The range of operations on solids supported by current geometric modelling systems is very limited. Typically, solids represented in a modeller can be transformed by rigid motions and combined by Boolean operations. This paper introduces another family of transformations, called solid offsetting, which map solids into solids. Offset solids are expanded or contracted versions of an original obje...

We present a mathematical model for geometric modelling based on the concept of extended simplicial chain (ESC) defined in previous works. With this model, a solid is defined by means of an algebraic sum of non− disjoint extended cells, applying the divide and conquer concept. This allows us to obtain the traditional Boo− lean operations in geometric modelling through the operations defined for...

In this paper, we define complex solids by real functions. Just from relatively small formulae we produce highly detailed complex objects and are able to manipulate and transform them producing more complex ones. We show how complex static and time-dependent objects can be created with using of socalled R-functions. Then, we consider just one long-standing problems, hair modelling, and show how...

One of the difficulties in solid log modelling is working with huge data sets, such as those that come from computed axial tomographic imaging. Algorithmic procedures are described in this paper that have successfully reduced data without sacrificing modelling integrity.

Solid waste management is arguably one of the most important municipal services provided by government1. Given the rapid socio-economic changes that are projected to take place in the UK2 it is important that we plan our future waste management capacity to ensure the continuance of this valuable service. The Solid Waste Infrastructure Management System (SWIMS) model was designed to model the cu...

The subject of geometric modelling is a blend of different types of geometry, some mathematical modelling, some numerical analysis, and discipline specific applications. In these course notes, we will concentrate of the subdiscipline of geometric modelling known as computeraided geometric design, which was formed from the mathematical structures and methods used in CAD/CAM systems and subsequen...