منابع مشابه
Rigidity of Polyhedral Surfaces
We study the rigidity of polyhedral surfaces using variational principle. The action functionals are derived from the cosine laws. The main focus of this paper is on the cosine law for a non-triangular region bounded by three possibly disjoint geodesics. Several of these cosine laws were first discovered and used by Fenchel and Nielsen. By studying the derivative of the cosine laws, we discover...
متن کاملCurvature Smoothness of Subdivision Surfaces
We examine the smoothness properties of the principal curvatures of subdivision surfaces near extraordinary points. In particular we give an estimate of their Lp class based on the eigen structure of the subdivision matrix. As a result we can show that the popular Loop and Catmull-Clark schemes (among many others) have square integrable principal curvatures justifying their use as shape functio...
متن کاملInflating polyhedral surfaces
Can you have a non-convex polyhedron with a bigger volume than a convex polyhedron with the isometric surface? Imagine you start blowing air into a polyhedron with a bendable but non-stretchable surface. What can be said about the limiting shape? These are the key questions I will consider. I will start the talk by discussing the history of the problem, presenting examples, and surveying earlie...
متن کاملPeriod Matrices of Polyhedral Surfaces
Finding a conformal parameterization for a surface and computing its period matrix is a classical problem which is useful in a lot of contexts, from statistical mechanics to computer graphics. The 2D-Ising model [Mer01, CSM02, CSM03] for example can be realized on a cellular decomposition of a surface whose edges are decorated by interaction constants, understood as a discrete conformal structu...
متن کاملPolyhedral surfaces of high genus
The construction of the combinatorial data for a surface with n vertices of maximal genus is a classical problem: The maximal genus g = ⌊ 1 12 (n − 3)(n − 4)⌋ was achieved in the famous “Map Color Theorem” by Ringel et al. (1968). We present the nicest one of Ringel’s constructions, for the case n ≡ 7 mod 12, but also an alternative construction, essentially due to Heffter (1898), which easily ...
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: ACM Transactions on Graphics
سال: 2019
ISSN: 0730-0301,1557-7368
DOI: 10.1145/3306346.3322975