This dissertation explores techniques for interactive simulation and visualization for large protein datasets. My thesis is that using efficient representations for geometric and illumination data can help in developing algorithms that achieve better interactivity for visual and computational proteomics. I show this by developing new algorithms for computation and visualization for proteins. I also show that the same insights that resulted in better algorithms for visual proteomics can also be turned around and used for more efficient graphics rendering.

Molecular electrostatics is important for studying the structures and interactions of proteins, and is vital in many computational biology applications, such as protein folding and rational drug design. We have developed a system to efficiently solve the non-linear Poisson-Boltzmann equation governing molecular electrostatics. Our system simultaneously improves the accuracy and the efficiency of the solution by adaptively refining the computational grid near the solute-solvent interface. In addition, we have explored the possibility of mapping the PBE solution onto GPUs. We use pre-computed accumulation of transparency with spherical-harmonics-based compression to accelerate volume rendering of molecular electrostatics.

We have also designed a time- and memory-efficient algorithm for interactive visualization of large dynamic molecules. With view-dependent precision control and memory-bandwidth reduction, we have achieved real-time visualization of dynamic molecular datasets with tens of thousands of atoms. Our algorithm is linearly scalable in the size of the molecular datasets.

In addition, we present a compact mathematical model to efficiently represent the six-dimensional integrals of bidirectional surface scattering reflectance distribution functions (BSSRDFs) to render scattering effects in translucent materials interactively. Our analysis first reduces the complexity and dimensionality of the problem by decomposing the reflectance field into non-scattered and subsurface-scattered reflectance fields. While the non-scattered reflectance field can be described by 4D bidirectional reflectance distribution functions (BRDFs), we show that the scattered reflectance field can also be represented by a 4D field through pre-processing the neighborhood scattering radiance transfer integrals. We use a novel reference-points scheme to compactly represent the pre-computed integrals using a hierarchical and progressive spherical harmonics representation. Our algorithm scales linearly with the number of mesh vertices.