T-junctions in Spline Surfaces

Karčiauskas, Kȩstutis; Panozzo, Daniele; Peters, Jörg

doi:10.1145/3136954

Cited by 11 publications

(15 citation statements)

References 26 publications

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“…Besides its ability to handle much tighter configurations than [KPP17] the unified construction yields visually smoother highlight lines. The arrows ← in Fig.…”

Section: Examples and Discussionmentioning

confidence: 99%

“…) results in a mesh with a τ 0 ‐subnet. And, despite its smaller footprint, the τ 0 construction developed in this paper is of higher quality than the T 3 construction in [KPP17].…”

Section: Setup and Toolsmentioning

confidence: 99%

“…shows the practically relevant τ configurations consisting of one non‐quadrilateral facet, called T‐gon , surrounded by quadrilateral facets (quads). In contrast to the larger footprint T‐nets defined in [KPP17], a τ‐net has no restrictions on the nodes that do not belong to the T‐gon: all outer nodes in Fig. may be irregular , i.e.…”

Section: Setup and Toolsmentioning

confidence: 99%

“…[KPP17] introduced G‐splines for T 1 ‐and T 2 ‐gons. The construction requires T‐gons to be isolated by at least two layers of quadrilaterals, and so forces careful placement of T‐gons and irregular points.…”

Section: Introductionmentioning

confidence: 99%

“…have more or fewer than four neighbors, or can belong to another T-gon. The key advantages of the new spline over the prior state-of-the art exemplified by [KPP17] are:…”

Section: Introductionmentioning

confidence: 99%

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High quality refinable G‐splines for locally quad‐dominant meshes with T‐gons

Karčiauskas

Peters

2019

Computer Graphics Forum

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Polyhedral modeling and re‐meshing algorithms use T‐junctions to add or remove feature lines in a quadrilateral mesh. In many ways this is akin to adaptive knot insertion in a tensor‐product spline, but differs in that the designer or meshing algorithm does not necessarily protect the consistent combinatorial structure that is required to interpret the resulting quad‐dominant mesh as the control net of a hierarchical spline – and so associate a smooth surface with the mesh as in the popular tensor‐product spline paradigm. While G‐splines for multi‐sided holes or generalized subdivision can, in principle, convert quad‐dominant meshes with T‐junctions into smooth surfaces, they do not preserve the two preferred directions and so cause visible shape artifacts. Only recently have n‐gons with T‐junctions (T‐gons) in unstructured quad‐dominant meshes been recognized as a distinct challenge for generalized splines. This paper makes precise the notion of locally quad‐dominant mesh as quad‐meshes including τ‐nets, i.e. T‐gons surrounded by quads; and presents the first high‐quality G‐spline construction that can use τ‐nets as control nets for spline surfaces suitable, e.g., for automobile outer surfaces. Remarkably, T‐gons can be neighbors, separated by only one quad, both of T‐gons and of points where many quads meet. A τ‐net surface cap consists of 16 polynomial pieces of degree (3,5) and is refinable in a way that is consistent with the surrounding surface. An alternative, everywhere bi‐3 cap is not formally smooth, but achieves the same high‐quality highlight line distribution.

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“…Besides its ability to handle much tighter configurations than [KPP17] the unified construction yields visually smoother highlight lines. The arrows ← in Fig.…”

Section: Examples and Discussionmentioning

confidence: 99%

“…) results in a mesh with a τ 0 ‐subnet. And, despite its smaller footprint, the τ 0 construction developed in this paper is of higher quality than the T 3 construction in [KPP17].…”

Section: Setup and Toolsmentioning

confidence: 99%

Section: Setup and Toolsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…have more or fewer than four neighbors, or can belong to another T-gon. The key advantages of the new spline over the prior state-of-the art exemplified by [KPP17] are:…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations