Refinable G1 functions on G1 free-form surfaces
For two high-quality piecewise polynomial geometrically smooth (G1) surface constructions, explicit G1 functions are derived that form the basis of a function space on the G1 surfaces. The spaces are refinable and nested, i.e. the functions can be re-represented at a finer level. By choosing all bas...
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| Published in | Computer aided geometric design Vol. 54; pp. 61 - 73 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
01.05.2017
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| Abstract | For two high-quality piecewise polynomial geometrically smooth (G1) surface constructions, explicit G1 functions are derived that form the basis of a function space on the G1 surfaces. The spaces are refinable and nested, i.e. the functions can be re-represented at a finer level. By choosing all basis functions to be first order smooth a maximal set of degrees of freedom is obtained that have small support and near-uniform layout.
•For two G1 surface constructions, an explicit G1 basis is derived.•The G1 basis generates functions on these surfaces.•The spaces of functions are refinable and nested.•Enforcing only first-order smoothness yields a maximal set of free functions.•The maximal set has small support and near-uniform layout. |
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| AbstractList | For two high-quality piecewise polynomial geometrically smooth (G1) surface constructions, explicit G1 functions are derived that form the basis of a function space on the G1 surfaces. The spaces are refinable and nested, i.e. the functions can be re-represented at a finer level. By choosing all basis functions to be first order smooth a maximal set of degrees of freedom is obtained that have small support and near-uniform layout.
•For two G1 surface constructions, an explicit G1 basis is derived.•The G1 basis generates functions on these surfaces.•The spaces of functions are refinable and nested.•Enforcing only first-order smoothness yields a maximal set of free functions.•The maximal set has small support and near-uniform layout. |
| Author | Peters, Jörg Karčiauskas, Kȩstutis |
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| Cites_doi | 10.1016/j.cad.2015.07.014 10.1016/S0010-4485(01)00061-6 10.1016/j.gmod.2015.06.006 10.1017/CBO9780511721588 10.1016/j.cagd.2015.02.002 10.3390/axioms3020280 10.1016/j.cagd.2016.03.003 10.1016/j.camwa.2015.04.004 10.1016/0010-4485(78)90110-0 10.1002/(SICI)1097-0207(20000430)47:12<2039::AID-NME872>3.0.CO;2-1 10.1016/j.cagd.2016.02.009 |
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| Keywords | Multi-resolution Functions on surfaces Geometric continuity Refinable space Free-form surfaces |
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| References | Nguyen, Karčiauskas, Peters (br0130) 2016; 272 Mourrain, Vidunas, Villamizar (br0110) 2016; 45 Karčiauskas, Nguyen, Peters (br0070) Jan. 2016; 70 Cirak, Ortiz, Schröder (br0020) 2000; 47 Collin, Sangalli, Takacs (br0040) 2015 Nguyen, Karčiauskas, Peters (br0120) 2014; 3 Catmull, Clark (br0010) September 1978; 10 Lai, Schumaker (br0100) 2007 Karčiauskas, Peters (br0080) 2015; 8 Groisser, Peters (br0050) 2015; 34 Halstead, Kass, DeRose (br0060) 1993 Cirak, Scott, Antonsson, Ortiz, Schröder (br0030) 2002; 34 Kapl, Vitrih, Jüttler, Birner (br0090) 2015; 70 Nguyen, Peters (br0140) March 2016 Mourrain (10.1016/j.cagd.2017.02.014_br0110) 2016; 45 Lai (10.1016/j.cagd.2017.02.014_br0100) 2007 Karčiauskas (10.1016/j.cagd.2017.02.014_br0070) 2016; 70 Cirak (10.1016/j.cagd.2017.02.014_br0030) 2002; 34 Halstead (10.1016/j.cagd.2017.02.014_br0060) 1993 Groisser (10.1016/j.cagd.2017.02.014_br0050) 2015; 34 Nguyen (10.1016/j.cagd.2017.02.014_br0140) 2016 Karčiauskas (10.1016/j.cagd.2017.02.014_br0080) 2015; 8 Kapl (10.1016/j.cagd.2017.02.014_br0090) 2015; 70 Catmull (10.1016/j.cagd.2017.02.014_br0010) 1978; 10 Collin (10.1016/j.cagd.2017.02.014_br0040) Cirak (10.1016/j.cagd.2017.02.014_br0020) 2000; 47 Nguyen (10.1016/j.cagd.2017.02.014_br0130) 2016; 272 Nguyen (10.1016/j.cagd.2017.02.014_br0120) 2014; 3 |
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| SubjectTerms | Free-form surfaces Functions on surfaces Geometric continuity Multi-resolution Refinable space |
| Title | Refinable G1 functions on G1 free-form surfaces |
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