We develop technology for multi-scale shape analysis of massive geometric models (100s of millions of triangles) on commodity computers. This technology was used to detect many minute connectivity flaws in these models; a task that was not possible with existing methods.

Scientific investigation into many natural and experimental phenomena, ranging from the rate of formation of heavy elements in supernovae to the design of capsules for Inertial Confinement Fusion, requires the study of hydrodynamic instabilities. We design and implement new data analysis tools that can process massive quantities of simulation data, detect and track features, and generate statistical information that reveals distinct turbulent mixing phases in the simulation.

Time-varying computational simulation data must be analyzed to validate the mathematical model used in developing the simulation and to understand the physical phenomena under study. As part of my Ph.D. thesis, I developed the mathematical theory and robust combinatorial algorithms to compute the topological evolution, both in time and space, of isosurfaces in time-varying data.

We propose a compressed on-disk representation for regular volume grids that allows streaming, I/O-efficient, out-of-core isosurface extraction. As grid cells are decompressed, we immediately extract vertices and triangles of the isosurface. Our output is a coherent streaming mesh, which facilitates subsequent processing, including on-the-fly simplification and compression.

Haptic interface devices enable the sense of touch in virtual environments, but this capability comes at a cost; force and torque must be displayed at 1000 Hz to achieve realism. We develop algorithms and systems that can handle moderate-sized polygon count (in the 100s) models, and vector-fields for realistic haptic rendering.

We develop a geometric model of the hydrogen bond and software to test geometric alignment of hydrogen bonds to identify potential ligand binding conformations in the Human Pregnane X Receptor (hPXR), and use them as a starting point for further refinement.

- Time-varying Reeb Graphs for Continuous Space-Time Data, H. Edelsbrunner, J. Harer, A. Mascarenhas, J. Snoeyink, and V. Pascucci, in Computation Geometry: Theory and Applications. 41, 3, pages 149-166, Nov. 2008
- Robust On-line Computation of Reeb Graphs: Simplicity and Speed, V. Pascucci, G. Scorzelli, P.-T. Bremer, and A. Mascarenhas, in ACM Transactions on graphics, pages 58.1-58.9, 2007, Proceedings of SIGGRAPH 2007.
- Understanding the Structure of the Turbulent Mixing Layer in Hydrodynamic Instabilities, D. Laney, P.-T. Bremer, A. Mascarenhas, P. Miller, and V. Pascucci, in IEEE Transactions on Visualization and Computer Graphics Vol. 12, No.5, pages 1053-1060, 2006. Proceedings of IEEE VIS 2006.
- Topological Feature Extraction and Tracking, P.-T. Bremer, E. Bringa, M. Duchaineau, A. Gyulassy, D. Laney, A. Mascarenhas, V. Pascucci, in Proceedings of SciDAC 2007 Scientific Discovery through Advanced Computing, volume 78, page 012032 (5pp). Journal of Physics Conference Series, June 2007.
- Understanding the Structure of the Turbulent Mixing Layer in Hydrodynamic Instabilities, P.-T. Bremer, W. Cabot, A. Cook, D. Laney, A. Mascarenhas, P. Miller, and V. Pascucci, in Proceedings of SciDAC 2006 – Scientific Discovery through Advanced Computing, volume 46, pages 556–560. Journal of Physics Conference Series, June 2006.

- Time-varying Reeb Graphs for Continuous Space-Time Data, H. Edelsbrunner, J. Harer, A. Mascarenhas, and V. Pascucci, in Symposium on Computational Geometry, 2004, pages 366-372. (extended version to appear in CGTA journal, 2008)
- Encoding Volumetric Grids for Streaming Isosurface Extraction, A. Mascarenhas, M. Isenburg, V. Pascucci, and J. Snoeyink, in Second International Symposium on 3D Data Processing, Visualization and Transmission, 2004, pages 665-672.
- Six Degrees-of-Freedom Haptic Display of Polygonal Models, A. Gregory, A. Mascarenhas, S. Ehmann, M. Lin and D. Manocha, in IEEE Visualization 2001, pages 139-146.

- Isocontour-based Visualization of time-varying data, A. Mascarenhas, J. Snoeyink, in Mathematical Foundations of Scientific Visualization, Computer Graphics, and Massive Data Exploration, Editors: T. Moeller, B. Hamann, and B. Russell, Springer-Verlag, to appear December 2008.
- Six Degrees-of-freedom Haptic Visualization, A. Mascarenhas, S. Ehmann, A. Gregory, M. Lin and D. Manocha, in Touch in Virtual Environments: Haptics and the Design of Interactive Systems. Editors: M. L. McLaughlin, J. P. Hespanha, G. S. Sukhatme. Prentice Hall, 2002.
- Scientific Data Managment Challenges in High Performance Visual Data Analysis, E. W. Bethel, H. Childs, A. Mascarenhas, V. Pascucci, Prabhat.. In Arie Shoshani and Doron Rotem, editors, Scientific Data Management: Challenges, Existing Technology, and Deployment. Chapman & Hall/CRC Press, 2008.

- Application of Morse Theory to Analysis of Rayleigh-Taylor topology, P. L. Miller, P-T. Bremer, W. Cabot, A. Cook, D. Laney, A. Mascarenhas, V. Pascucci, in International Workshop on the Physics of Compressible Turbulent Mixing, Paris, France, Jul 17 - Jul 21, 2006.
- Topological Feature Extraction for Exploration of Terascale Combustion Data, A. Mascarenhas, R. W. Grout, P.-T. Bremer, E. R. Hawkes, V. Pascucci, J. H. Chen, in Topoinvis ’09: Topological Methods in Data Analysis and Visualization, Snowbird, Utah, February 23-24, 2009.

- Ligand Binding to the Pregnane X Receptor by Geometric Matching of Hydrogen Bonds, R.P. Berretty, D. Hsu, L. Kettner, A. Mascarenhas, M. Redinbo, J. Snoeyink, R. Watkins, in Currents in Computational Molecular Biology (RECOMB 2002), L. Florea, B. Walenz, S. Hannenhalli, editors, 2002, pages 22-23.
- Implementing Time-varying Contour Trees, A. Mascarenhas, J. Snoeyink, in ACM Computational Geometry Conference, Video Publications 2005.
- Analysis of the relationship between high scalar dissipation rate features, flow, and combustion, R.W. Grout, E.R. Hawkes, J.H. Chen, A. Mascarenhas, P.-T. Bremer, V. Pascucci, in 32nd International Symposium on Combustion, 2008, Montreal, Canada.