Related papers: Smooth polyhedral surfaces
Partial differential equations can be solved on general polygonal and polyhedral meshes, through Polytopal Element Methods (PEMs). Unfortunately, the relation between geometry and analysis is still unknown and subject to ongoing research in…
The investigation of 3D euclidean symmetry sets (SS) and medial axis is an important area, due in particular to their various important applications. The pre-symmetry set of a surface M in 3-space (resp. smooth closed curve in 2D) is the…
The aim of this paper is to investigate the sufficient condition for the invariance of a normal curve on a smooth immersed surface under isometry. We also find the the deviations of the tangential and normal components of the curve with…
Soft membranes are commonly employed in shape-morphing applications, where the material is programmed to achieve a target shape upon activation by an external trigger, and as coating layers that alter the surface characteristics of bulk…
Skeletal polyhedra are discrete structures made up of finite, flat or skew, or infinite, helical or zigzag, polygons as faces, with two faces on each edge and a circular vertex-figure at each vertex. When a variant of Wythoff's construction…
A smooth T-surface can be thought of as a generalization of a surface of revolution in such a way that the axis of rotation is not fixed at one point but rather traces a smooth path on the base plane. Furthermore, the action, by which the…
We present a computational scheme that derives a global polynomial level set parametrisation for smooth closed surfaces from a regular surface-point set and prove its uniqueness. This enables us to approximate a broad class of smooth…
Cone spherical surfaces are orientable Riemannian surfaces with constant curvature one and a finite set of conical singularities. A subset of these surfaces, referred to as dihedral surfaces, is characterized by their monodromy groups,…
We prove necessary and sufficient conditions for a smooth surface in a 4-manifold X to be pseudoholomorphic with respect to some almost complex structure on X. This provides a systematic approach to the construction of pseudoholomorphic…
We consider differentiable maps in the setting of Abstract Differential Geometry and we study the conditions that ensure the uniqueness of differentials in this setting. In particular, we prove that smooth maps between smooth manifolds…
Many innovative applications require establishing correspondences among 3D geometric objects. However, the countless possible deformations of smooth surfaces make shape matching a challenging task. Finding an embedding to represent the…
It is a well known phenomenon that many classical minimal surfaces in Euclidean space also exist with higher dihedral symmetry. More precisely, these surfaces are solutions to free boundary problems in a wedge bounded by two vertical planes…
This paper discusses the geometry of a surface endowed with a slope metric. We obtain necessary and sufficient conditions for any surface of revolution to admit a strongly convex slope metric. Such conditions involve certain inequalities…
Numerical solutions of differential equations are usually not smooth functions. However, they should resemble the smoothness of the corresponding real solutions in one way or another. In two of our recent papers, a kind of spacial…
We state that any constant curvature Riemannian metric with conical singularities of constant sign curvature on a compact (orientable) surface $S$ can be realized as a convex polyhedron in a Riemannian or Lorentzian) space-form. Moreover…
It is a widely observed phenomenon in computer graphics that the size of the silhouette of a polyhedron is much smaller than the size of the whole polyhedron. This paper provides, for the first time, theoretical evidence supporting this for…
In this paper we provide, first, a general symbolic algorithm for computing the symmetries of a given rational surface, based on the classical differential invariants of surfaces, i.e. Gauss curvature and mean curvature. In practice, the…
In this paper we try to introduce a good smoothness notion for a functor. We consider properties and conditions from geometry and algebraic geometry which we expect a smooth functor should to have.
Models for fluid deformable surfaces provide valid theories to describe the dynamics of thin fluidic sheets of soft materials. To use such models in morphogenesis and development requires to incorporate active forces. We consider active…
Skeletal polyhedra are discrete connected structures consisting of finite (planar or skew) or infinite (linear, planar, or spatial) polygons as faces, with two faces on each edge and a circular vertex figure at each vertex. The present…