A new class of discrete conformal structures on surfaces with boundary
نویسندگان
چکیده
We introduce a new class of discrete conformal structures on surfaces with boundary, which have nice interpretations in 3-dimensional hyperbolic geometry. Then we prove the global rigidity using variational principles, is complement Guo–Luo’s Guo and Luo (Geom Topol 13(3):1265–1312, 2009) Guo’s vertex scaling (Commun Contemp Math 13(5):827–842, 2011) boundary. As byproduct, results convexity volume generalized pyramids right-angled hexagonal bases are obtained. Motivated by Chow–Luo’s combinatorial Ricci flow Luo’s Yamabe closed surfaces, further Calabi flows to deform The basic properties these curvature established. These provide effective algorithms for constructing metrics totally geodesic boundary components prescribed lengths.
منابع مشابه
Conformal Structures of Surfaces ∗
This paper solves the problem of computing conformal structures of general 2manifolds represented as triangular meshes. We approximate the De Rham cohomology by simplicial cohomology and represent the Laplace-Beltrami operator, the Hodge star operator by linear systems. A basis of holomorphic one-forms is constructed explicitly. We then obtain a period matrix by integrating holomorphic differen...
متن کاملComputing Conformal Structures of Surfaces
According to Klein’s Erlangen program, different geometry branches study invariants of a space under different transformation groups. Topology and Euclidean geometry have been widely applied in computer graphics and vision. Between topological transformation group and Euclidean transformation group, there exists a conformal transformation group, which has not been well studied by computer scien...
متن کاملMAGMA-JOINED-MAGMAS: A CLASS OF NEW ALGEBRAIC STRUCTURES
By left magma-$e$-magma, I mean a set containingthe fixed element $e$, and equipped by two binary operations "$cdot$", $odot$ with the property $eodot (xcdot y)=eodot(xodot y)$, namelyleft $e$-join law. So, $(X,cdot,e,odot)$ is a left magma-$e$-magmaif and only if $(X,cdot)$, $(X,odot)$ are magmas (groupoids), $ein X$ and the left $e$-join law holds.Right (and two-sided) magma-$e$-magmas are de...
متن کاملMultiresolution Computation of Conformal Structures of Surfaces
An efficient multiresolution method to compute global conformal structures of nonzero genus triangle meshes is introduced. The homology, cohomology groups of meshes are computed explicitly, then a basis of harmonic one forms and a basis of holomorphic one forms are constructed. A progressive mesh is generated to represent the original surface at different resolutions. The conformal structure is...
متن کاملDiscrete Topology-Revealing Vector Fields on Simplicial Surfaces with Boundary
We present a discrete Hodge-Morrey-Friedrichs decomposition for piecewise constant vector fields on simplicial surfaces with boundary which is structurally consistent with the smooth theory. In particular, it preserves a deep linkage between metric properties of the spaces of harmonic Dirichlet and Neumann fields and the topology of the underlying geometry, which reveals itself as a discrete de...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Calculus of Variations and Partial Differential Equations
سال: 2022
ISSN: ['0944-2669', '1432-0835']
DOI: https://doi.org/10.1007/s00526-022-02248-x