On Triangular Splines:CAD and Quadrature

The standard representation of CAD (computer aided design) models is based on the boundary representation (B-reps) with trimmed and (topologically) stitched tensor-product NURBS patches. Due to trimming, this leads to gaps and overlaps in the models. While these can be made arbitrarily small for visualisation and manufacturing purposes, they still pose problems in downstream applications such as (isogeometric) analysis and 3D printing. It is therefore worthwhile to investigate conversion methods which (necessarily approximately) convert these models into water-tight or even smooth representations. After briefly surveying existing conversion methods, we will focus on techniques that convert CAD models into triangular spline surfaces of various levels of continuity. In the second part, we will investigate efficient quadrature rules for triangular spline space

Resistance spot welding

Tato práce popisuje princip bodového odporového svařování a stanovuje parametry, na kterých kvalita svarové čočky závisí. Dále srovnává makrostrukturu a mechanické vlastnosti bodových svarů zhotovených měkkým a tvrdým režimem svařování. V rámci experimentu vyhodnocuje pevnost svaru, přesněji řečeno soudržnost svařence v závislosti na počtu bodových svarů a jejich vzájemné poloze.The project describes the principle of resistance spot welding and sets the parameters which the quality of the weld nugget depends on. Moreover, it compares the macrostructure and mechanical properties of the spot welds made by soft or hard welding mode. In the experimental part, there is evaluating the strength of weld, precisely said cohesiveness weldments depending on the number of spot welds and their mutual position.

A unified Pythagorean hodograph approach to the medial axis transform and offset approximation

AbstractAlgorithms based on Pythagorean hodographs (PH) in the Euclidean plane and in Minkowski space share common goals, the main one being rationality of offsets of planar domains. However, only separate interpolation techniques based on these curves can be found in the literature. It was recently revealed that rational PH curves in the Euclidean plane and in Minkowski space are very closely related. In this paper, we continue the discussion of the interplay between spatial MPH curves and their associated planar PH curves from the point of view of Hermite interpolation. On the basis of this approach we design a new, simple interpolation algorithm. The main advantage of the unifying method presented lies in the fact that it uses, after only some simple additional computations, an arbitrary algorithm for interpolation using planar PH curves also for interpolation using spatial MPH curves. We present the functionality of our method for G1 Hermite data; however, one could also obtain higher order algorithms

Quantitative Analysis of Saliency Models

Previous saliency detection research required the reader to evaluate performance qualitatively, based on renderings of saliency maps on a few shapes. This qualitative approach meant it was unclear which saliency models were better, or how well they compared to human perception. This paper provides a quantitative evaluation framework that addresses this issue. In the first quantitative analysis of 3D computational saliency models, we evaluate four computational saliency models and two baseline models against ground-truth saliency collected in previous work.Comment: 10 page

Subdivision surface fitting to a dense mesh using ridges and umbilics

Fitting a sparse surface to approximate vast dense data is of interest for many applications: reverse engineering, recognition and compression, etc. The present work provides an approach to fit a Loop subdivision surface to a dense triangular mesh of arbitrary topology, whilst preserving and aligning the original features. The natural ridge-joined connectivity of umbilics and ridge-crossings is used as the connectivity of the control mesh for subdivision, so that the edges follow salient features on the surface. Furthermore, the chosen features and connectivity characterise the overall shape of the original mesh, since ridges capture extreme principal curvatures and ridges start and end at umbilics. A metric of Hausdorff distance including curvature vectors is proposed and implemented in a distance transform algorithm to construct the connectivity. Ridge-colour matching is introduced as a criterion for edge flipping to improve feature alignment. Several examples are provided to demonstrate the feature-preserving capability of the proposed approach