Refinable Multi-sided Caps for Bi-quadratic Splines

Karciauskas, Kestutis; Peters, Jörg

Refinable Multi-sided Caps for Bi-quadratic Splines

Files

055-062.pdf (4.99 MB)

Date

2021

Authors

Karciauskas, Kestutis
Peters, Jörg

Publisher

The Eurographics Association

Abstract

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.

        @inproceedings{10.2312:vmv.20211371
,
booktitle = {Vision, Modeling, and Visualization
},
editor = {Andres, Bjoern and Campen, Marcel and Sedlmair, Michael
},
title = {{Refinable Multi-sided Caps for Bi-quadratic Splines
}},
author = {Karciauskas, Kestutis and 
Peters, Jörg
},
year = {2021
},
publisher = {The Eurographics Association
},
ISBN = {978-3-03868-161-8
},
DOI = {10.2312/vmv.20211371
}
}