Multi-sided implicit surfacing with I-patches

Sipos, Ágoston; Várady, Tamás; Salvi, Péter; Vaitkus, Márton

doi:10.1016/j.cag.2020.05.009

Cited by 4 publications

(4 citation statements)

References 34 publications

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“…The I-patch representation is inherently multi-sided, with implicitly defined, but exact boundary curves and cross-derivative constraints. This sets it apart from the other blending methods outlined above-see our previous paper [18] for more information and some comparisons.…”

Section: Previous Workmentioning

confidence: 99%

“…(1) would guarantee a higher order of continuity.) When two or more bounding surfaces coincide, special handling is needed [18].…”

Section: Preliminaries: I-patchesmentioning

confidence: 99%

“…It should be noted, that although we always attempt to use the simplest ribbon-bounding surface pair, the use of Liming-surfaces is not always possible. If the boundary to be approximated has a point of inflection, or the corner normals are twisted, only I-lofts can be used [18].…”

Section: Ribbons and Bounding Surfacesmentioning

confidence: 99%

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Approximating triangular meshes by implicit, multi-sided surfaces

Sipos,

Várady,

Salvi

2022

Preprint

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The I-patch is a multi-sided surface representation, defined as a combination of implicit ribbon and bounding surfaces, whose pairwise intersections determine the natural boundaries of the patch. Our goal is to show how a collection of smoothly connected Ipatches can be used to approximate triangular meshes. We start from a coarse, user-defined vertex graph which specifies an initial subdivision of the surface. Based on this, we create ribbons that tightly fit the mesh along its edges in both positional and tangential sense, then we optimize the free parameters of the patch to better approximate the interior. If the surfaces are not sufficiently accurate, the network needs to be refined; here we exploit that the I-patch construction naturally supports T-nodes. We also describe a normalization method that nicely approximates the Euclidean distance field, and can be efficiently evaluated. The capabilities and limitations of the approach are analyzed through several examples.

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Section: Previous Workmentioning

confidence: 99%

“…(1) would guarantee a higher order of continuity.) When two or more bounding surfaces coincide, special handling is needed [18].…”

Section: Preliminaries: I-patchesmentioning

confidence: 99%

See 1 more Smart Citation

Approximating triangular meshes by implicit, multi-sided surfaces

Sipos,

Várady,

Salvi

2022

Preprint

Self Cite

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show abstract

“…Subdivision II Multi-sided implicit surfacing with I-patches, A. Sipos et al [17] Data-driven quasi-interpolant spline surfaces for point cloud approximation , A. Raffo et al [18] On Hamiltonian cycles in the FCC grid , L. Comic et al [19] …”

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confidence: 99%