A Multi-sided Bézier Patch with a Simple Control Structure

A new n‐sided surface scheme is presented, that generalizes tensor product Bézier patches. Boundaries and corresponding cross‐derivatives are specified as conventional Bézier surfaces of arbitrary degrees. The surface is defined over a convex polygonal domain; local coordinates are computed from gen...

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Veröffentlicht in:	Computer graphics forum Jg. 35; H. 2; S. 307 - 317
Hauptverfasser:	Várady, Tamás, Salvi, Péter, Karikó, György
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Oxford Blackwell Publishing Ltd 01.05.2016
Schlagworte:	Algorithms Analysis and object representations Bezier Bezier patches Boundaries Categories and Subject Descriptors (according to ACM CCS) Displacement I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling-Curve I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Curve, surface, solid, and object representations Image processing systems Mathematical analysis Mathematical models Representations solid Studies surface Topological manifolds
ISSN:	0167-7055, 1467-8659
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Abstract	A new n‐sided surface scheme is presented, that generalizes tensor product Bézier patches. Boundaries and corresponding cross‐derivatives are specified as conventional Bézier surfaces of arbitrary degrees. The surface is defined over a convex polygonal domain; local coordinates are computed from generalized barycentric coordinates; control points are multiplied by weighted, biparametric Bernstein functions. A method for interpolating a middle point is also presented. This Generalized Bézier (GB) patch is based on a new displacement scheme that builds up multi‐sided patches as a combination of a base patch, n displacement patches and an interior patch; this is considered to be an alternative to the Boolean sum concept. The input ribbons may have different degrees, but the final patch representation has a uniform degree. Interior control points—other than those specified by the user—are placed automatically by a special degree elevation algorithm. GB patches connect to adjacent Bézier surfaces with G1continuity. The control structure is simple and intuitive; the number of control points is proportional to those of quadrilateral control grids. The scheme is introduced through simple examples; suggestions for future work are also discussed.
AbstractList	A new n-sided surface scheme is presented, that generalizes tensor product Bezier patches. Boundaries and corresponding cross-derivatives are specified as conventional Bezier surfaces of arbitrary degrees. The surface is defined over a convex polygonal domain; local coordinates are computed from generalized barycentric coordinates; control points are multiplied by weighted, biparametric Bernstein functions. A method for interpolating a middle point is also presented. This Generalized Bezier (GB) patch is based on a new displacement scheme that builds up multi-sided patches as a combination of a base patch, n displacement patches and an interior patch; this is considered to be an alternative to the Boolean sum concept. The input ribbons may have different degrees, but the final patch representation has a uniform degree. Interior control points-other than those specified by the user-are placed automatically by a special degree elevation algorithm. GB patches connect to adjacent Bezier surfaces with G super(1)continuity. The control structure is simple and intuitive; the number of control points is proportional to those of quadrilateral control grids. The scheme is introduced through simple examples; suggestions for future work are also discussed. A new n‐sided surface scheme is presented, that generalizes tensor product Bézier patches. Boundaries and corresponding cross‐derivatives are specified as conventional Bézier surfaces of arbitrary degrees. The surface is defined over a convex polygonal domain; local coordinates are computed from generalized barycentric coordinates; control points are multiplied by weighted, biparametric Bernstein functions. A method for interpolating a middle point is also presented. This Generalized Bézier (GB) patch is based on a new displacement scheme that builds up multi‐sided patches as a combination of a base patch, n displacement patches and an interior patch; this is considered to be an alternative to the Boolean sum concept. The input ribbons may have different degrees, but the final patch representation has a uniform degree. Interior control points—other than those specified by the user—are placed automatically by a special degree elevation algorithm. GB patches connect to adjacent Bézier surfaces with G1continuity. The control structure is simple and intuitive; the number of control points is proportional to those of quadrilateral control grids. The scheme is introduced through simple examples; suggestions for future work are also discussed. A new n-sided surface scheme is presented, that generalizes tensor product Bézier patches. Boundaries and corresponding cross-derivatives are specified as conventional Bézier surfaces of arbitrary degrees. The surface is defined over a convex polygonal domain; local coordinates are computed from generalized barycentric coordinates; control points are multiplied by weighted, biparametric Bernstein functions. A method for interpolating a middle point is also presented. This Generalized Bézier (GB) patch is based on a new displacement scheme that builds up multi-sided patches as a combination of a base patch, n displacement patches and an interior patch; this is considered to be an alternative to the Boolean sum concept. The input ribbons may have different degrees, but the final patch representation has a uniform degree. Interior control points--other than those specified by the user--are placed automatically by a special degree elevation algorithm. GB patches connect to adjacent Bézier surfaces with G1continuity. The control structure is simple and intuitive; the number of control points is proportional to those of quadrilateral control grids. The scheme is introduced through simple examples; suggestions for future work are also discussed. A new n‐sided surface scheme is presented, that generalizes tensor product Bézier patches. Boundaries and corresponding cross‐derivatives are specified as conventional Bézier surfaces of arbitrary degrees. The surface is defined over a convex polygonal domain; local coordinates are computed from generalized barycentric coordinates; control points are multiplied by weighted, biparametric Bernstein functions. A method for interpolating a middle point is also presented. This Generalized Bézier (GB) patch is based on a new displacement scheme that builds up multi‐sided patches as a combination of a base patch, n displacement patches and an interior patch; this is considered to be an alternative to the Boolean sum concept. The input ribbons may have different degrees, but the final patch representation has a uniform degree. Interior control points—other than those specified by the user—are placed automatically by a special degree elevation algorithm. GB patches connect to adjacent Bézier surfaces with G 1 continuity. The control structure is simple and intuitive; the number of control points is proportional to those of quadrilateral control grids. The scheme is introduced through simple examples; suggestions for future work are also discussed.
Author	Karikó, György Salvi, Péter Várady, Tamás
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Cites_doi	10.1111/cgf.12588 10.1016/j.cad.2011.08.028 10.1145/130826.130828 10.1016/j.cagd.2015.03.017 10.21236/AD0663504 10.1145/1183287.1183295 10.1016/j.cad.2015.07.014 10.1016/S0167-8396(01)00019-X 10.1016/S0167-8396(97)00007-1 10.1016/j.cagd.2014.06.006 10.1145/77055.77059 10.1016/0167-8396(94)90205-4 10.1016/0167-8396(84)90005-0 10.1016/S0167-8396(96)00029-5
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Copyright	2016 The Author(s) Computer Graphics Forum © 2016 The Eurographics Association and John Wiley & Sons Ltd. Published by John Wiley & Sons Ltd. 2016 The Eurographics Association and John Wiley & Sons Ltd.
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References	Várady T., Rockwood A., Salvi P.: Transfinite surface interpolation over irregular n-sided domains. Computer Aided Design 43, 11 (2011), 1330-1340. 2 Warren J.: Creating multisided rational Bézier surfaces using base points. Transactions on Graphics 11 (1992), 127-139. 2 Gregory J. A., Zhou J.: Filling polygonal holes with bicubic patches. Computer Aided Geometric Design 11, 4 (1994), 391-410. 2 Zheng J., Ball A.: Control point surfaces over non-four-sided areas. Computer Aided Geometric Design 14, 9 (1997), 807-821. 2 Loop C. T., DeRose T. D.: A multisided generalization of Bézier surfaces. Transactions on Graphics 8 (1989), 204-234. 2 Zheng J.: The n-sided control point surfaces without twist constraints. Computer Aided Geometric Design 18, 2 (2001), 129-134. 2 Salvi P., Várady T., Rockwood A.: Ribbon-based transfinite surfaces. Computer Aided Geometric Design 31, 9 (2014), 613-630. 1, 2, 9 Coons S. A.: Surfaces for Computer-Aided Design of Space Forms. Tech. Rep. MIT/LCS/TR-41, Massachusetts Institute of Technology, 1967. 2 Smith J., Schaefer S.: Selective degree elevation for multisided Bézier patches. Computer Graphics Forum 34, 2 (2015), 609-615. 2 Hosaka M., Kimura F.: Non-four-sided patch expressions with control points. Computer Aided Geometric Design 1, 1 (1984), 75-86. 2 Sun L.-Y., Zhu C.-G.: G1 continuity between toric surface patches. Computer Aided Geometric Design 35-36 (2015), 255-267. Geometric Modeling and Processing 2015. 2 Hormann K., Floater M. S.: Mean value coordinates for arbitrary planar polygons. Transactions on Graphics 25, 4 (2006), 1424-1441. 3 Prautzsch H.: Freeform splines. Computer Aided Geometric Design 14, 3 (1997), 201-206. 2 2015; 34 1984; 1 1997; 14 2006; 25 2008; 27 1989; 8 1998 1986 1994; 11 2011; 43 1994 1983 2015 2001; 18 1992; 11 2015; 35–36 1967 2014; 31 Loop C. (e_1_2_9_9_2) 2008 e_1_2_9_20_2 e_1_2_9_12_2 e_1_2_9_7_2 e_1_2_9_6_2 e_1_2_9_5_2 e_1_2_9_4_2 Malraison P. (e_1_2_9_10_2) 1998 Gregory J. A. (e_1_2_9_3_2) 1986 Peters J. (e_1_2_9_11_2) 1994 e_1_2_9_8_2 e_1_2_9_14_2 e_1_2_9_16_2 Sabin M. (e_1_2_9_13_2) 1983 e_1_2_9_15_2 Coons S. A. (e_1_2_9_2_2) 1967 e_1_2_9_18_2 e_1_2_9_17_2 e_1_2_9_19_2
References_xml	– reference: Sun L.-Y., Zhu C.-G.: G1 continuity between toric surface patches. Computer Aided Geometric Design 35-36 (2015), 255-267. Geometric Modeling and Processing 2015. 2 – reference: Várady T., Rockwood A., Salvi P.: Transfinite surface interpolation over irregular n-sided domains. Computer Aided Design 43, 11 (2011), 1330-1340. 2 – reference: Hosaka M., Kimura F.: Non-four-sided patch expressions with control points. Computer Aided Geometric Design 1, 1 (1984), 75-86. 2 – reference: Salvi P., Várady T., Rockwood A.: Ribbon-based transfinite surfaces. Computer Aided Geometric Design 31, 9 (2014), 613-630. 1, 2, 9 – reference: Gregory J. A., Zhou J.: Filling polygonal holes with bicubic patches. Computer Aided Geometric Design 11, 4 (1994), 391-410. 2 – reference: Hormann K., Floater M. S.: Mean value coordinates for arbitrary planar polygons. Transactions on Graphics 25, 4 (2006), 1424-1441. 3 – reference: Smith J., Schaefer S.: Selective degree elevation for multisided Bézier patches. Computer Graphics Forum 34, 2 (2015), 609-615. 2 – reference: Warren J.: Creating multisided rational Bézier surfaces using base points. Transactions on Graphics 11 (1992), 127-139. 2 – reference: Zheng J., Ball A.: Control point surfaces over non-four-sided areas. Computer Aided Geometric Design 14, 9 (1997), 807-821. 2 – reference: Loop C. T., DeRose T. D.: A multisided generalization of Bézier surfaces. Transactions on Graphics 8 (1989), 204-234. 2 – reference: Zheng J.: The n-sided control point surfaces without twist constraints. Computer Aided Geometric Design 18, 2 (2001), 129-134. 2 – reference: Coons S. A.: Surfaces for Computer-Aided Design of Space Forms. Tech. Rep. MIT/LCS/TR-41, Massachusetts Institute of Technology, 1967. 2 – reference: Prautzsch H.: Freeform splines. Computer Aided Geometric Design 14, 3 (1997), 201-206. 2 – volume: 34 start-page: 609 issue: 2 year: 2015 end-page: 615 article-title: Selective degree elevation for multisided Bézier patches publication-title: Computer Graphics Forum – start-page: 2 year: 1967 – start-page: 419 year: 1998 end-page: 430 article-title: A bibliography for n‐sided surfaces – volume: 35–36 start-page: 255 year: 2015 end-page: 267 article-title: continuity between toric surface patches publication-title: Computer Aided Geometric Design – volume: 11 start-page: 127 year: 1992 end-page: 139 article-title: Creating multisided rational Bézier surfaces using base points publication-title: Transactions on Graphics – volume: 1 start-page: 75 issue: 1 year: 1984 end-page: 86 article-title: Non‐four‐sided patch expressions with control points publication-title: Computer Aided Geometric Design – volume: 8 start-page: 204 year: 1989 end-page: 234 article-title: A multisided generalization of Bézier surfaces publication-title: Transactions on Graphics – start-page: 217 year: 1986 end-page: 232 article-title: N‐sided surface patches – start-page: 57 year: 1983 end-page: 70 article-title: Non‐rectangular surface patches suitable for inclusion in a B‐spline surface – volume: 25 start-page: 1424 issue: 4 year: 2006 end-page: 1441 article-title: Mean value coordinates for arbitrary planar polygons publication-title: Transactions on Graphics – volume: 27 start-page: 1373 year: 2008 end-page: 1382 article-title: tensor product splines over extraordinary vertices – volume: 31 start-page: 613 issue: 9 year: 2014 end-page: 630 article-title: Ribbon‐based transfinite surfaces publication-title: Computer Aided Geometric Design – start-page: 2 year: 1994 article-title: Constructing surfaces of arbitrary topology using biquadratic and bicubic splines – volume: 18 start-page: 129 issue: 2 year: 2001 end-page: 134 article-title: The n‐sided control point surfaces without twist constraints publication-title: Computer Aided Geometric Design – volume: 14 start-page: 807 issue: 9 year: 1997 end-page: 821 article-title: Control point surfaces over non‐four‐sided areas publication-title: Computer Aided Geometric Design – volume: 11 start-page: 391 issue: 4 year: 1994 end-page: 410 article-title: Filling polygonal holes with bicubic patches publication-title: Computer Aided Geometric Design – volume: 14 start-page: 201 issue: 3 year: 1997 end-page: 206 article-title: Freeform splines publication-title: Computer Aided Geometric Design – volume: 43 start-page: 1330 issue: 11 year: 2011 end-page: 1340 article-title: Transfinite surface interpolation over irregular n‐sided domains publication-title: Computer Aided Design – start-page: 2 year: 2015 article-title: Generalizing bicubic splines for modeling and IGA with irregular layout – ident: e_1_2_9_14_2 doi: 10.1111/cgf.12588 – start-page: 217 volume-title: Mathematics of Surfaces I year: 1986 ident: e_1_2_9_3_2 – ident: e_1_2_9_17_2 doi: 10.1016/j.cad.2011.08.028 – ident: e_1_2_9_18_2 doi: 10.1145/130826.130828 – start-page: 419 volume-title: Mathematics of Surfaces VIII year: 1998 ident: e_1_2_9_10_2 – ident: e_1_2_9_16_2 doi: 10.1016/j.cagd.2015.03.017 – start-page: 2 volume-title: Surfaces for Computer‐Aided Design of Space Forms year: 1967 ident: e_1_2_9_2_2 doi: 10.21236/AD0663504 – start-page: 2 volume-title: Designing Fair Curves and Surfaces: Shape Quality in Geometric Modeling and Computer‐Aided Design year: 1994 ident: e_1_2_9_11_2 – ident: e_1_2_9_5_2 doi: 10.1145/1183287.1183295 – ident: e_1_2_9_7_2 doi: 10.1016/j.cad.2015.07.014 – start-page: 57 volume-title: EuroGraphics year: 1983 ident: e_1_2_9_13_2 – ident: e_1_2_9_20_2 doi: 10.1016/S0167-8396(01)00019-X – ident: e_1_2_9_19_2 doi: 10.1016/S0167-8396(97)00007-1 – ident: e_1_2_9_15_2 doi: 10.1016/j.cagd.2014.06.006 – ident: e_1_2_9_8_2 doi: 10.1145/77055.77059 – ident: e_1_2_9_4_2 doi: 10.1016/0167-8396(94)90205-4 – ident: e_1_2_9_6_2 doi: 10.1016/0167-8396(84)90005-0 – start-page: 1373 volume-title: Computer Graphics Forum year: 2008 ident: e_1_2_9_9_2 – ident: e_1_2_9_12_2 doi: 10.1016/S0167-8396(96)00029-5
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Snippet	A new n‐sided surface scheme is presented, that generalizes tensor product Bézier patches. Boundaries and corresponding cross‐derivatives are specified as... A new n-sided surface scheme is presented, that generalizes tensor product Bézier patches. Boundaries and corresponding cross-derivatives are specified as... A new n-sided surface scheme is presented, that generalizes tensor product Bezier patches. Boundaries and corresponding cross-derivatives are specified as...
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SubjectTerms	Algorithms Analysis and object representations Bezier Bezier patches Boundaries Categories and Subject Descriptors (according to ACM CCS) Displacement I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling-Curve I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Curve, surface, solid, and object representations Image processing systems Mathematical analysis Mathematical models Representations solid Studies surface Topological manifolds
Title	A Multi-sided Bézier Patch with a Simple Control Structure
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