The time-optimal trajectory for an airplane from some starting point to some final point is studied by many authors. Here, we consider the extension of robot planer motion of Dubins model in three dimensional spaces. In this model, the system has independent bounded control over both the altitude velocity and the turning rate of airplane movement in a non-obstacle space. Here, in this paper a g...

this paper demonstrates a preliminary investigation of geometry, function and its relation to dfx principles, namely dfm (design for manufacturing). this is the starting point for research on the development of an expert system that assesses design goals along dfx principles in a feature-based cad environment. there is a need for a deeper level of understanding of the relationship between geome...

In this paper, we prove that every metric line in the Poincare ball model of hyperbolic geometry is exactly a classical line of itself. We also proved nonexistence of periodic lines in the Poincare ball model of hyperbolic geometry.

In this paper we will 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 has.

Additive Manufacturing describes the technologies that can produce a physical model out of a computer model with a layer-by-layer production process. Additive Manufacturing technologies, as compared to traditional manufacturing methods, have the high capability of manufacturing the complex components using minimum energy and minimum consumption. These technologies have brought about the possibi...

Introduction: There has been a curiosity about the spheroid geometry for PET scanners developments since several years ago, therefore in this study, we are aiming to evaluate the performance of this geometry and compare its performance with cylindrical geometry using Monte Carlo simulation. Methods: We simulated a spheroid geometry with a radius of 199 mm...