1,940 research outputs found
Convexity preserving interpolatory subdivision with conic precision
The paper is concerned with the problem of shape preserving interpolatory
subdivision. For arbitrarily spaced, planar input data an efficient non-linear
subdivision algorithm is presented that results in limit curves,
reproduces conic sections and respects the convexity properties of the initial
data. Significant numerical examples illustrate the effectiveness of the
proposed method
Doctor of Philosophy
dissertationWhile boundary representations, such as nonuniform rational B-spline (NURBS) surfaces, have traditionally well served the needs of the modeling community, they have not seen widespread adoption among the wider engineering discipline. There is a common perception that NURBS are slow to evaluate and complex to implement. Whereas computer-aided design commonly deals with surfaces, the engineering community must deal with materials that have thickness. Traditional visualization techniques have avoided NURBS, and there has been little cross-talk between the rich spline approximation community and the larger engineering field. Recently there has been a strong desire to marry the modeling and analysis phases of the iterative design cycle, be it in car design, turbulent flow simulation around an airfoil, or lighting design. Research has demonstrated that employing a single representation throughout the cycle has key advantages. Furthermore, novel manufacturing techniques employing heterogeneous materials require the introduction of volumetric modeling representations. There is little question that fields such as scientific visualization and mechanical engineering could benefit from the powerful approximation properties of splines. In this dissertation, we remove several hurdles to the application of NURBS to problems in engineering and demonstrate how their unique properties can be leveraged to solve problems of interest
A comparison of smooth basis constructions for isogeometric analysis
In order to perform isogeometric analysis with increased smoothness on
complex domains, trimming, variational coupling or unstructured spline methods
can be used. The latter two classes of methods require a multi-patch
segmentation of the domain, and provide continuous bases along patch
interfaces. In the context of shell modeling, variational methods are widely
used, whereas the application of unstructured spline methods on shell problems
is rather scarce. In this paper, we therefore provide a qualitative and a
quantitative comparison of a selection of unstructured spline constructions, in
particular the D-Patch, Almost-, Analysis-Suitable and the
Approximate constructions. Using this comparison, we aim to provide
insight into the selection of methods for practical problems, as well as
directions for future research. In the qualitative comparison, the properties
of each method are evaluated and compared. In the quantitative comparison, a
selection of numerical examples is used to highlight different advantages and
disadvantages of each method. In the latter, comparison with weak coupling
methods such as Nitsche's method or penalty methods is made as well. In brief,
it is concluded that the Approximate and Analysis-Suitable converge
optimally in the analysis of a bi-harmonic problem, without the need of special
refinement procedures. Furthermore, these methods provide accurate stress
fields. On the other hand, the Almost- and D-Patch provide relatively easy
construction on complex geometries. The Almost- method does not have
limitations on the valence of boundary vertices, unlike the D-Patch, but is
only applicable to biquadratic local bases. Following from these conclusions,
future research directions are proposed, for example towards making the
Approximate and Analysis-Suitable applicable to more complex
geometries
Learning quadrangulated patches for 3D shape parameterization and completion
We propose a novel 3D shape parameterization by surface patches, that are
oriented by 3D mesh quadrangulation of the shape. By encoding 3D surface detail
on local patches, we learn a patch dictionary that identifies principal surface
features of the shape. Unlike previous methods, we are able to encode surface
patches of variable size as determined by the user. We propose novel methods
for dictionary learning and patch reconstruction based on the query of a noisy
input patch with holes. We evaluate the patch dictionary towards various
applications in 3D shape inpainting, denoising and compression. Our method is
able to predict missing vertices and inpaint moderately sized holes. We
demonstrate a complete pipeline for reconstructing the 3D mesh from the patch
encoding. We validate our shape parameterization and reconstruction methods on
both synthetic shapes and real world scans. We show that our patch dictionary
performs successful shape completion of complicated surface textures.Comment: To be presented at International Conference on 3D Vision 2017, 201
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