (minimal size) Brep with standard trimmed NURBS representation;
 parametric Brep model of the solvent accessible surface useful for animation
 the classification of the solvent contact surface and computation of its representation
as a trimmed NURBS.

Papers
[1] 
C. Bajaj, H.Y. Lee, R. Merkert, V. Pascucci
NURBS based Brep Models from Macromolecules and their Properties
( ps ),
In Proceedings Fourth Symposium on Solid Modeling and Applications, Atlanta, Georgia, 1997,
C. Hoffmann and W. Bronsvort Eds., ACM Press. pp. 217228 
[2] 
C. L. Bajaj, V. Pascucci, A. Shamir, R. Holt, A. Netravali
Multiresolution Molecular Shapes,
TICAM Report No. 9942 (
pdf )

Links
Molecular Surfaces
Molecular Visualization Presentation
2.2 Isosurfaces of Molecular Electron Density
Papers
[1] 
C. Bajaj, V. Pascucci, D. Schikore.
Fast Isocontouring for Improved Interactivity
Proceedings: ACM Siggraph/IEEE Symposium on Volume Visualization,
ACM Press, (1996), San Francisco, CA (
ps.gz )

[2] 
C. Bajaj, V. Pascucci, R. Holt, A. Netravali.
Dynamic Maintenance and Visualization of Molecular Surfaces
Fourth issue in the special series of Discrete Applied Mathematics on
Computational Molecular Biology
( pdf ),
( psgz pages 117 ),
( psgz pages 1931 ),
Color Plate (page 18) ( pdf ),
( psgz ),
( Abstract )

[3] 
C. L. Bajaj, V. Pascucci, A. Shamir, R. Holt, A. Netravali.
Multiresolution Molecular Shapes
TICAM report # 9942
( ps.gz )
( pdf )

[4] 
C. Bajaj, H.Y. Lee, R. Merkert, V. Pascucci
NURBS based Brep Models from Macromolecules and their Properties,
In Proceedings Fourth Symposium on Solid Modeling and Applications,
Atlanta,Georgia, 1997,C. Hoffmann and W. Bronsvort Eds., ACM Press. pp. 217228
( ps.gz )

[5] 
C. Bajaj, F. Bernardini, K. Sugihara
A Geometric Approach to Molecular Docking and Similarity
Technical Report 94017 (20 pages), Purdue University, Computer Sciences (3/94)
( pdf )
( ps.gz )

[6] 
X. Zhang, C. Bajaj, V. Ramachandra
Parallel and Outofcore Viewdependent Isocontour Visualization
Using Random Data Distribution
Joint EurographicsIEEE TCVG Symposium on Visualization 2002, pages 918.
( pdf )

[7] 
C. Bajaj, V. Pascucci,D.Thompson, X.Y. Zhang
Parallel Accelerated Isocontouring for OutOfCore Visualization, i
In Proceedings of IEEE Parallel Visualization and Graphics Symposium, October
2429,1999 San Francisco, CA, pages 97  104.
( ps )
( pdf )

[8] 
C. Bajaj, V. Pascucci
Progressive IsoContouring, TICAM report #9936i
( ps.gz )
( pdf )

[9] 
C. Bajaj, V. Pascucci, D.Schikore
Accelerated IsoContouring of Scalar Fields, Data Visualization Techniques,
edited by C. Bajaj, John Wiley and Sons
( psgz )
( pdf )

[10] 
C. Bajaj, V. Pascucci, D. Schikore
Fast Isocontouring for Improved Interactivity,
Proceedings: ACM Siggraph/IEEE Symposium on Volume Visualization,
ACM Press, (1996), San Francisco, CA
( ps.gz )

[11] 
C. Bajaj, V. Pascucci, D. Schikore
Fast Isocontouring for Improved Interactivity,
Technical Report 96024, Purdue University, Computer Sciences(1996)
( ps.gz )

2.3 CryoEM
From electron density field, we compute isosurfaces of molecules and
using properties of molecules such as static electricity, we can also
compute electro static field from which we can compute the color values
used to color isosurfaces of molecular shapes.
