The task of planning a path between two spatial configurations of an artifact moving among obstacles is an important problem in practically all geometrically-intensive applications. Despite the ubiquity of the problem, the existing approaches make specific limiting assumptions about the geometry and mobility of the obstacles, or those of the environment in which the motion of the artifact takes...

There is considerable current interest in deriving accurate dimensional measurements of the internal ge ometry of complex manufactured parts particularly castings This paper describes an approach to the re construction of D part geometry from multiple dig ital X ray images A novel method for radiographic stereo is described which takes into account the spe cial imaging geometry of the digital X...

This is an in-progress set of notes describing the often-neglected geometrical, dynamical interpretation of a connection on a manifold. The essential idea is that, while the Levi-Civita connection is associated to the sliding action of parallel transport, it is perhaps more natural to think of a tangent space to a surface being rolled around as we move from point to point. The difference manife...

Discrete and continuous refinement equations have been widely studied in the literature for the last few years, due to their applications to the areas of wavelet analysis and geometric modeling. However, there is no “universal” theorem that deals with the problem about the existence of compactly supported distributional solutions for both discrete and continuous refinement equations simultaneou...

The spine of an object is an entity that can characterise the object’s topology and describes the object by a lower dimension. It has an intuitive appeal for supporting geometric modelling operations. The aim of this paper is to show how a spine for a PDE surface can be generated. For the purpose of the work presented here an analytic solution form for the chosen PDE is utilised. It is shown th...

The paper describes a concept of induced rational parametrisation for curves. Parametrisations of curves are defined in terms of rational parametrisations of simpler or ‘primitive’ curves. The technique has applications in computer graphics and geometric modeling. A range of examples is given.

The commonly used radial distortion model for camera calibration is in fact an assumption or a restriction. In practice, camera distortion could happen in a general geometrical manner that is not limited to the radial sense. This paper proposes a simplified geometrical distortion modeling method by using two different radial distortion functions in the two image axes. A family of simplified geo...

In this paper, we propose and integrate two Bayesian methods, one of them for junction detection, and the other one for junction grouping. Our junction detection method relies on a probabilistic edge model and a log-likelihood test. Our junction grouping method relies on 6nding connecting paths between pairs of junctions. Path searching is performed by applying a Bayesian A∗ algorithm. Such alg...

Geometric Constraint Solving Problems (GCSP) are nowadays routinely investigated in geometric modeling. The 3D Pentahedron problem is a GCSP defined by the lengths of its edges and the planarity of its quadrilateral faces, yielding to an under-constrained system of twelve equations in eighteen unknowns. In this work, we focus on solving the 3D Pentahedron problem in a more robust and efficient ...

This article studies families of curves with monotonic curvature function (MCcurves) and their applications in geometric modelling and aesthetic design. Aesthetic analysis and assessment of the structure and plastic qualities of pseudospirals, which are curves with monotonic curvature function, are conducted for the first time in the field of geometric modelling from the position of technical a...