Add to ORKGIn this paper we provide a new characterization of cell de- composition (called slope complex) of a given 2-dimensional continuous surface. Each patch (cell) in the decomposition must satisfy that there exists a monotonic path for any two points in the cell. We prove that any triangulation of such surface is a slope complex and explain how to obtain new slope complexes with a smaller number of slope regions decomposing the surface. We give the minimal number of slope regions by counting certain bounding edges of a triangulation of the surface obtained from its critical points.Ministerio de Economía y Competitividad MTM2015-67072-
An algebraic domain is a closed topological subsurface of a real affine plane whose boundary consist...
Doctor of PhilosophyMathematicsIlia ZharkovA smooth affine hypersurface of complex dimension n is ho...
Given a triangulated closed surface, the problem of constructing a hierarchy of surface models of d...
The discrete version of a continuous surface sampled at optimum sampling rate can be well expresse...
This paper provides a theoretical characterization of monotonically connected image surface regions...
The vertices of the neighborhood graph of a digital picture P can be interpolated to form a 2-manifo...
Critical points of a scalar function (minima, saddle points and maxima) are important features to ch...
The slope variety of a graph G is an algebraic variety whose points correspond to the slopes arising...
Abstract. Slopes needed to obtain a monotone piecewise cubic Hermite interpolant are constructed. Th...
The task of finding all physically relevant solutions to mathematical models of physical systems rem...
lines con-necting n points in general position in the plane. The ideal In of all algebraic relations...
The planar slope number of a planar graph G is defined as the minimum number of slopes that is requi...
Flips and flops are elementary birational maps which first appear in dimension three. We give exampl...
AbstractA procedure is proposed to follow the “minimum path” of a hypersurface starting anywhere in ...
The curve complex of a closed surface S of genus g ≥ 2, C(S), is the complex whose vertices are isot...
An algebraic domain is a closed topological subsurface of a real affine plane whose boundary consist...
Doctor of PhilosophyMathematicsIlia ZharkovA smooth affine hypersurface of complex dimension n is ho...
Given a triangulated closed surface, the problem of constructing a hierarchy of surface models of d...
The discrete version of a continuous surface sampled at optimum sampling rate can be well expresse...
This paper provides a theoretical characterization of monotonically connected image surface regions...
The vertices of the neighborhood graph of a digital picture P can be interpolated to form a 2-manifo...
Critical points of a scalar function (minima, saddle points and maxima) are important features to ch...
The slope variety of a graph G is an algebraic variety whose points correspond to the slopes arising...
Abstract. Slopes needed to obtain a monotone piecewise cubic Hermite interpolant are constructed. Th...
The task of finding all physically relevant solutions to mathematical models of physical systems rem...
lines con-necting n points in general position in the plane. The ideal In of all algebraic relations...
The planar slope number of a planar graph G is defined as the minimum number of slopes that is requi...
Flips and flops are elementary birational maps which first appear in dimension three. We give exampl...
AbstractA procedure is proposed to follow the “minimum path” of a hypersurface starting anywhere in ...
The curve complex of a closed surface S of genus g ≥ 2, C(S), is the complex whose vertices are isot...
An algebraic domain is a closed topological subsurface of a real affine plane whose boundary consist...
Doctor of PhilosophyMathematicsIlia ZharkovA smooth affine hypersurface of complex dimension n is ho...
Given a triangulated closed surface, the problem of constructing a hierarchy of surface models of d...