In this paper we propose a new scheme for freeform shape optimization on arbitrary polygonal or polyhedral meshes. The approach consists of three main steps: (1) surface partitioning of polygonal meshes into different patches; (2) a new freeform perturbation scheme of using the Cox–de Boor basis function over arbitrary polygonal meshes, which supports multi-resolution shape optimization and doe...

We present a technique for steganography in polygonal meshes. Our method hides a message in the indexed representation of a mesh by permuting the order in which faces and vertices are stored. The permutation is relative to a reference ordering that encoder and decoder derive from the mesh connectivity in a consistent manner. Our method is distortion-free because it does not modify the geometry ...

We address the problem of building 3D object models from image sequences obtained with known camera motion. An approach based on a local reconstruction method is presented. Recovered surfaces are described as polygonal meshes. To this purpose, reconstructed points are triangulated and surface areas which are not covered by rims are detected since they may lead to false reconstructed points. Res...

The vibratory bowl feeder is the oldest and still most common approach to the automated feeding (orienting) of industrial parts. In this paper we consider a class of vibratory bowl filters that can be described by removing polygonal sections from the track; we refer to this class of filters as traps. For an n-sided polygonal part and an m-sided polygonal trap, we give an O(nm log n) algorithm t...

We develop a valuation theory for generalized polygons similar to the existing theory for dense near polygons. This valuation theory has applications for the study and classification of generalized polygons that have full subpolygons as subgeometries.

This paper revisits the existence and construction problems for polygonal designs (a special class of partially balanced incomplete block designs associated with regular polygons). We present new polygonal designs with various parameter sets by explicit construction. In doing so we employ several construction methods – some conventional and some new. We also establish a link between a class of ...

A near-polygonal graph is a graph Γ which has a set C of m-cycles for some positive integer m such that each 2-path of Γ is contained in exactly one cycle in C. If m is the girth of Γ , then the graph is called polygonal. We provide a construction of an infinite family of polygonal graphs of arbitrary even girth with 2-arc transitive automorphism groups, showing that there are infinitely many 2...

A polygonal domain P with n corners V and h holes is a connected polygonal region of genus h whose boundary consists of h + 1 closed chains of n total line segments. The holes and the outer boundary of P are regarded as obstacles. Then, the geodesic distance d(p, q) between any two points p, q in polygonal domain P is defined to be the (Euclidean) length of a shortest obstacle-avoiding path bet...

This paper describes a new spline formulation that supports deformation of polygonal shapes into smooth spline surface models. Once a polygonal shape with underlying rectangular topology is specified by the user, it is deformed into a smooth surface that interpolates all the polygonal vertices. The user can then modify the default smooth surface by increasing or decreasing the amount of deforma...