5,529 research outputs found
Density-equalizing maps for simply-connected open surfaces
In this paper, we are concerned with the problem of creating flattening maps
of simply-connected open surfaces in . Using a natural principle
of density diffusion in physics, we propose an effective algorithm for
computing density-equalizing flattening maps with any prescribed density
distribution. By varying the initial density distribution, a large variety of
mappings with different properties can be achieved. For instance,
area-preserving parameterizations of simply-connected open surfaces can be
easily computed. Experimental results are presented to demonstrate the
effectiveness of our proposed method. Applications to data visualization and
surface remeshing are explored
Non-oriented solutions of the eikonal equation
We study a new formulation for the eikonal equation |grad u| =1 on a bounded
subset of R^2. Instead of a vector field grad u, we consider a field P of
orthogonal projections on 1-dimensional subspaces, with div P in L^2. We prove
existence and uniqueness for solutions of the equation P div P=0. We give a
geometric description, comparable with the classical case, and we prove that
such solutions exist only if the domain is a tubular neighbourhood of a regular
closed curve. The idea of the proof is to apply a generalized method of
characteristics introduced in Jabin, Otto, Perthame, "Line-energy
Ginzburg-Landau models: zero-energy states", Ann. Sc. Norm. Super. Pisa Cl.
Sci. (5) 1 (2002), to a suitable vector field m satisfying P = m \otimes m.
This formulation provides a useful approach to the analysis of stripe
patterns. It is specifically suited to systems where the physical properties of
the pattern are invariant under rotation over 180 degrees, such as systems of
block copolymers or liquid crystals.Comment: 14 pages, 4 figures, submitte
Smooth 2D Coordinate Systems on Discrete Surfaces
International audienceWe introduce a new method to compute conformal param- eterizations using a recent definition of discrete conformity, and estab- lish a discrete version of the Riemann mapping theorem. Our algorithm can parameterize triangular, quadrangular and digital meshes. It can be adapted to preserve metric properties. To demonstrate the efficiency of our method, many examples are shown in the experiment section
Global smoothness of quasiconformal mappings in the Triebel-Lizorkin scale
We give sufficient conditions for quasiconformal mappings between simply
connected Lipschitz domains to have H\"older, Sobolev and Triebel-Lizorkin
regularity in terms of the regularity of the boundary of the domains and the
regularity of the Beltrami coefficients of the mappings. The results can be
understood as a counterpart for the Kellogg-Warchawski Theorem in the context
of quasiconformal mappings.Comment: 45 pages, 3 figure
- …