Wavelet multiresolution analysis produces a hierarchical series of best lower-resolution approximations in a least-squares sense. Wavelets can decompose any function: a 2D image, a curve, a surface, or a volume. This provides an elegant representation of the level of detail present.
A multiresolution representation for end-point interpolating B-spline curves was developed using wavelets by Finkelstein and Salesin [1]. This multiresolution curve (MRC) formulation allows continuous levels of smoothing and approximating the curve with a given error tolerance. It also allows editing of the overall sweep of the curve at a lower resolution while maintaining the fine details at high resolution.
The protein folding process, where the linear sequence of amino acids determines the unique three-dimensional path of the backbone, remains a major unsolved problem in biology and chemistry. Ribbon splines are used to model the backbone. The wavelet analysis should establish limits on the minimum information required to specify the winding of the backbone through space.
The manipulation and comparison of protein backbones using computers and graphics is vital to protein crystallography and molecular modeling. Multiresolution comparison and editing are powerful new tools. Techniques to interactively make large changes of a protein backbone with a minimal amount of user manipulation should improve user interfaces for molecular modeling.
Molecular surface complementarity is critical in the binding of ligand to receptor. The 'docking problem' is central to computer-aided structure-based drug design. The problem has been addressed in many ways [2], all computationally intensive. Wavelets extended to surfaces and texture mapping apply to any molecule and should yield simplified representations. To assess the potential of wavelets applied to molecular structure, the ideas suggested by Finkelstein and Salesin [1] were implemented as interactive computer graphics programs.
This paper is based on a presentation given at the 14th Molecular Graphics and Modeling Society Conference, held in Cairns, Australia, August 27-September 1, 1995.