Applied computational geometry: Towards robust solutions of basic problems

AbstractGeometric computations, like all numerical procedures, are extremely prone to roundoff error. However, virtually none of the numerical analysis literature directly applies to geometric calculations. Even for line intersection, the most basic geometric operation, there is no robust and efficient algorithm. Compounding the difficulties, many geometric algorithms perform iterations of calculations reusing previously computed data. In this paper, we explore some of the main issues in geometric computations and the methods that have been proposed to handle roundoff errors. In particular, we focus on one method and apply it to a general iterative intersection problem. Our initial results seem promising and will hopefully lead to robust solutions for more complex problems of applied computational geometry

Interferences and events: on epistemic shifts in physics through computer simulations

Computer simulations are omnipresent media in today's knowledge production. For scientific endeavors such as the detection of gravitational waves and the exploration of subatomic worlds, simulations are essential; however, the epistemic status of computer simulations is rather controversial as they are neither just theory nor just experiment. Therefore, computer simulations have challenged well-established insights and common scientific practices as well as our very understanding of knowledge. This volume contributes to the ongoing discussion on the epistemic position of computer simulations in a variety of physical disciplines, such as quantum optics, quantum mechanics, and computational physics. Originating from an interdisciplinary event, it shows that accounts of contemporary physics can constructively interfere with media theory, philosophy, and the history of science