Rotational flaring of square trumpet at the butt-end of cylindrical pipes

В статті проаналізовані найпоширеніші технології виготовлення гранованих, зокрема, квадратних розтрубів на торцях круглих труб, виявлені їх переваги і недоліки та сформульована доцільність використання технології ротаційної роздачі таких розтрубів. Наведені нові аналітичні формули для розрахунків контурів поперечного перетину інструментів для ротаційної роздачі. За цими формулами можна точніше розраховувати контури трикутника Рьоло, а також краплі, що падає, в перетинах інструменту, що деформує торець труби за рахунок складного обертання біля двох центрів. Вказано, що при ротаційній роздачі неможливо отримати розтруб з перетином у вигляді квадрата ідеальної форми. В кутах квадрату суміжні його сторони будуть сполучатися за певним радіусом спряження, який залежить від відносних розмірів сторін трикутника Рьоло, краплі, відстані між центрами обертання інструменту і стороною розтруба. Експериментами по ротаційній роздачі квадратних розтрубів на алюмінієвих циліндричних трубах доказана доцільність використання інструменту з контуром краплі в поперечному перерізі та формул для розрахунків його розмірів. Запропонована суперформула Йохана Геліса для створення належного контуру краплі за даними нових формул, наведених в статті. Суперформула є універсальною для всіх видів інструментів, що використовують при ротаційній роздачі гранованих розтрубів, і дозволяє конструювати шаблони, за допомогою яких копіровально-фрезерними роботами виготовляють деформуючий інструмент.The article analyzes the most common technologies for the manufacture of faceted, in particular, square trumpet at the ends of round pipes, identifies their advantages and disadvantages and formulates the feasibility of using the technology of rotational flaring of such trumpet. The new analytical formulas for calculating the cross-section contours of tools for rotational flaring are given. Using these formulas, you can more accurately calculate the contours of the Reuleaux triangle, as well as the falling drop in the cross sections of the tool that deforms the end of the pipe due to complex rotation about two centers. It is indicated that with the rotational flaring it is impossible to obtain a trumpet with a cross section in the form of a square of ideal shape. In the corners of a square, its adjacent sides will mate along a certain radius, which depends on the relative sizes of the sides of the Reuleaux triangle and the drops, as well as the distance between the centers of rotation of the tool and the side of the trumpet. Experiments on the rotational flaring of square trumpet on aluminum cylindrical pipes proved the feasibility of using a tool with a drop contour in cross section and formulas for calculating its dimensions. A Gielis superformula was proposed for creating a proper drop contour according to the formulas given in the article. The superformula is universal for all types of tools for rotational flaring and allows you to make templates used in copying and milling operations in the manufacture of deforming tools

Hybrid modelling of time-variant heterogeneous objects.

The physical world consists of a wide range of objects of a diverse constitution. Past research was mainly focussed on the modelling of simple homogeneous objects of a uniform constitution. Such research resulted in the development of a number of advanced theoretical concepts and practical techniques for describing such physical objects. As a result, the process of modelling and animating certain types of homogeneous objects became feasible. In fact most physical objects are not homogeneous but heterogeneous in their constitution and it is thus important that one is able to deal with such heterogeneous objects that are composed of diverse materials and may have complex internal structures. Heterogeneous object modelling is still a very new and evolving research area, which is likely to prove useful in a wide range of application areas. Despite its great promise, heterogeneous object modelling is still at an embryonic state of development and there is a dearth of extant tools that would allow one to work with static and dynamic heterogeneous objects. In addition, the heterogeneous nature of the modelled objects makes it appealing to employ a combination of different representations resulting in the creation of hybrid models. In this thesis we present a new dynamic Implicit Complexes (IC) framework incorporating a number of existing representations and animation techniques. This framework can be used for the modelling of dynamic multidimensional heterogeneous objects. We then introduce an Implicit Complexes Application Programming Interface (IC API). This IC API is designed to provide various applications with a unified set of tools allowing these to model time-variant heterogeneous objects. We also present a new Function Representation (FRep) API, which is used for the integration of FReps into complex time-variant hybrid models. This approach allows us to create a practical multilevel modelling system suited for complex multidimensional hybrid modelling of dynamic heterogeneous objects. We demonstrate the advantages of our approach through the introduction of a novel set of tools tailored to problems encountered in simulation applications, computer animation and computer games. These new tools empower users and amplify their creativity by allowing them to overcome a large number of extant modelling and animation problems, which were previously considered difficult or even impossible to solve

Hybrid modelling of time-variant heterogeneous objects

The physical world consists of a wide range of objects of a diverse constitution. Past research was mainly focussed on the modelling of simple homogeneous objects of a uniform constitution. Such research resulted in the development of a number of advanced theoretical concepts and practical techniques for describing such physical objects. As a result, the process of modelling and animating certain types of homogeneous objects became feasible. In fact most physical objects are not homogeneous but heterogeneous in their constitution and it is thus important that one is able to deal with such heterogeneous objects that are composed of diverse materials and may have complex internal structures. Heterogeneous object modelling is still a very new and evolving research area, which is likely to prove useful in a wide range of application areas. Despite its great promise, heterogeneous object modelling is still at an embryonic state of development and there is a dearth of extant tools that would allow one to work with static and dynamic heterogeneous objects. In addition, the heterogeneous nature of the modelled objects makes it appealing to employ a combination of different representations resulting in the creation of hybrid models. In this thesis we present a new dynamic Implicit Complexes (IC) framework incorporating a number of existing representations and animation techniques. This framework can be used for the modelling of dynamic multidimensional heterogeneous objects. We then introduce an Implicit Complexes Application Programming Interface (IC API). This IC API is designed to provide various applications with a unified set of tools allowing these to model time-variant heterogeneous objects. We also present a new Function Representation (FRep) API, which is used for the integration of FReps into complex time-variant hybrid models. This approach allows us to create a practical multilevel modelling system suited for complex multidimensional hybrid modelling of dynamic heterogeneous objects. We demonstrate the advantages of our approach through the introduction of a novel set of tools tailored to problems encountered in simulation applications, computer animation and computer games. These new tools empower users and amplify their creativity by allowing them to overcome a large number of extant modelling and animation problems, which were previously considered difficult or even impossible to solve.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Superquadrics with rational and irrational symmetry

Superquadrics are important models for part level-description in computer graphics and computer vision. Their power resides in their compact characterization. To further extend the representational power of superquadrics several methods have been proposed for local and global deformations. This notwithstanding, it is very difficult, for example, to represent polygons or polyhedrons using classical superquadrics. In this paper we present a new approach to model natural and abstract shapes for computer graphics, using a Generalized Superellipse Equation, which solves the problem of symmetries. Our approach provides an elegant analytical way to fold or unfold the coordinate axis systems like a fan, thereby generalizing superquadrics and superellipses (and hyperspheres in general) to supershapes for any symmetry, rational or irrational. Very compact representations of various shapes with different symmetries are possible and this provides opportunities for CAD at the level of graphics kernels, CAD-users and their clients. For example, parts and assemblies can be represented in very small file sizes allowing to use the 3-D solid model throughout the design and manufacturing process. Our approach presents an elegant way to use 3-D models both for solid modeling and boundary representations, for rigid as well as soft models