Search results for "Computer-aided design"
showing 10 items of 312 documents
Reversing arrows: Duality
2021
What do you get reversing all arrows? The drawing ‘Duality’ is an homage to mirrors, classical art themes, and abstract mathematics.I’m looking for beauty in the arts and beauty in science. It’s a ...
A comic page for the first isomorphism theorem
2022
Given a homomorphism between algebras, there exists an isomorphism between the quotient of the domain by its kernel and the subalgebra in the codomain given by its image. This theorem, commonly known as the first isomorphism theorem, is a fundamental algebraic result. Different problems have been identified in its instruction, mainly related to the abstraction inherent to its content and to the lack of conceptual models to improve its understanding. In response to this situation, in this paper, we present an illustration that explores the narrative and graphical resources of comics with the aim of describing the set-theoretic elements that are involved in the proof of this theorem.
Visualizing Confidence in Cluster-based Ensemble Weather Forecast Analyses
2020
In meteorology, cluster analysis is frequently used to determine representative trends in ensemble weather predictions in a selected spatio-temporal region, e.g., to reduce a set of ensemble members to simplify and improve their analysis. Identified clusters (i.e., groups of similar members), however, can be very sensitive to small changes of the selected region, so that clustering results can be misleading and bias subsequent analyses. In this article, we — a team of visualization scientists and meteorologists-deliver visual analytics solutions to analyze the sensitivity of clustering results with respect to changes of a selected region. We propose an interactive visual interface that enab…
CheS-Mapper 2.0 for visual validation of (Q)SAR models
2014
Abstract Background Sound statistical validation is important to evaluate and compare the overall performance of (Q)SAR models. However, classical validation does not support the user in better understanding the properties of the model or the underlying data. Even though, a number of visualization tools for analyzing (Q)SAR information in small molecule datasets exist, integrated visualization methods that allow the investigation of model validation results are still lacking. Results We propose visual validation, as an approach for the graphical inspection of (Q)SAR model validation results. The approach applies the 3D viewer CheS-Mapper, an open-source application for the exploration of sm…
Analysis of the depth of field of integral imaging displays based on wave optics.
2013
In this paper, we analyze the depth of field (DOF) of integral imaging displays based on wave optics. With considering the diffraction effect, we analyze the intensity distribution of light with multiple micro-lenses and derive a DOF calculation formula for integral imaging display system. We study the variations of DOF values with different system parameters. Experimental results are provided to verify the accuracy of the theoretical analysis. The analyses and experimental results presented in this paper could be beneficial for better understanding and designing of integral imaging displays.
Efficient analysis of in-line waveguide filters and frequency-selective surfaces with stepped holes
2003
This paper presents a novel method for the analysis of large classes of microwave and mm-wave passive components, including in-line waveguide filters, single- and multi-layer frequency selective surfaces, and open-ended waveguide array antennas. This method is based on the segmentation technique, which permits us to reduce complex components to cascaded waveguide step discontinuities, which are separately characterized through their generalized impedance matrices, as calculated by the integral equation (IE) technique and the boundary integral-resonant mode expansion (BI-RME) method. Some examples demonstrate the flexibility and efficiency of the IE/BI-RME method, and its utility in investig…
EM Based Synthesis and Design of Bandpass Waveguide Filters Including Manufacturing Effects with FEST3D
2011
This article aims at the industry interest on automated design tools that are able to take into account manufacturing effects. First, an efficient design strategy for bandpass waveguide filters including the rounded corners arising from low-cost manufacturing procedures is presented. This technique is based on a recent enhanced prototype and synthesis methodology able to consider the real structure parts. Using the resulting electromagnetic (EM)-based synthesis technique, an excellent structure is extracted, which requires, at most, only a slight final EM optimization. Second, this article presents analytical expressions providing error estimates for the different filter performances in ter…
Optimization of conducting structures by using the homogenization method
2002
Approximation and numerical realization of a class of optimization problems with control variables represented by coefficients of linear elliptic state equations is considered. Convergence analysis of well-posed problems is performed by using one- and two-level approximation strategies. The latter is utilized in an optimization layout problem for two conductive constituents, for which the necessary steps to transfer the well-posed problem into a computational form are described and some numerical experiments are given.
Extending CSG with projections: Towards formally certified geometric modeling
2015
We extend traditional Constructive Solid Geometry (CSG) trees to support the projection operator. Existing algorithms in the literature prove various topological properties of CSG sets. Our extension readily allows these algorithms to work on a greater variety of sets, in particular parametric sets, which are extensively used in CAD/CAM systems. Constructive Solid Geometry allows for algebraic representation which makes it easy for certification tools to apply. A geometric primitive may be defined in terms of a characteristic function, which can be seen as the zero-set of a corresponding system along with inequality constraints. To handle projections, we exploit the Disjunctive Normal Form,…
Extensions of the witness method to characterize under-, over- and well-constrained geometric constraint systems
2011
International audience; This paper describes new ways to tackle several important problems encountered in geometric constraint solving, in the context of CAD, and which are linked to the handling of under- and over-constrained systems. It presents a powerful decomposition algorithm of such systems. Our methods are based on the witness principle whose theoretical background is recalled in a first step. A method to generate a witness is then explained. We show that having a witness can be used to incrementally detect over-constrainedness and thus to compute a well-constrained boundary system. An algorithm is introduced to check if anchoring a given subset of the coordinates brings the number …