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address: Computer Science Department,
Lindley Hall 215, 150 S. Woodlawn Ave.,
Bloomington, IN 47405
email: 
phone:
Lab: (812) 856 5230
Cell: (203) 252 4478
Latest news: I recently completed my Ph.D. degree at the Computer Science Department at IUB. I am joining Renaissance Computing Institute (www.renci.org) as a visualization researcher.
My dissertation titled "Framework for Visualizing and Exploring High-Dimensional Geometry" will appear on www.proquest.com soon.
Note: this page may not be available after a few weeks. My stable web url is http://sidsweb.googlepages.com.
My research spans two complementary areas: Scientific visualization of mathematical models, and Perceptual issues associated with the visualizations of these high-dimensional objects and their complex spaces.
The problem in the first area concerns the investigation of
the techniques for the exploration, and
visualization of the geometric objects embedded in high-dimensional
Euclidean space (RN). The second area
focuses on the perception of the motion of the high-dimensional objects, which result when high-dimensional
geometric objects, undergoing rotational or scaling transformations, are projected into two, or three dimensions.
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Mathematical Visualization
in High Dimensions Visualizing high-dimensional geometric data is challenging because our visual system, and cognitive capabilities are adapted to (visually) interpreting the structure of physical objects in at most three dimensions. How can we then learn to perceive salient properties, and features of geometric structure in high dimensions? One possible solution is to automate the task of discovering interesting low-dimensional views (or projections) of the high-dimensional based on projection pursuit techniques. This objective is to define suitable objective functions, which capture the geometric information in the views projected to the two or three dimensions. In this work, we are investigating different objective functions that are useful for finding the desired low-dimensional views, and navigation techniques to explore the set of such views in high-dimensional space. The images on the right show examples two objects in four and six dimensions respectively; these projections were chosen to highlight the interesting topological, and geometric features of this object. |
 Image of a hyper torus, which is a 2D manifold in 4D, shown in two different three-dimensional projections. 
 Images of the two variants of the Steiner surface, which is the image of the Real Projective plane (RP) in Euclidean three-space (i.e. the map RP2->R3). Left: Roman surface, and right: Cross Cap. |
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Perception of the 4D
Perception in 4D deals with the understanding of our perceptual abilities to comprehend, and interact with objects in four-dimensional Euclidean space, and understand their spatial transformations. In the psychological experiments we conducted, we found that naive subjects could reliably identify 4D objects from their 3D projections after being trained. We are extending these experiments to answer a broader question: what perceptual learning about complex 4D spaces is facilitated by exposing subjects to novel transformations of 4D objects? And even further: how can such understanding assist in the improvement of visual interfaces that tackle complex, multi-dimensional data? The image and animation on the right depict some
frames from our psychometric experiment. The example
shown is that of a
cloud of points on the surface of 4D objects as seen in
3D, and undergoing rigid rotation in 4D
(shape-preserving transformation). |
  Left: Image of a 4D torus made of points on the surface, and projected to three dimensions. Right: Animation of a 4D pillow-shaped object undergoing 4D rigid (shape-preserving) rotation. (5MB file size) |
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Quaternion Visualization
I. Belt Trick: In the recent years, Dr. Hanson's tutorial on Quaternion visualization at the IEE Visualization and SIGGRAPH conferences has included a nifty demonstration involving the famous belt trick. The trick involves transforming a twisted belt (without cutting it) until it is straightened. Curiously, a 360-degrees twisted belt cannot be untwisted but a 720-degree twisted belt can be. I wrote a quaternion visualization, which relates the behavior of the belt to continuous quaternion curves, and exposes the differences in the behavior of a singly, and doubly-twisted belt. The demonstration is available via the link given below, and provides an interactive interface to experience the belt trick first hand. Download demonstration software here: |
  Animations showing the 360-degrees and 720-degrees belt trick. In the first animation notice that moving the belt in space does not straighten it, but only changes the sign in the twist (clock-wise to anti clock-wise). (14MB file size) |
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II. Tubing: Quaternion visualization is very
useful for understanding properties of a set of
orientation frames, such as those defined on a
continuous curve. The figures on the right show a
3D-space curve having orientation frames based on the
Parallel Transport framing method used
for computing the tube structure. The quaternion
visualization of the frames is depicted as the green curve
shown in the second image. The mesh structure
corresponds to all of the available degrees of freedom
corresponding to each tangent on the 3D-space curve. Reverse Parallel Transport (PT) Transformation: An intuitive method for understanding the properties of curves for tubing purposes is the inverse or reverse PT transformation, which involves straightening out a curve by incrementally bending it along some fixed direction. This visualization is useful for studying properties of a set of frames by separating the orientation components due to the turning (bending) of the curve, and due to the twisting of the frame about the tangent. The sequence of frames shown below depict the reverse PT transformation applied to an open 3D-space curve, and having frames twisted about the tangents. After unfurling or straightening the curve, only the twisted component remains.
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 Left: A continuous 3D-space curve having at C0 and C1 continuity, and its orientation frames. Right: The quaternion plot showing the quaternion curve (green curve), which corresponds to the frames in the 3D-space curve.
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Protein Structure Visualization
Protein 3D spatial structure is very crucial in allowing proteins to function as essential biochemical agents in several life processes. We propose to visualize, and explore spatial orientation relations among the constituent amino acid units by employing quaternion-based visualizations. The images on the right show a protein complex with a single strand, modeled as a continuous B-Spline curve. Although the spline curve is an approximation to the physical protein strand, it allows us to attach orientation frames based on the orientations derived from the amino acid tetrahedral structure. The image on the bottom corresponds to the quaternion map of the orientation frames; the helical pattern of the frames appears as ellipses in the map. This approach provides an alternate way of looking at global relations among protein structures. |
   Image of a single stranded, helical protein and its quaternion map |
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Zhang, H., Thakur, S., Hanson, A.J. (2007). Haptic Exploration of Mathematical Knots. 3rd International Symposium on Visual Computing, ISVC (1) 2007 p. 745-756 [pdf]
Thakur, S., Hanson, A. J., & Bingham, G. P. (2006). Active visualization methods enable perception of structure and motion in higher dimensional spaces: Comparing active vs. passive perception of the rigidity of 3D and 4d objects. Journal of Vision, 6(6), 864a, http://journalofvision.org/6/6/864/, doi:10.1167/6.6.864. [link]
Ord, T. J., E. P. Martins, S. Thakur, K. K. Mane, K. Borner. (2005). Trends in animal behavior research (1968-2002): ethoinformatics and mining library databases. Animal Behaviour 69: 1399-1413. [pdf]
Thakur, S., Mane, K. Börner, K., Martins, E. & Ord, T. (2004). Content coverage of animal behavior data. Visualization and Data Analysis, 5295: 305-311. [pdf]
Mane Ketan, Mostafa Javed and Thakur Sidharth (2003), Oncosifter: A Customized Approach to Cancer Information. Presented at JCDL conference, Houston, TX. [pdf]
Work In Progress
Thakur, S. and Hanson, A. J. Quaternion based Optimization for Tube Textures.
Hanson, A. J. and Thakur, S. Quaternion Maps of Global Protein Structures.
Thakur, S. and Bingham, G. P. and Hanson, A.J. Perception of Objects in Four-Dimensional Space.
Developed demonstration software for visualizing the properties of quaternions for the book Visualizing Quaternions by Dr. Andrew Hanson, Morgan Kauffman 2005. The software is available via the url: www.cs.indiana.edu/~hanson/quatvis/
Contributed to the development of KnotExplorer, a haptic-based interface for exploring and interacting with mathematical knots. The application won an honorable mention during Sensable Technology’s 2005 Developer Challenge (keywords: Sensable 2005 challenge) [media].
Implemented the initial version of KnotInfo, a web-based knot repository, which is now a vast online resource on several categories of knot invariants and their properties. The website is available via this url: www.indiana.edu/~knotinfo
Contributed a software tutorial, and developed a learning module for InfoVis CyberInfrastructure, which is a web-based repository for various data mining and information visualization tools. The repository is available via this url: http://iv.slis.indiana.edu/index.html
