A projective invariant generalization of the de Casteljau algorithm

A projective invariant generalization of the de Casteljau algorithm is described by using the cross ratio and an auxiliary line. We describe the implicit form of the section conics obtained by the algorithm proposed in this paper. Finally, we show how to construct specific conic sections using this approach. © 2010 Elsevier Ltd. All rights reserved.Benítez López, J. (2011). A projective invariant generalization of the de Casteljau algorithm. Computer-Aided Design. 43(1):3-11. doi:10.1016/j.cad.2010.09.005S31143

On the design of innovative heterogeneous sheet metal tests using a shape optimization approach

The development of full-field measurement methods has enabled a newtrend of heterogeneous mechanical tests. The inhomogeneous strain fields retrieved from these tests are being widely used in the calibration of constitutive models for sheet metals. However, today, there is no mechanical test able to characterize the material in a large range of strain states. The aim of this work is to present a heterogeneous mechanical test with an innovative tool/specimen shape, capable of producing rich heterogeneous strain paths and thus providing extensive information on material behavior. The proposed specimen is found using a shape optimization process where an index that evaluates the richness of strain information is used. In this work, the methodology and results are extended to non-specimen geometry dependence and to the non-dependence of the geometry parametrization through the use of the Ritz method for boundary value problems. Different curvemodels, such as splines, B-splines, and NURBS, are used, and C1 continuity throughout the specimen is guaranteed. Moreover, several deterministic and stochastic optimization methods are used in order to find the method or the combination of methods able to minimize the cost function effectively. Results demonstrated that the solution is dependent on the geometry definition, as well as on the optimization methodology. Nevertheless, the obtained solutions provided a wider spectrum of strain states than standard tests.publishe

Implicit Density Functional Theory

A fermion ground state energy functional is set up in terms of particle density, relative pair density, and kinetic energy tensor density. It satisfies a minimum principle if constrained by a complete set of compatibility conditions. A partial set, which thereby results in a lower bound energy under minimization, is obtained from the solution of model systems, as well as a small number of exact sum rules. Prototypical application is made to several one-dimensional spinless non-interacting models. The effectiveness of "atomic" constraints on model "molecules" is observed, as well as the structure of systems with only finitely many bound states.Comment: 9 pages, 4 figure

Leveraging Peer Feedback to Improve Visualization Education

Peer review is a widely utilized pedagogical feedback mechanism for engaging students, which has been shown to improve educational outcomes. However, we find limited discussion and empirical measurement of peer review in visualization coursework. In addition to engagement, peer review provides direct and diverse feedback and reinforces recently-learned course concepts through critical evaluation of others' work. In this paper, we discuss the construction and application of peer review in a computer science visualization course, including: projects that reuse code and visualizations in a feedback-guided, continual improvement process and a peer review rubric to reinforce key course concepts. To measure the effectiveness of the approach, we evaluate student projects, peer review text, and a post-course questionnaire from 3 semesters of mixed undergraduate and graduate courses. The results indicate that course concepts are reinforced with peer review---82% reported learning more because of peer review, and 75% of students recommended continuing it. Finally, we provide a road-map for adapting peer review to other visualization courses to produce more highly engaged students

A sampling strategy based on B-wavelets decomposition

Finding optimal sampling strategy is a central problem in surface reconstruction. In this paper a sampling strategy on different scales of a free-form surface is proposed. Non-Uniform Rational B-spline (NURBS) surfaces are used to represent the nominal shape; the decomposition is performed through the orthogonal B-wavelet basis. A sampling based on each level of the shape decomposition is then proposed to detect the points of interest that reflect the variations between different levels. The number of the samples is selected according to the complexity of the shape, which is represented by the number of the internal knots

Contact Modelling in Isogeometric Analysis: Application to Sheet Metal Forming Processes

Isogeometric Analysis (IGA) has been growing in popularity in the past few years essentially due to the extra exibility it introduces with the use of higher degrees in the basis functions leading to higher convergence rates. IGA also o ers the capability of easily reproducing discontinuous displacement and/or strain elds by just manipulating the multiplicity of the knot parametric coordinates. Another advantage of IGA is that it uses the Non-Uniform Rational B-Splines (NURBS) basis functions, that are very common in CAD solid modelling, and consequently it makes easier the transition from CAD models to numerical analysis. In this work it is explored the contact analysis in IGA for both implicit and explicit time integration schemes. Special focus will be given on contact search and contact detection techniques under NURBS patches for both the rigid tools and the deformed sheet blank

Exploiting lattice structures in shape grammar implementations

The ability to work with ambiguity and compute new designs based on both defined and emergent shapes are unique advantages of shape grammars. Realizing these benefits in design practice requires the implementation of general purpose shape grammar interpreters that support: (a) the detection of arbitrary subshapes in arbitrary shapes and (b) the application of shape rules that use these subshapes to create new shapes. The complexity of currently available interpreters results from their combination of shape computation (for subshape detection and the application of rules) with computational geometry (for the geometric operations need to generate new shapes). This paper proposes a shape grammar implementation method for three-dimensional circular arcs represented as rational quadratic Bézier curves based on lattice theory that reduces this complexity by separating steps in a shape computation process from the geometrical operations associated with specific grammars and shapes. The method is demonstrated through application to two well-known shape grammars: Stiny's triangles grammar and Jowers and Earl's trefoil grammar. A prototype computer implementation of an interpreter kernel has been built and its application to both grammars is presented. The use of Bézier curves in three dimensions opens the possibility to extend shape grammar implementations to cover the wider range of applications that are needed before practical implementations for use in real life product design and development processes become feasible

3D Geometrical Inspection of Complex Geometry Parts Using a Novel Laser Triangulation Sensor and a Robot

This article discusses different non contact 3D measuring strategies and presents a model for measuring complex geometry parts, manipulated through a robot arm, using a novel vision system consisting of a laser triangulation sensor and a motorized linear stage. First, the geometric model incorporating an automatic simple module for long term stability improvement will be outlined in the article. The new method used in the automatic module allows the sensor set up, including the motorized linear stage, for the scanning avoiding external measurement devices. In the measurement model the robot is just a positioning of parts with high repeatability. Its position and orientation data are not used for the measurement and therefore it is not directly “coupled” as an active component in the model. The function of the robot is to present the various surfaces of the workpiece along the measurement range of the vision system, which is responsible for the measurement. Thus, the whole system is not affected by the robot own errors following a trajectory, except those due to the lack of static repeatability. For the indirect link between the vision system and the robot, the original model developed needs only one first piece measuring as a “zero” or master piece, known by its accurate measurement using, for example, a Coordinate Measurement Machine. The strategy proposed presents a different approach to traditional laser triangulation systems on board the robot in order to improve the measurement accuracy, and several important cues for self-recalibration are explored using only a master piece. Experimental results are also presented to demonstrate the technique and the final 3D measurement accuracy

The Influence of Quadrature Errors on Isogeometric Mortar Methods

Mortar methods have recently been shown to be well suited for isogeometric analysis. We review the recent mathematical analysis and then investigate the variational crime introduced by quadrature formulas for the coupling integrals. Motivated by finite element observations, we consider a quadrature rule purely based on the slave mesh as well as a method using quadrature rules based on the slave mesh and on the master mesh, resulting in a non-symmetric saddle point problem. While in the first case reduced convergence rates can be observed, in the second case the influence of the variational crime is less significant