Computational Methods for Geometric Processing. Applications to Industry

Iglesias, Andrés; Gálvez, Antonio; Puig-Pey, Jaime

doi:10.1007/3-540-45545-0_81

Cited by 6 publications

(3 citation statements)

References 79 publications

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“…However, there is clearly a demand for more flexible modelling in engineering: Dassault Systèmes introduce subdivision surfaces in their CATIA product Imagine and Shape , and T‐splines [SZBN03] make subdivision surfaces available to CAD packages such as Rhinoceros 3D and SolidWorks. One barrier to adoption is the high‐level interface these modellers present to users: tools such as intersections, offsets, fillets and blends [IGPP01] leave a typical CAD model as the union of many approximating trimmed NURBS surfaces [SFL*08]. There is nothing to gain from replacing many trimmed NURBS surfaces with many trimmed subdivision surfaces, and it is not clear that subdivision surfaces make it any easier to provide these high‐level operators.…”

Section: Subdivision Schemes In Practicementioning

confidence: 99%

Beyond Catmull–Clark? A Survey of Advances in Subdivision Surface Methods

Cashman¹

2011

Computer Graphics Forum

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Subdivision surfaces allow smooth free-form surface modelling without topological constraints. They have become a fundamental representation for smooth geometry, particularly in the animation and entertainment industries. This survey summarizes research on subdivision surfaces over the last 15 years in three major strands: analysis, integration into existing systems and the development of new schemes. We also examine the reason for the low adoption of new schemes with theoretical advantages, explain why Catmull-Clark surfaces have become a de facto standard in geometric modelling, and conclude by identifying directions for future research.

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Section: Subdivision Schemes In Practicementioning

confidence: 99%

Beyond Catmull–Clark? A Survey of Advances in Subdivision Surface Methods

Cashman¹

2011

Computer Graphics Forum

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“…in this regard, intervals are used to handle uncertainties, mathematical approximations, and arithmetic roundoff on values of physical and technical parameters obtained from measurement errors. Applications of intervals also extend to many other fields of theoretical and applied mathematics, such as optimization and linear programming [7,13], functional equations [2,3], complex variable [23], inequalities solving [9,11] equation systems solving [22], robust control and robotics [12], geometric modeling and processing [6,8,10,24,25,26], statistics [28], circuit analysis [14], computer graphics and CAD [29], data processing [17], dynamical systems [4] and so on.…”

Section: Introductionmentioning

confidence: 99%

New Package in Maxima for Single-Valued Interval Computation on Real Numbers

Ipanaqué

Sandoval

Sosa

et al. 2011

2011 International Conference on Computational Science and Its Applications

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Intervals play a pivotal role in both theoretical mathematics and applied mathematics. As a consequence, interval computation is becoming increasingly used in several fields of Mathematics and other applied sciences. However, only a few computer programs include specialized tools and libraries for interval computation so far. In this paper we describe a new package for dealing with single-valued interval computation on real numbers. The package, developed by the authors in freeware program Maxima, version 5.23.2, allows the user to manipulate single-valued real and extended intervals and carry out the most typical set operations on intervals (such as union, intersection and difference) in a smoothly and user-friendly way. The main features of our package are discussed throughout the paper.Several illustrative examples, aimed to show the good performance of the package, are also given.

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“…This option allows the object design to users who are unfamiliar with the manufacturing processes. As a consequence, after the design phase, a subsequent set of complex operations is needed to obtain the machining paths, including offset calculation, machining strategies and so on [1][2][3]. In these cases, the quality of the manufactured pieces is usually affected because the strategies for the trajectories generation may not be suitable for the designed objects.…”

Section: Introductionmentioning

confidence: 99%

A Morphological Approach to the Design of Complex Objects

Sarabia

Jimeno-Morenilla

Molina-Carmona

2010

Journal of Manufacturing Science and Engineering

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Background. The Surface-Trajectory model gives solution to some of the problems presented by the general geometric models where the design of an object is separated from its manufacture. In fact, in this model, the internal representation of objects is made up of machining trajectories. As the display systems usually need triangles to represent the objects, a process of triangulation is needed to visualise them. In other words, a secondary surrface model is needed to display the objects. Conclusions. The model is generic and robust, there are no special cases or complex objects in which the model does not provide a correct solution. It also naturally incorporates the realistic display of the machined objects in a quickly and accurately way. Method of

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Computational Methods for Geometric Processing. Applications to Industry

Cited by 6 publications

References 79 publications

Beyond Catmull–Clark? A Survey of Advances in Subdivision Surface Methods

Beyond Catmull–Clark? A Survey of Advances in Subdivision Surface Methods

New Package in Maxima for Single-Valued Interval Computation on Real Numbers

A Morphological Approach to the Design of Complex Objects

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