Browsing by Author "Peters, Jörg"

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    A New Class of Guided C2 Subdivision Surfaces Combining Good Shape with Nested Refinement
    (© 2018 The Eurographics Association and John Wiley & Sons Ltd., 2018) Karčiauskas, Kęstutis; Peters, Jörg; Chen, Min and Benes, Bedrich
    Converting quadrilateral meshes to smooth manifolds, guided subdivision offers a way to combine the good highlight line distribution of recent G‐spline constructions with the refinability of subdivision surfaces. This avoids the complex refinement of G‐spline constructions and the poor shape of standard subdivision. Guided subdivision can then be used both to generate the surface and hierarchically compute functions on the surface. Specifically, we present a subdivision algorithm of polynomial degree bi‐6 and a curvature bounded algorithm of degree bi‐5. We prove that the common eigenstructure of this class of subdivision algorithms is determined by their guide and demonstrate that their eigenspectrum (speed of contraction) can be adjusted without harming the shape. For practical implementation, a finite number of subdivision steps can be completed by a high‐quality cap. Near irregular points this allows leveraging standard polynomial tools both for rendering of the surface and for approximately integrating functions on the surface.Converting quadrilateral meshes to smooth manifolds, guided subdivision offers a way to combine the good highlight line distribution of recent G‐spline constructions with the refinability of subdivision surfaces.This avoids the complex refinement of G‐spline constructions and the poor shape of standard subdivision. Guided subdivision can then be used both to generate the surface and hierarchically compute functions on the surface. Specifically, we present a subdivision algorithm of polynomial degree bi‐6 and a curvature bounded algorithm of degree bi‐5.
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    Refinable Multi-sided Caps for Bi-quadratic Splines
    (The Eurographics Association, 2021) Karciauskas, Kestutis; Peters, Jörg; Andres, Bjoern and Campen, Marcel and Sedlmair, Michael
    Subdivision surfaces based on bi-quadratic splines have a control net, the DS-net, whose irregularities are n-sided facets. To date their limit shape is poor due to a small footprint of the refinement rules and the difficulty of controlling shape at the center irregularity. By contrast, a control net where vertices are surrounded by n quadrilateral faces, a CC-net, admits higher-quality subdivision and finite polynomial constructions. It would therefore be convenient to leverage these constructions to fill holes in a C1 bi-quadratic spline complex. In principle the switch in layout from a control net with central n-sided facet to one with a central irregular point is easy: just apply one step of Catmull-Clark refinement. The challenge, however, is to define the transition between the bi-quadratic bulk and the n-sided cap construction to be of sufficiently good shape to not destroy the advantage of higher-quality algorithms. This challenge is addressed here by explicit formulas for conversion from a DS-net to a CC-net.