
Discrete Gradient Line Fields on Surfaces
A line field on a manifold is a smooth map which assigns a tangent line ...
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Floer Homology: From Generalized MorseSmale Dynamical Systems to Forman's Combinatorial Vector Fields
We construct a Floer type boundary operator for generalised MorseSmale ...
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Finding and Classifying Critical Points of 2D Vector Fields: A CellOriented Approach Using Group Theory
We present a novel approach to finding critical points in cellwise bary...
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Critical Sets of PL and Discrete Morse Theory: a Correspondence
Piecewiselinear (PL) Morse theory and discrete Morse theory are used in...
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Combinatorial Gradient Fields for 2D Images with Empirically Convergent Separatrices
This paper proposes an efficient probabilistic method that computes comb...
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Toward a deeper understanding of a basic cascade
Towards the end of the last century, B. Mandelbrot saw the importance, r...
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A bisector line field approach to interpolation of orientation fields
We propose an approach to the problem of global reconstruction of an ori...
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Discrete Line Fields on Surfaces
Vector fields and line fields, their counterparts without orientations on tangent lines, are familiar objects in the theory of dynamical systems. Among the techniques used in their study, the Morse–Smale decomposition of a (generic) field plays a fundamental role, relating the geometric structure of phase space to a combinatorial object consisting of critical points and separatrices. Such concepts led Forman to a satisfactory theory of discrete vector fields, in close analogy to the continuous case. In this paper, we introduce discrete line fields. Again, our definition is rich enough to provide the counterparts of the basic results in the theory of continuous line fields: a EulerPoincaré formula, a Morse–Smale decomposition and a topologically consistent cancellation of critical elements, which allows for topological simplification of the original discrete line field.
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