Geometric modelling using Partial Differential Equations (PDEs) has been gradually recognised due to its smooth instinct, as well as the ability to generate a variety of geometric shapes by intuitively manipulating a relatively small set of PDE boundary curves. In this paper we explore and demonstrate the feasibility of the PDE method in facial geometry parameterisation. The geometry of a gener...

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...

Most scroll compressor models are based on a geometrical description of the scroll wraps. Since geometry is one of the main factors affecting the efficiency of the compressor, a complete description of the geometry of scroll wraps has to be known in order to establish an accurate thermodynamic model. Most authors do not yield an analytical expression of the discharge chamber, also because their...

Previous parametric representations of smooth genus-zero surfaces require a collection of abutting patches (e.g. splines, NURBS, recursively subdivided polygons). We introduce a simple construction for these surfaces using a single uniform bi-cubic B-spline. Due to its tensor-product structure, the spline control points are conveniently stored as a geometry image with simple boundary symmetries...

We present a novel broad-band miniature antenna and employ it in a multi-element geometry with diversity capabilities for wireless communications. This antenna (diameter 0.2 and thickness 0.06 ) consists of two stacked circular patches that create two cylindrical slots resonating at two slightly different frequencies, fed by a strategically positioned coaxial probe. An extensive parametric stud...

With the increased freedom in layout selection possible when designing an Unmanned Air Vehicle (UAV) concept (compared, for example, to the relatively constrained and mature world of commercial airliner design), comes the significant challenge of building a geometry engine that will provide the variety of airframe models demanded by the highly global nature of the design search. In order to ena...

General offset curves are treated in the context of Minkowski geometry, the geometry of the two-dimensional plane, stemming from the consideration of a strictly convex, centrally symmetric given curve as its unit circle. Minkowski geometry permits us to move beyond classical confines and provides us with a framework in which to generalize the notion of Pythagorean-hodograph curves in the case o...

A theoretical study analyzing three-dimensional combustion acoustic instabilities in a liquid propellant rocket engine combustor has been conducted. A linear theory based on Crocco’s pressure sensitive time lag model is used. To apply this theory the combustor is divided into two main components, including the combustion chamber and the converging part of the nozzle. The assumption of concentra...

Computer-extended Descriptive Geometry (CeDG) is a new approach to solving and building computer models of three-dimensional (3D) geometrical systems through descriptive geometry procedures (thus inheriting invariant-symmetry properties from projective geometry) that have demonstrated reliability accuracy. CeDG may calculate parametric implicit functional form for the spatial curves generated i...