Pieter van Gelder

H. R. N. van Erp, R. O. Linger, P. H. A. J. M. van Gelder

We introduce here Cartesian splines or, for short, C-splines. C- splines are piecewise polynomials which are defined on adjacent Cartesian coordinate systems and are Cr continuous throughout. The Cr continuity is enforced by constraining the coefficients of the polynomial to lie in the null-space of some smoothness matrix H. The matrix-product of the null-space of the smoothness matrix H and the original polynomial base results in a new base, the so-called C-spline base, which automatically enforces Cr continuity throughout. In this article we give a derivation of this C-spline base as well as an algorithm to construct C-spline models.

R. O. Linger, H. R. N. van Erp, P. H. A. J. M. van Gelder

We introduce here a direct method to construct multivariate explicit B-spline bases. B-splines are piecewise polynomials, which are defined on adjacent tetrahedra and which are $C^{r}$ continuous throughout. The $C^{r}$ continuity is enforced by making sure that all directional derivatives of order $r$, and lower, on the boundaries of adjacent tetrahedra give the same values for both tetrahedra. The method presented here is explicit, in that we will provide an algorithm with which one can analytically construct the B-spline base that enforces $C^{r}$ continuity for a given geometry.

Sabarathinam Chockalingam, Dina Hadziosmanovic, Wolter Pieters et al.

Over the last years, we have seen several security incidents that compromised system safety, of which some caused physical harm to people. Meanwhile, various risk assessment methods have been developed that integrate safety and security, and these could help to address the corresponding threats by implementing suitable risk treatment plans. However, an overarching overview of these methods, systematizing the characteristics of such methods, is missing. In this paper, we conduct a systematic literature review, and identify 7 integrated safety and security risk assessment methods. We analyze these methods based on 5 different criteria, and identify key characteristics and applications. A key outcome is the distinction between sequential and non-sequential integration of safety and security, related to the order in which safety and security risks are assessed. This study provides a basis for developing more effective integrated safety and security risk assessment methods in the future.