Heidi E. I. Dahl

Using dependent CORAS diagrams to analyse mutual dependency

The CORAS method for security risk analysis provides a customized language, the CORAS diagrams, for threat and risk modelling. In this paper, we extend this language to capture context dependencies, and use it as a means to analyse mutual dependency. We refer to the extension as dependent CORAS diagrams. We define a textual syntax using EBNF and explain how a dependent CORAS diagram may be schematically translated via the textual syntax into a paragraph in English, characterizing its intended meaning. Then we demonstrate the suitability of the language by means of a core example.

Piecewise Rational Parametrizations of Canal Surfaces

Canal surfaces, as envelopes of one-parameter families of spheres, correspond to curves in Minkowski space. We show that the continuity properties of a canal surface are inherited from the continuity properties of the associated curve, i.e., two curves joined with G 1 or G 2 continuity in Minkowski space correspond to two canal surfaces joined with the same level of continuity.We also describe an algorithm for minimal bi-degree rational parametrizations of patches on canal surfaces, and show how this can be used to parametrize piecewise rational corner and edge blends.

Deconfliction and Surface Generation from Bathymetry Data Using LR B-splines

A set of bathymetry point clouds acquired by different measurement techniques at different times, having different accuracy and varying patterns of points, are approximated by an LR B-spline surface. The aim is to represent the sea bottom with good accuracy and at the same time reduce the data size considerably. In this process the point clouds must be cleaned by selecting the “best” points for surface generation. This cleaning process is called deconfliction, and we use a rough approximation of the combined point clouds as a reference surface to select a consistent set of points. The reference surface is updated using only the selected points to create an accurate approximation. LR B-splines is the selected surface format due to its suitability for adaptive refinement and approximation, and its ability to represent local detail without a global increase in the data size of the surface.

Isotropic Möbius Geometry and i-M Circles on Singular Isotropic Cyclides

The Mobius geometry of \({\mathbb R}^3\) has an isotropic counterpart in \(\mathbb {R}^{3}_{++0}\). We describe the isotropic Mobius model of surfaces in \(\mathbb {R}^{3}_{++0}\) and show how the degree of a surface changes under i-M inversions while the number of families of i-M circles remain constant. This gives us a generalization of the classification of families of lines and i-M circles on quadratic surfaces in \(\mathbb {R}^{3}_{++0}\) to isotropic cyclides with real singularities, containing up to 4 such families.

Rational Parametrizations of Edge and Corner Blends for Isogeometric Analysis

Rational variable radius rolling ball blends between pairs of natural quadrics can be constructed from rational curves in their bisector surface in \(\mathbb{R}^{3,1}\). For certain configurations of natural quadrics, these curves can be constructed by taking hyperplane sections, or by constructing Bezier curves in the bisector surface. When blending a configuration of edges and corners in a composite corner, we need to ensure that adjacent corner and edge blends are joined with at least G 1 continuity. In this paper we show, using an example corner, how such a rational composite blend can be constructed, guided by the placement of control spheres specifying the blending radius at certain key points. The construction is watertight, i.e., the boundary curves of the blend lies on the original surfaces, thus it is well-suited for applications in Isogeometric Analysis where this is a requirement.