The efficient construction of simplified models is a central problem in the field of visualization. We combine topological and geometric methods to construct a multi-resolution data structure for functions over two-dimensional domains. Starting with the MorseSmale complex we build a hierarchy by progressively canceling critical points in pairs. The data structure supports mesh traversal operations similar to traditional multi-resolution representations
We address the problem of representing and processing 3D objects, described through simplicial meshe...
168 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2001.The thesis also gives algorit...
Abstract. We introduce a method for analyzing high-dimensional data. Our approach is inspired by Mor...
We present an approach to hierarchically encode the topology of functions over triangulated surfaces...
We present an approach to hierarchically encode the topology of functions over triangulated surfaces...
The Morse-Smale complex is a useful topological data structure for the analysis and visualization of...
Morse theory offers a natural and mathematically-sound tool for shape analysis and understanding. It...
The Morse complex can be used for studying the topology of a function, e.g., an image or terrain hei...
The Morse-Smale complex is an efficient representation of the gradient behavior of a scalar function...
Classical Morse Theory [8] considers the topological changes of the level sets Mh = { x ∈ M | f(x) ...
We address the problem of representing the geometry and the morphology of a triangulated surface end...
We consider the problem of efficiently computing a discrete Morse complex on simplicial complexes of...
The 3D Morse-Smale complex is a fundamental topological construct that partitions the domain of a re...
The field of computational topology has developed many powerful tools to describe the shape of data,...
Ascending and descending Morse complexes, determined by a scalar field f defined over a manifold M, ...
We address the problem of representing and processing 3D objects, described through simplicial meshe...
168 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2001.The thesis also gives algorit...
Abstract. We introduce a method for analyzing high-dimensional data. Our approach is inspired by Mor...
We present an approach to hierarchically encode the topology of functions over triangulated surfaces...
We present an approach to hierarchically encode the topology of functions over triangulated surfaces...
The Morse-Smale complex is a useful topological data structure for the analysis and visualization of...
Morse theory offers a natural and mathematically-sound tool for shape analysis and understanding. It...
The Morse complex can be used for studying the topology of a function, e.g., an image or terrain hei...
The Morse-Smale complex is an efficient representation of the gradient behavior of a scalar function...
Classical Morse Theory [8] considers the topological changes of the level sets Mh = { x ∈ M | f(x) ...
We address the problem of representing the geometry and the morphology of a triangulated surface end...
We consider the problem of efficiently computing a discrete Morse complex on simplicial complexes of...
The 3D Morse-Smale complex is a fundamental topological construct that partitions the domain of a re...
The field of computational topology has developed many powerful tools to describe the shape of data,...
Ascending and descending Morse complexes, determined by a scalar field f defined over a manifold M, ...
We address the problem of representing and processing 3D objects, described through simplicial meshe...
168 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2001.The thesis also gives algorit...
Abstract. We introduce a method for analyzing high-dimensional data. Our approach is inspired by Mor...