A Robust Two-Step Procedure for Quad-Dominant Remeshing
We propose a new technique for quad‐dominant remeshing which separates the local regularity requirements from the global alignment requirements by working in two steps. In the first step, we apply a slight variant of variational shape approximation in order to segment the input mesh into patches whi...
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| Published in: | Computer graphics forum Vol. 25; no. 3; pp. 537 - 546 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
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Oxford, UK and Boston, USA
Blackwell Publishing, Inc
01.09.2006
Blackwell Publishing Ltd |
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| ISSN: | 0167-7055, 1467-8659 |
| Online Access: | Get full text |
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| Abstract | We propose a new technique for quad‐dominant remeshing which separates the local regularity requirements from the global alignment requirements by working in two steps. In the first step, we apply a slight variant of variational shape approximation in order to segment the input mesh into patches which capture the global structure of the processed object. Then we compute an optimized quad‐mesh for every patch by generating a finite set of candidate curves and applying a combinatorial optimization procedure. Since the optimization is performed independently for each patch, we can afford more complex operations while keeping the overall computation times at a reasonable level. Our quad‐meshing technique is robust even for noisy meshes and meshes with isotropic or flat regions since it does not rely on the generation of curves by integration along estimated principal curvature directions. Instead we compute a conformal parametrization for each patch and generate the quad‐mesh from curves with minimum bending energy in the 2D parameter domain. Mesh consistency between patches is guaranteed by simply using the same set of sample points along the common boundary curve. The resulting quad‐meshes are of high‐quality locally (shape of the quads) as well as globally (global alignment) which allows us to even generate fairly coarse quad‐meshes that can be used as Catmull‐Clark control meshes.
Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Geometric algorithms, languages, and systems |
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| AbstractList | We propose a new technique for quad‐dominant remeshing which separates the local regularity requirements from the global alignment requirements by working in two steps. In the first step, we apply a slight variant of variational shape approximation in order to segment the input mesh into patches which capture the global structure of the processed object. Then we compute an optimized quad‐mesh for every patch by generating a finite set of candidate curves and applying a combinatorial optimization procedure. Since the optimization is performed independently for each patch, we can afford more complex operations while keeping the overall computation times at a reasonable level. Our quad‐meshing technique is robust even for noisy meshes and meshes with isotropic or flat regions since it does not rely on the generation of curves by integration along estimated principal curvature directions. Instead we compute a conformal parametrization for each patch and generate the quad‐mesh from curves with minimum bending energy in the 2D parameter domain. Mesh consistency between patches is guaranteed by simply using the same set of sample points along the common boundary curve. The resulting quad‐meshes are of high‐quality locally (shape of the quads) as well as globally (global alignment) which allows us to even generate fairly coarse quad‐meshes that can be used as Catmull‐Clark control meshes.
Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Geometric algorithms, languages, and systems We propose a new technique for quad-dominant remeshing which separates the local regularity requirements from the global alignment requirements by working in two steps. In the first step, we apply a slight variant of variational shape approximation in order to segment the input mesh into patches which capture the global structure of the processed object. Then we compute an optimized quad-mesh for every patch by generating a finite set of candidate curves and applying a combinatorial optimization procedure. Since the optimization is performed independently for each patch, we can afford more complex operations while keeping the overall computation times at a reasonable level. Our quad-meshing technique is robust even for noisy meshes and meshes with isotropic or flat regions since it does not rely on the generation of curves by integration along estimated principal curvature directions. Instead we compute a conformal parametrization for each patch and generate the quad-mesh from curves with minimum bending energy in the 2D parameter domain. Mesh consistency between patches is guaranteed by simply using the same set of sample points along the common boundary curve. The resulting quad-meshes are of high-quality locally (shape of the quads) as well as globally (global alignment) which allows us to even generate fairly coarse quad-meshes that can be used as Catmull-Clark control meshes. [PUBLICATION ABSTRACT] We propose a new technique for quad-dominant remeshing which separates the local regularity requirements from the global alignment requirements by working in two steps. In the first step, we apply a slight variant of variational shape approximation in order to segment the input mesh into patches which capture the global structure of the processed object. Then we compute an optimized quad-mesh for every patch by generating a finite set of candidate curves and applying a combinatorial optimization procedure. Since the optimization is performed independently for each patch, we can afford more complex operations while keeping the overall computation times at a reasonable level. Our quad-meshing technique is robust even for noisy meshes and meshes with isotropic or flat regions since it does not rely on the generation of curves by integration along estimated principal curvature directions. Instead we compute a conformal parametrization for each patch and generate the quad-mesh from curves with minimum bending energy in the 2D parameter domain. Mesh consistency between patches is guaranteed by simply using the same set of sample points along the common boundary curve. The resulting quad-meshes are of high-quality locally (shape of the quads) as well as globally (global alignment) which allows us to even generate fairly coarse quad-meshes that can be used as Catmull-Clark control meshes. |
| Author | Kobbelt, Leif Marinov, Martin |
| Author_xml | – sequence: 1 givenname: Martin surname: Marinov fullname: Marinov, Martin organization: Computer Graphics Group, RWTH Aachen, Germany – sequence: 2 givenname: Leif surname: Kobbelt fullname: Kobbelt, Leif organization: Computer Graphics Group, RWTH Aachen, Germany |
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| Cites_doi | 10.1111/1467-8659.00533 10.1145/1141911.1141993 10.1145/258734.258849 10.1145/1015706.1015817 10.1002/(SICI)1097-0207(19980315)41:5<915::AID-NME318>3.0.CO;2-Y 10.1016/j.cagd.2005.04.004 10.1016/0010-4485(78)90110-0 10.1145/566654.566590 10.1145/882262.882275 10.1145/6187.6192 10.1145/566654.566588 10.1016/S0925-7721(99)00030-9 10.1002/nme.1620320410 10.1145/566654.566589 10.1145/882262.882296 10.1111/j.1467-8659.2005.00873.x 10.1145/1183287.1183297 10.1145/1015706.1015716 |
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| References | DONG S., BREMER P.-T., GARLAND M., PASCUCCI V., HART J.C.: Spectral surface quadrangulation. ACM Trans. Graph. (2006), to appear. HOFER M., POTTMANN H.: Energy-minimizing splines in manifolds. ACM Trans. Graph. 23, 3 (2004), 284-293. MARINOV M., KOBBELT L.: Direct anisotropic quad-dominant remeshing. In Pacific Graphics (2004), pp. 207-216. CATMULL E., CLARK J.: Recursively generated B-spline surfaces on arbitrary topological meshes. Computer-Aided Geometric Design 10, 6 (Sep 1978), 350-355. GU X., GORTLER S.J., HOPPE H.: Geometry images. In ACM Trans. Graph. 21(3) (2002), pp. 355-361. HECKBERT P.S., GARLAND M.: Optimal triangulation and quadric-based surface simplification. Computational Geometry: Theory and Applications 14, 1-3 (Nov. 1999), 49-65. ALLIEZ P., COHEN-STEINER D., DEVILLERS O., LÉVY B., DESBRUN M.: Anisotropic polygonal remeshing. ACM Trans. Graph. (2003), 485-493. ALLIEZ P., MEYER M., DESBRUN M.: Interactive geometry remeshing. ACM Trans. Graph. 21(3) (2002), 347-354. KHODAKOVSKY A., LITKE N., SCHRÖDER P.: Globally smooth parameterizations with low distortion. ACM Trans. Graph. 22, 3 (July 2003), 350-357. DONG S., KIRCHER S., GARLAND M.: Harmonic functions for quadrilateral remeshing of arbitrary manifolds. Computer-Aided Geometric Design 22, 5 (2005), 392-423. COHEN-STEINER D., ALLIEZ P., DESBRUN M.: Variational shape approximation. ACM Trans. Graph. 23, 3 (Aug. 2004), 905-914. ALLIEZ P., UCELLI G., GOTSMAN C., ATTENE M.: Recent Advances in Remeshing of Surfaces. Technical report, AIM@SHAPE Network of Excellence, 2005. SCHNABEL R.B., KOONTZ J.E., WEISS B.E.: A modular system of algorithms for unconstrained minimization. ACM Trans. Math. Software 11 (1985), 419-440. BOTSCH M., KOBBELT L.: Resampling feature and blend regions in polygonal meshes for surface anti-aliasing. Computer Graphics Forum 20, 3 (2001), 402-410. LÉVY B., PETITJEAN S., RAY N., MAILLOT J.: Least squares conformal maps for automatic texture atlas generation. ACM Trans. Graph. 21, 3 (July 2002), 362-371. RAY N., LI W.C., LÉVY B., SHEFFER A., ALLIEZ P.: Periodic global parameterization. In ACM Trans. Graph. (to appear) (2006). BLACKER T., STEPHENSON M.: Paving: A new approach to automated quadrilateral mesh generation. Numerical Methods in Engineering 32 (1991), 811-847. BOROUCHAKI H., FREY P.J.: Adaptive triangular-quadrilateral mesh generation. Numerical Methods in Engineering 41 (1998), 915-934. MARINOV M., KOBBELT L.: Automatic generation of structure preserving multiresolution models. Computer Graphics Forum 24, 3 (2005), 479-486. Sep 1978; 10 July 2003; 22 1991; 32 Nov. 1999; 14 2002; 21 2004; 23 Aug. 1997 1998 Aug. 2004; 23 1996 2006 2005 2004 2003 July 2002; 21 1998; 41 1985; 11 2005; 22 2001; 20 2005; 24 e_1_2_10_21_2 e_1_2_10_19_2 e_1_2_10_3_2 e_1_2_10_17_2 SANDER P.V. (e_1_2_10_27_2) 2003 e_1_2_10_2_2 e_1_2_10_18_2 e_1_2_10_5_2 BOIER‐MARTIN I. (e_1_2_10_7_2) 2004 e_1_2_10_15_2 e_1_2_10_16_2 e_1_2_10_6_2 e_1_2_10_14_2 e_1_2_10_9_2 e_1_2_10_11_2 ECK M. (e_1_2_10_13_2) 1996 e_1_2_10_8_2 e_1_2_10_12_2 e_1_2_10_10_2 SHIMADA K. (e_1_2_10_26_2) 1998 OWEN S.J. (e_1_2_10_23_2) 1998 OWEN S.J. (e_1_2_10_22_2) 1998 ALLIEZ P. (e_1_2_10_4_2) 2005 MARINOV M. (e_1_2_10_20_2) 2004 e_1_2_10_24_2 e_1_2_10_25_2 |
| References_xml | – reference: ALLIEZ P., UCELLI G., GOTSMAN C., ATTENE M.: Recent Advances in Remeshing of Surfaces. Technical report, AIM@SHAPE Network of Excellence, 2005. – reference: ALLIEZ P., MEYER M., DESBRUN M.: Interactive geometry remeshing. ACM Trans. Graph. 21(3) (2002), 347-354. – reference: CATMULL E., CLARK J.: Recursively generated B-spline surfaces on arbitrary topological meshes. Computer-Aided Geometric Design 10, 6 (Sep 1978), 350-355. – reference: SCHNABEL R.B., KOONTZ J.E., WEISS B.E.: A modular system of algorithms for unconstrained minimization. ACM Trans. Math. Software 11 (1985), 419-440. – reference: KHODAKOVSKY A., LITKE N., SCHRÖDER P.: Globally smooth parameterizations with low distortion. ACM Trans. Graph. 22, 3 (July 2003), 350-357. – reference: HOFER M., POTTMANN H.: Energy-minimizing splines in manifolds. ACM Trans. Graph. 23, 3 (2004), 284-293. – reference: DONG S., BREMER P.-T., GARLAND M., PASCUCCI V., HART J.C.: Spectral surface quadrangulation. ACM Trans. Graph. (2006), to appear. – reference: MARINOV M., KOBBELT L.: Direct anisotropic quad-dominant remeshing. In Pacific Graphics (2004), pp. 207-216. – reference: MARINOV M., KOBBELT L.: Automatic generation of structure preserving multiresolution models. Computer Graphics Forum 24, 3 (2005), 479-486. – reference: COHEN-STEINER D., ALLIEZ P., DESBRUN M.: Variational shape approximation. ACM Trans. Graph. 23, 3 (Aug. 2004), 905-914. – reference: HECKBERT P.S., GARLAND M.: Optimal triangulation and quadric-based surface simplification. Computational Geometry: Theory and Applications 14, 1-3 (Nov. 1999), 49-65. – reference: LÉVY B., PETITJEAN S., RAY N., MAILLOT J.: Least squares conformal maps for automatic texture atlas generation. ACM Trans. Graph. 21, 3 (July 2002), 362-371. – reference: RAY N., LI W.C., LÉVY B., SHEFFER A., ALLIEZ P.: Periodic global parameterization. In ACM Trans. Graph. (to appear) (2006). – reference: ALLIEZ P., COHEN-STEINER D., DEVILLERS O., LÉVY B., DESBRUN M.: Anisotropic polygonal remeshing. ACM Trans. Graph. (2003), 485-493. – reference: BOTSCH M., KOBBELT L.: Resampling feature and blend regions in polygonal meshes for surface anti-aliasing. Computer Graphics Forum 20, 3 (2001), 402-410. – reference: BLACKER T., STEPHENSON M.: Paving: A new approach to automated quadrilateral mesh generation. Numerical Methods in Engineering 32 (1991), 811-847. – reference: BOROUCHAKI H., FREY P.J.: Adaptive triangular-quadrilateral mesh generation. Numerical Methods in Engineering 41 (1998), 915-934. – reference: DONG S., KIRCHER S., GARLAND M.: Harmonic functions for quadrilateral remeshing of arbitrary manifolds. Computer-Aided Geometric Design 22, 5 (2005), 392-423. – reference: GU X., GORTLER S.J., HOPPE H.: Geometry images. In ACM Trans. Graph. 21(3) (2002), pp. 355-361. – volume: 41 start-page: 915 year: 1998 end-page: 934 article-title: Adaptive triangular‐quadrilateral mesh generation publication-title: Numerical Methods in Engineering – year: 2005 – year: 2006 article-title: Periodic global parameterization publication-title: ACM Trans. Graph – start-page: 209 year: Aug. 1997 end-page: 216 – volume: 24 start-page: 479 issue: 3 year: 2005 end-page: 486 article-title: Automatic generation of structure preserving multiresolution models publication-title: Computer Graphics Forum – volume: 11 start-page: 419 year: 1985 end-page: 440 article-title: A modular system of algorithms for unconstrained minimization publication-title: ACM Trans. Math. Software – volume: 14 start-page: 49 issue: 1 year: Nov. 1999 end-page: 65 article-title: Optimal triangulation and quadric‐based surface simplification publication-title: Computational Geometry: Theory and Applications – year: 1996 – volume: 22 start-page: 392 issue: 5 year: 2005 end-page: 423 article-title: Harmonic functions for quadrilateral remeshing of arbitrary manifolds publication-title: Computer-Aided Geometric Design – start-page: 485 year: 2003 end-page: 493 article-title: Anisotropic polygonal remeshing publication-title: ACM Trans. Graph – start-page: 207 year: 2004 end-page: 216 article-title: Direct anisotropic quad‐dominant remeshing publication-title: Pacific Graphics – start-page: 409 year: 1998 end-page: 428 – start-page: 239 year: 1998 end-page: 267 – start-page: 146 year: 2003 end-page: 155 – volume: 32 start-page: 811 year: 1991 end-page: 847 article-title: Paving: A new approach to automated quadrilateral mesh generation publication-title: Numerical Methods in Engineering – volume: 23 start-page: 284 issue: 3 year: 2004 end-page: 293 article-title: Energy‐minimizing splines in manifolds publication-title: ACM Trans. Graph – volume: 23 start-page: 905 issue: 3 year: Aug. 2004 end-page: 914 article-title: Variational shape approximation publication-title: ACM Trans. Graph – year: 2006 article-title: Spectral surface quadrangulation publication-title: ACM Trans. Graph – volume: 20 start-page: 402 issue: 3 year: 2001 end-page: 410 article-title: Resampling feature and blend regions in polygonal meshes for surface anti‐aliasing publication-title: Computer Graphics Forum – year: 2004 – volume: 22 start-page: 350 issue: 3 year: July 2003 end-page: 357 article-title: Globally smooth parameterizations with low distortion publication-title: ACM Trans. Graph – volume: 21 start-page: 362 issue: 3 year: July 2002 end-page: 371 article-title: Least squares conformal maps for automatic texture atlas generation publication-title: ACM Trans. Graph – volume: 21 start-page: 347 issue: 3 year: 2002 end-page: 354 article-title: Interactive geometry remeshing publication-title: ACM Trans. Graph – volume: 10 start-page: 350 issue: 6 year: Sep 1978 end-page: 355 article-title: Recursively generated B‐spline surfaces on arbitrary topological meshes publication-title: Computer-Aided Geometric Design – volume: 21 start-page: 355 issue: 3 year: 2002 end-page: 361 article-title: Geometry images publication-title: ACM Trans. Graph – start-page: 61 year: 1998 end-page: 75 – ident: e_1_2_10_6_2 doi: 10.1111/1467-8659.00533 – volume-title: Proc. of the Symposium on Geometry Processing year: 2004 ident: e_1_2_10_7_2 – ident: e_1_2_10_11_2 doi: 10.1145/1141911.1141993 – volume-title: Proc. of SIGGRAPH 96 year: 1996 ident: e_1_2_10_13_2 – ident: e_1_2_10_15_2 doi: 10.1145/258734.258849 – ident: e_1_2_10_10_2 doi: 10.1145/1015706.1015817 – ident: e_1_2_10_5_2 doi: 10.1002/(SICI)1097-0207(19980315)41:5<915::AID-NME318>3.0.CO;2-Y – start-page: 239 volume-title: Proc. of the 7th Int. Meshing Roundtable year: 1998 ident: e_1_2_10_23_2 – ident: e_1_2_10_12_2 doi: 10.1016/j.cagd.2005.04.004 – start-page: 207 year: 2004 ident: e_1_2_10_20_2 article-title: Direct anisotropic quad‐dominant remeshing publication-title: Pacific Graphics – ident: e_1_2_10_9_2 doi: 10.1016/0010-4485(78)90110-0 – ident: e_1_2_10_19_2 doi: 10.1145/566654.566590 – start-page: 146 volume-title: Proc. of the Symposium on Geometry Processing year: 2003 ident: e_1_2_10_27_2 – ident: e_1_2_10_18_2 doi: 10.1145/882262.882275 – ident: e_1_2_10_25_2 doi: 10.1145/6187.6192 – ident: e_1_2_10_3_2 doi: 10.1145/566654.566588 – ident: e_1_2_10_16_2 doi: 10.1016/S0925-7721(99)00030-9 – ident: e_1_2_10_8_2 doi: 10.1002/nme.1620320410 – ident: e_1_2_10_14_2 doi: 10.1145/566654.566589 – ident: e_1_2_10_2_2 doi: 10.1145/882262.882296 – ident: e_1_2_10_21_2 doi: 10.1111/j.1467-8659.2005.00873.x – volume-title: Recent Advances in Remeshing of Surfaces year: 2005 ident: e_1_2_10_4_2 – start-page: 61 volume-title: Proc. of the 7th Int. Meshing Roundtable year: 1998 ident: e_1_2_10_26_2 – ident: e_1_2_10_24_2 doi: 10.1145/1183287.1183297 – ident: e_1_2_10_17_2 doi: 10.1145/1015706.1015716 – start-page: 409 volume-title: Proc. of the 7th Int. Meshing Roundtable year: 1998 ident: e_1_2_10_22_2 |
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| SubjectTerms | Combinatorics Computer graphics Computer programming Optimization Studies |
| Title | A Robust Two-Step Procedure for Quad-Dominant Remeshing |
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