Browsing by Author "Peters, Jorg"

Now showing 1 - 4 of 4
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    Evolving Guide Subdivision
    (The Eurographics Association and John Wiley & Sons Ltd., 2023) Karciauskas, Kestutis; Peters, Jorg; Myszkowski, Karol; Niessner, Matthias
    To overcome the well-known shape deficiencies of bi-cubic subdivision surfaces, Evolving Guide subdivision (EG subdivision) generalizes C2 bi-quartic (bi-4) splines that approximate a sequence of piecewise polynomial surface pieces near extraordinary points. Unlike guided subdivision, which achieves good shape by following a guide surface in a two-stage, geometry-dependent process, EG subdivision is defined by five new explicit subdivision rules. While formally only C1 at extraordinary points, EG subdivision applied to an obstacle course of inputs generates surfaces without the oscillations and pinched highlight lines typical for Catmull-Clark subdivision. EG subdivision surfaces join C2 with bi-3 surface pieces obtained by interpreting regular sub-nets as bi-cubic tensor-product splines and C2 with adjacent EG surfaces. The EG subdivision control net surrounding an extraordinary node can have the same structure as Catmull-Clark subdivision: two rings of 4-sided facets around each extraordinary nodes so that extraordinary nodes are separated by at least one regular node.
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    High Quality Refinable G-splines for Locally Quad-dominant Meshes With T-gons
    (The Eurographics Association and John Wiley & Sons Ltd., 2019) Karciauskas, Kestutis; Peters, Jorg; Bommes, David and Huang, Hui
    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 t-nets, i.e. T-gons surrounded by quads; and presents the first high-quality G-spline construction that can use t-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 t-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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    Point-augmented Bi-cubic Subdivision Surfaces
    (The Eurographics Association and John Wiley & Sons Ltd., 2022) Karciauskas, Kestutis; Peters, Jorg; Umetani, Nobuyuki; Wojtan, Chris; Vouga, Etienne
    Point-Augmented Subdivision (PAS) replaces complex geometry-dependent guided subdivision, known to yield high-quality surfaces, by explicit subdivision formulas that yield similarly-good limit surfaces and are easy to implement using any subdivision infrastructure: map the control net d augmented by a fixed central limit point C, to a finer net (˜d;C) = M(d;C), where the subdivision matrix M is assembled from the provided stencil Tables. Point-augmented bi-cubic subdivision improves the state of the art so that bi-cubic subdivision surfaces can be used in high-end geometric design: the highlight line distribution for challenging configurations lacks the shape artifacts usually associated with explicit iterative generalized subdivision operators near extraordinary points. Five explicit formulas define Point-augmented bi-cubic subdivision in addition to uniform B-spline knot insertion. Point-augmented bi-cubic subdivision comes in two flavors, either generating a sequence of C2-joined surface rings (PAS2) or C1-joined rings (PAS1) that have fewer pieces.
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    Quadratic-Attraction Subdivision
    (The Eurographics Association and John Wiley & Sons Ltd., 2023) Karciauskas, Kestutis; Peters, Jorg; Memari, Pooran; Solomon, Justin
    The idea of improving multi-sided piecewise polynomial surfaces, by explicitly prescribing their behavior at a central surface point, allows for decoupling shape finding from enforcing local smoothness constraints. Quadratic-Attraction Subdivision determines the completion of a quadratic expansion at the central point to attract a differentiable subdivision surface towards bounded curvature, with good shape also in-the-large.