Interpolation of syzygies for implicit matrix representations

We examine matrix representations of curves and surfaces based on syzygies and constructed by interpolation through points. They are implicit representations of objects given as point clouds. The corresponding theory, including moving lines, curves and surfaces, has been developed for parametric models. Our contribution is to show how to compute the required syzygies by interpolation, when the geometric object is given by a point cloud whose sampling satisfies mild assumptions. We focus on planar and space curves, where the theory of syzygies allows us to design an exact algorithm yielding the optimal implicit expression. The method extends readily to surfaces without base points defined over triangular patches. Our Maple implementation has served to produce the examples in this paper and is available upon demand by the authors

Computational Design of Cold Bent Glass Fa\c{c}ades

Cold bent glass is a promising and cost-efficient method for realizing doubly curved glass fa\c{c}ades. They are produced by attaching planar glass sheets to curved frames and require keeping the occurring stress within safe limits. However, it is very challenging to navigate the design space of cold bent glass panels due to the fragility of the material, which impedes the form-finding for practically feasible and aesthetically pleasing cold bent glass fa\c{c}ades. We propose an interactive, data-driven approach for designing cold bent glass fa\c{c}ades that can be seamlessly integrated into a typical architectural design pipeline. Our method allows non-expert users to interactively edit a parametric surface while providing real-time feedback on the deformed shape and maximum stress of cold bent glass panels. Designs are automatically refined to minimize several fairness criteria while maximal stresses are kept within glass limits. We achieve interactive frame rates by using a differentiable Mixture Density Network trained from more than a million simulations. Given a curved boundary, our regression model is capable of handling multistable configurations and accurately predicting the equilibrium shape of the panel and its corresponding maximal stress. We show predictions are highly accurate and validate our results with a physical realization of a cold bent glass surface

Data-driven geometric modelling methods for digital twinning: manufacturing, geospatial and medical applications

In recent years there has been an explosion of interest in digital twinning in many disciplines, including the manufacturing, geospatial, and medical domains. A core topic of importance in modelling digital twins, is reconstruction of geometric models from raw data. Despite the diversity of requirements in the vast space of digital twin applications, methods for geometric reconstruction can often be transferred between disciplines with only minor modifications. In this paper we present some recent results related to how advances in machine learning over the last decade can be used for data-driven geometric reconstruction in the medical, geospatial and manufacturing domains

Strongly magnetized pulsars: explosive events and evolution

Well before the radio discovery of pulsars offered the first observational confirmation for their existence (Hewish et al., 1968), it had been suggested that neutron stars might be endowed with very strong magnetic fields of $10^{10}$-$10^{14}$G (Hoyle et al., 1964; Pacini, 1967). It is because of their magnetic fields that these otherwise small ed inert, cooling dead stars emit radio pulses and shine in various part of the electromagnetic spectrum. But the presence of a strong magnetic field has more subtle and sometimes dramatic consequences: In the last decades of observations indeed, evidence mounted that it is likely the magnetic field that makes of an isolated neutron star what it is among the different observational manifestations in which they come. The contribution of the magnetic field to the energy budget of the neutron star can be comparable or even exceed the available kinetic energy. The most magnetised neutron stars in particular, the magnetars, exhibit an amazing assortment of explosive events, underlining the importance of their magnetic field in their lives. In this chapter we review the recent observational and theoretical achievements, which not only confirmed the importance of the magnetic field in the evolution of neutron stars, but also provide a promising unification scheme for the different observational manifestations in which they appear. We focus on the role of their magnetic field as an energy source behind their persistent emission, but also its critical role in explosive events.Comment: Review commissioned for publication in the White Book of "NewCompStar" European COST Action MP1304, 43 pages, 8 figure

Interactive freeform architectural design with nearly developables and cold bent glass

Interactive design of freeform architectural surface panelizations is at the coreof this PhD thesis. We provide the computational framework for dealing with two important types of paneling elements. Specifically, we focus on certain types of developable surfaces and cold bent glass panels, all relevant to contemporary freeform architecture.To this end, we initially present a novel method for increasing the developabilityof a B-spline surface. We use the property that the Gauss image of a developable surfaceis 1-dimensional and can be locally well approximated by circles. This is cast intoan algorithm for thinning the Gauss image by increasing the planarity of the Gaussimages of appropriate neighborhoods. A variation of the main method allows us totackle the problem of paneling a freeform architectural surface with developable panels,in particular enforcing rotational cylindrical, rotational conical and planar panels,which are the main preferred types of developable panels in architecture due to there duced cost of manufacturing. We are interested in near developability, rather than exact developability, so the optimization approach is sucient. The motivation behind this is the fact that most materials allow for a little bit of stretching and therefore developability needs not be satised to a high degree.One such material is glass which is the main focus of the second panelizationproblem of this thesis. Toughened glass can with stand higher stresses, and therefore allows initially planar glass panels to be elastically bent and xed at ambient temperatures to a curved frame. This process is called cold bending and it produces panels that can exhibit double curvature, providing a cost- and energy-ecient alternative of higher optical quality than traditional hot bent glass panels. However, it is very challenging to navigate the design space of cold bent glass panels due to the fragility of the material, which impedes the form-nding for practically feasible and aesthetically pleasing cold bent glass façades. We present an interactive, data-driven approachfor designing cold bent glass façades that can be seamlessly integrated into a typical architectural design pipeline. Our method allows non-expert users to interactively edit a parametric surface while providing real-time feedback on the deformed shape and maximum stress of cold bent glass panels. Designs are automatically rened to minimize several fairness criteria while maximal stresses are kept within glass limits.We achieve interactive frame rates by using a dierentiable mixture density network trained from more than a million simulations. Given a curved boundary, our regressionmodel is capable of handling multistable congurations and accurately predicting the equilibrium shape of the panel and its corresponding maximal stress. We show predictions are highly accurate and validate our results with a physical realization ofa cold bent glass surface. For both applications explored in this work, a plethora ofresults and examples are provided.7

The In Vitro Impact of the Herbicide Roundup on Human Sperm Motility and Sperm Mitochondria

Toxicants, such as herbicides, have been hypothesized to affect sperm parameters. The most common method of exposure to herbicides is through spraying or diet. The aim of the present study was to investigate the effect of direct exposure of sperm to 1 mg/L of the herbicide Roundup on sperm motility and mitochondrial integrity. Sperm samples from 66 healthy men who were seeking semen analysis were investigated after written informed consent was taken. Semen analysis was performed according to the World Health Organization guidelines (WHO, 2010). Mitochondrial integrity was assessed through mitochondrial staining using a mitochondria-specific dye, which is exclusively incorporated into functionally active mitochondria. A quantity of 1 mg/L of Roundup was found to exert a deleterious effect on sperm’s progressive motility, after 1 h of incubation (mean difference between treated and control samples = 11.2%) in comparison with the effect after three hours of incubation (mean difference = 6.33%, p < 0.05), while the relative incorporation of the mitochondrial dye in mitochondria of the mid-piece region of Roundup-treated spermatozoa was significantly reduced compared to relative controls at the first hour of incubation, indicating mitochondrial dysfunction by Roundup. Our results indicate that the direct exposure of semen samples to the active constituent of the herbicide Roundup at the relatively low concentration of 1 mg/L has adverse effects on sperm motility, and this may be related to the observed reduction in mitochondrial staining