1. Abstract Topology optimization yields an overall layout of a structure in the form of discrete density (e.g., SIMP) or continuous boundary geometry (e.g., level-set method). One of important drawbacks, however, is that it leads to a geometry with zigzag boundaries and/or irregular shapes, which is difficult to be interpreted for manufacturability, as well as to be utilized in subsequent appl...

A symbolic tool based on open source software that provides robust algebraic methods to handle automatic deduction tasks for a dynamic geometry construction is presented. The prototype has been developed as two different worksheets for the open source computer algebra system Sage, corresponding to two different ways of coding a geometric construction, namely with the open source dynamic geometr...

Graphics hardware has been progressively optimized to render more triangles with increasingly flexible shading. For highly detailed geometry, interactive applications restricted themselves to performing transforms on fixed geometry, since they could not incur the cost required to generate and transfer smooth or displaced geometry to the GPU at render time. As a result of recent advances in grap...

Context. Two fundamental questions regarding our description of the Universe concern the geometry and topology of its 3-dimensional space. While geometry is a local characteristic that gives the intrinsic curvature, topology is a global feature that characterizes the shape and size of the 3-space. The geometry constrains, but does not dictate, the spatial topology. Aims. We show that besides de...

OF PROPOSED STUDY The creation of meaningful geometry for architecture or simulations currently takes a considerable amount of time. Traditional geometry creation usually entails the creation of a rough layout of the architecture, the manual addition of geometric detail, and a final application of colors and textures to it. By automating large portions of this using the parametric generation of...

Byzantine church design depended heavily on natural light which was used for evocative purposes. The orientation of the main axis of the church, the form of the apse and the location and size of its windows are affected by the need for sunlight to shine at the altar on a desired time and for a certain duration. Until now the process of accurately taking account of all the above parameters has b...

We consider sparse (or toric) elimination theory in order to describe, by combinatorial means, the monomials appearing in the (sparse) resultant of a given overconstrained algebraic system. A modification of reverse search allows us to enumerate all mixed cell configurations of the given Newton polytopes so as to compute the extreme monomials of the Newton polytope of the resultant. We consider...

In this paper we deal with one of the homogeneous 3geometries, the Sol geometry. The Frenet frame and the curvature and torsion of a curve has been determined, moreover, we have computed the parametric form of geodesics, their curvatures and torsions in Theorem 4.1.

design of bridge deck with long-term strength, durability and permanence is a significant interest for engineers. one applicable solution to this challenge could be via using hybrid system consisting of conventional materials such as concrete and steel with frp plates which is also known as composite deck. since these deck are relatively new so their performance is not completely known. the pre...

in this work, the feasibility study for design of a laboratory sample rde which has an annular geometry with diameter of 76 mm and length of 101 mm has been performed. detonation engines are expected to be used as propulsion system in aerospace applications in the future. several types of detonation engines are currently under examination, including the rotating detonation engine (rde). first, ...