(see an mpeg example)

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 B-rep 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 tensor-product B-Spline with rational B-Spline trimming curves).  They are an industry-wide 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) B-rep with standard trimmed NURBS representation;
• parametric B-rep 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. 

C. Bajaj, H.Y. Lee, R. Merkert, V. Pascucci 
"NURBS based B-rep Models from Macromolecules and their Properties'', (ps.gz)
In Proceedings Fourth Symposium on Solid Modeling and Applications, Atlanta, Georgia, 1997,C. Hoffmann and W. Bronsvort Eds., ACM Press. pp. 217-228