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- Herbert Edelsbrunner, John Harer, Vijay Natarajan, Valerio Pascucci
- Symposium on Computational Geometry
- 2003

We define the Morse-Smale complex of a Morse function over a 3-manifold as the overlay of the descending and ascending manifolds of all critical points. In the generic case, its 3-dimensional cells are shaped like crystals and are separated by quadrangular faces. In this paper, we give a combinatorial algorithm for constructing such complexes for piecewiseâ€¦ (More)

- Kree Cole-McLaughlin, Herbert Edelsbrunner, John Harer, Vijay Natarajan, Valerio Pascucci
- Symposium on Computational Geometry
- 2003

Given a Morse function f over a 2-manifold with or without boundary, the Reeb graph is obtained by contracting the connected components of the level sets to points. We prove tight upper and lower bounds on the number of loops in the Reeb graph that depend on the genus, the number of boundary components, and whether or not the 2-manifold is orientable. Weâ€¦ (More)

- Harish Doraiswamy, Vijay Natarajan
- Comput. Geom.
- 2009

The Reeb graph tracks topology changes in level sets of a scalar function and finds applications in scientific visualization and geometric modeling. We describe an algorithm that constructs the Reeb graph of a Morse function defined on a 3-manifold. Our algorithm maintains connected components of the two dimensional levels sets as a dynamic graph andâ€¦ (More)

- Herbert Edelsbrunner, John Harer, Vijay Natarajan, Valerio Pascucci
- IEEE Visualization 2004
- 2004

We introduce local and global comparison measures for a collection of k Â¿ d real-valued smooth functions on a common d-dimensional Riemannian manifold. For k = d = 2 we relate the measures to the set of critical points of one function restricted to the level sets of the other. The definition of the measures extends to piecewise linear functions for whichâ€¦ (More)

- Vijay Natarajan
- 2009

The Jacobi set of two Morse functions defined on a 2-manifold is the collection of points where the gradients of the functions align with each other or where one of the gradients vanish. It describes the relationship between functions defined on the same domain, and hence plays an important role in multi-field visualization. The Jacobi set of two piecewiseâ€¦ (More)

- Attila Gyulassy, Vijay Natarajan, Valerio Pascucci, Peer-Timo Bremer, Bernd Hamann
- IEEE Transactions on Visualization and Computerâ€¦
- 2006

This paper describes an efficient combinatorial method for simplification of topological features in a 3D scalar function. The Morse-Smale complex, which provides a succinct representation of a function's associated gradient flow field, is used to identify topological features and their significance. The simplification process, guided by the Morse-Smaleâ€¦ (More)

- Harish Doraiswamy, Vijay Natarajan
- IEEE Transactions on Visualization and Computerâ€¦
- 2012

The Reeb graph of a scalar function represents the evolution of the topology of its level sets. This paper describes a near-optimal output-sensitive algorithm for computing the Reeb graph of scalar functions defined over manifolds or non-manifolds in any dimension. Key to the simplicity and efficiency of the algorithm is an alternate definition of the Reebâ€¦ (More)

- Senthilnathan Maadasamy, Harish Doraiswamy, Vijay Natarajan
- 2012 19th International Conference on Highâ€¦
- 2012

The contour tree is a topological abstraction of a scalar field that captures evolution in level set connectivity. It is an effective representation for visual exploration and analysis of scientific data. We describe a work-efficient, output sensitive, and scalable parallel algorithm for computing the contour tree of a scalar field defined on a domain thatâ€¦ (More)

- Harish Doraiswamy, Vijay Natarajan
- ISAAC
- 2008

The Reeb graph tracks topology changes in level sets of a scalar function and finds applications in scientific visualization and geometric modeling. This paper describes a near-optimal two-step algorithm that constructs the Reeb graph of a Morse function defined over manifolds in any dimension. The algorithm first identifies the critical points of the inputâ€¦ (More)

- Vijay Natarajan, Yusu Wang, Peer-Timo Bremer, Valerio Pascucci, Bernd Hamann
- Computer Aided Geometric Design
- 2006

This paper presents a new method for segmentation of molecular surfaces. Topological analysis of a scalar function defined on the surface and its associated gradient field reveals the relationship between the features of interest and critical points of the scalar function. The segmentation is obtained by associating segments with local minima/maxima.â€¦ (More)