the subject of geometry and proportions has been regarded as an issue which has a close relationship with architecture. since the entire universe, living beings and the human geometry can be seen clearly, that’s why our unconscious essence has accustomed to these proportions whereby reflection of this mentality can be seen in the architect’s hands and thought in the architecture. it can witness...

The concept of fairing applied to irregular triangular meshes has become more and more important. Previous contributions constructed better fairing operators, and applied them both to multiresolution editing tools and to multiresolution representations of meshes. In this paper, we generalize these powerful techniques to handle non-manifold models. Our framework computes a multilevel fairing of ...

We present several non-linear 4-point interpolatory schemes, derived from the “classical” linear 4-point scheme. These new schemes have variable tension parameter instead of the fixed tension parameter in the linear 4-point scheme. The tension parameter is adapted locally according to the geometry of the control polygon within the 4-point stencil. This allows the schemes to remain local and in ...

Existing data embedding algorithms for polygonal meshes and their attributes can’t be applied to the majority of (geometric) computer aided design (CAD) applications, for two major reasons. First, these CAD systems employ parametric curves and surfaces, not polygonal meshes, as their main shape-defining primitives. Second, most CAD applications do not tolerate modifications of model topology an...

A thinning algorithm is used to reduce unnecessary information by peeling objects layer by layer so that the result is sufficient to allow topological analysis. It has several applications, but is particularly useful for skeletonization. A new sequential thinning algorithm is introduced to preserve both the topology and geometry of the object. In sequential thinning, only a single point may be ...

This review considers the properties of classical solutions to supergravity theories with partially unbroken supersymmetry. These solutions saturate Bogomol’nyPrasad-Sommerfield bounds on their energy densities and are the carriers of the p-form charges that appear in the supersymmetry algebra. The simplest such solutions have the character of (p + 1)-dimensional Poincaré-invariant hyperplanes ...

Polygonal meshes are widely used to represent the shape of 3D objects and the generation of multi-resolution models has been a significant research topic in computer graphics. In this paper, we demonstrate how to generate multi-resolution models through 2D image processing techniques. The goal of generating multi-resolution models is accomplished by resizing the corresponding geometry images of...

This paper presents a novel method for converting any unstructured quadrilateral or hexahedral mesh to a generalized T-spline surface or solid T-spline, based on the rational T-spline basis functions. Our conversion algorithm consists of two stages: the topology stage and the geometry stage. In the topology stage, the input quadrilateral or hexahedral mesh is taken as the initial T-mesh. To con...

the aim of this paper is to show the importance of analytic hyperbolic geometry introduced in [9]. in [1], ungar and chen showed that the algebra of the group sl(2,c) naturally leads to the notion of gyrogroups and gyrovector spaces for dealing with the lorentz group and its underlying hyperbolic geometry. they defined the chen addition and then chen model of hyperbolic geometry. in this paper,...