Fleshing: Spine-driven Bending with Local Volume Preservation
Several design and animation techniques use a one‐dimensional proxy C (a spine curve in 3D) to control the deformation or behavior of a digital model of a 3D shape S. We propose a modification of these “skinning” techniques that ensures local volume preservation, which is important for the physical...
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| Veröffentlicht in: | Computer graphics forum Jg. 32; H. 2pt3; S. 295 - 304 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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Oxford, UK
Blackwell Publishing Ltd
01.05.2013
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| ISSN: | 0167-7055, 1467-8659 |
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| Abstract | Several design and animation techniques use a one‐dimensional proxy C (a spine curve in 3D) to control the deformation or behavior of a digital model of a 3D shape S. We propose a modification of these “skinning” techniques that ensures local volume preservation, which is important for the physical plausibility of digital simulations. In the proposed “fleshing” techniques, as input, we consider a smooth spine C0, a model S0 of a solid that lies “sufficiently close” to C0, and a deformed version C1 of C0 that is “not overly bent”. (We provide a precise characterization of these restrictions.) As output, we produce a bijective mapping M, that maps any point X of S onto a point M(X) of M(S). M satisfies two properties: (1) The closest projection of X on C0 and of M(X) on C1 have the same arc length parameter. (2) U and M(U) have the same volume, where U is any subset of S. We provide three different closed form expressions for radial, normal and binormal fleshing and discuss the details of their practical real‐time implementation. |
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| AbstractList | Several design and animation techniques use a one‐dimensional proxy C (a spine curve in 3D) to control the deformation or behavior of a digital model of a 3D shape S. We propose a modification of these “skinning” techniques that ensures local volume preservation, which is important for the physical plausibility of digital simulations. In the proposed “fleshing” techniques, as input, we consider a smooth spine C 0 , a model S 0 of a solid that lies “sufficiently close” to C 0 , and a deformed version C 1 of C 0 that is “not overly bent”. (We provide a precise characterization of these restrictions.) As output, we produce a bijective mapping M, that maps any point X of S onto a point M(X) of M(S). M satisfies two properties: (1) The closest projection of X on C 0 and of M(X) on C 1 have the same arc length parameter. (2) U and M(U) have the same volume, where U is any subset of S. We provide three different closed form expressions for radial, normal and binormal fleshing and discuss the details of their practical real‐time implementation. Several design and animation techniques use a one‐dimensional proxy C (a spine curve in 3D) to control the deformation or behavior of a digital model of a 3D shape S. We propose a modification of these “skinning” techniques that ensures local volume preservation, which is important for the physical plausibility of digital simulations. In the proposed “fleshing” techniques, as input, we consider a smooth spine C0, a model S0 of a solid that lies “sufficiently close” to C0, and a deformed version C1 of C0 that is “not overly bent”. (We provide a precise characterization of these restrictions.) As output, we produce a bijective mapping M, that maps any point X of S onto a point M(X) of M(S). M satisfies two properties: (1) The closest projection of X on C0 and of M(X) on C1 have the same arc length parameter. (2) U and M(U) have the same volume, where U is any subset of S. We provide three different closed form expressions for radial, normal and binormal fleshing and discuss the details of their practical real‐time implementation. Several design and animation techniques use a one-dimensional proxy C (a spine curve in 3D) to control the deformation or behavior of a digital model of a 3D shape S. We propose a modification of these "skinning" techniques that ensures local volume preservation, which is important for the physical plausibility of digital simulations. In the proposed "fleshing" techniques, as input, we consider a smooth spine C0, a model S0 of a solid that lies "sufficiently close" to C0, and a deformed version C1 of C0 that is "not overly bent". (We provide a precise characterization of these restrictions.) As output, we produce a bijective mapping M, that maps any point X of S onto a point M(X) of M(S). M satisfies two properties: (1) The closest projection of X on C0 and of M(X) on C1 have the same arc length parameter. (2) U and M(U) have the same volume, where U is any subset of S. We provide three different closed form expressions for radial, normal and binormal fleshing and discuss the details of their practical real-time implementation. [PUBLICATION ABSTRACT] |
| Author | Rossignac, Jarek Zhuo, Wei |
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| References | Chirikjian G. S.: Closed-form primitives for generating locally volume preserving deformations. Journal of Mechanical Design 117, 3 (1995), 347-354. 3. Kim B., Liu Y., Llamas I., Jiao X., Rossignac J.: Simulation of bubbles in foam with the volume control method. ACM Trans. Graph. 26, 3 (2007). 3. Foote R. L.: The volume swept out by a moving planar region. Mathematics Magazine 79 (2006), 289-297. 7. Rohmer D., Hahmann S., Cani M.-P.: Local volume preservation for skinned characters. Comput. Graph. Forum 27, 7 (2008), 1919-1927. 2, 3. Moon H. P.: Equivolumetric offset surfaces. Computer Aided Geometric Design 26 (2009), 17-36. 3. Rossignac J., Requicha A.: Piecewise-circular curves for geometric modeling. IBM Journal of Research and Development 3 (1987), 129-148. 4. Salomon D.: Computer Graphics and Geometric Modeling, 1st ed. Springer-Verlag New York, Inc., 1999. 4. Botsch M., Kobbelt L.: Multiresolution surface representation based on displacement volumes. Comput. Graph. Forum 22, 3 (2003), 483-492. 3. Capell S., Burkhart M., Curless B., Duchamp T., Popović Z.: Physically based rigging for deformable characters. Graph. Models 69, 1 (2007), 71-87. 3. Do Carmo M.P.: Riemannian Geometry, 1st ed. Birkhäuser, 1992. 4. Harris J. W., Stocker H.: The Handbook of Mathematics and Computational Science, 1st ed. Springer-Verlag New York, Inc., Secaucus , NJ , USA , 1997. 2. Moon H. P.: Equivolumetric offsets for 2d machining with constant material removal rate. Computer Aided Geometric Design 25, 6 (2008), 397-410. 3. Zhuo W., Rossignac J.: Curvature-based offset distance: Implementations and applications. Computers & Graphics 36, 5 (2012), 445-454. 2, 3. Farouki R. T., Han C. Y.: Rational approximation schemes for rotation-minimizing frames on pythagorean-hodograph curves. Computer Aided Geometric Design 20, 7 (2003), 435-454. 4. 1987; 3 2006; 79 2000 2008; 27 1995; 117 2008; 25 2009 1997 2007 1984 2006 1840 2004 1992 2012; 36 2003; 20 2007; 69 2009; 26 2003; 22 2007; 26 1999 e_1_2_8_23_2 e_1_2_8_24_2 e_1_2_8_25_2 e_1_2_8_26_2 e_1_2_8_9_2 e_1_2_8_2_2 e_1_2_8_4_2 e_1_2_8_3_2 e_1_2_8_6_2 e_1_2_8_5_2 e_1_2_8_8_2 e_1_2_8_7_2 e_1_2_8_20_2 e_1_2_8_22_2 Harris J. W. (e_1_2_8_13_2) 1997 e_1_2_8_16_2 e_1_2_8_17_2 e_1_2_8_18_2 e_1_2_8_19_2 e_1_2_8_12_2 e_1_2_8_14_2 e_1_2_8_15_2 e_1_2_8_10_2 e_1_2_8_11_2 Rossignac J. (e_1_2_8_21_2) 1987; 3 |
| References_xml | – reference: Salomon D.: Computer Graphics and Geometric Modeling, 1st ed. Springer-Verlag New York, Inc., 1999. 4. – reference: Foote R. L.: The volume swept out by a moving planar region. Mathematics Magazine 79 (2006), 289-297. 7. – reference: Kim B., Liu Y., Llamas I., Jiao X., Rossignac J.: Simulation of bubbles in foam with the volume control method. ACM Trans. Graph. 26, 3 (2007). 3. – reference: Moon H. P.: Equivolumetric offset surfaces. Computer Aided Geometric Design 26 (2009), 17-36. 3. – reference: Rohmer D., Hahmann S., Cani M.-P.: Local volume preservation for skinned characters. Comput. Graph. Forum 27, 7 (2008), 1919-1927. 2, 3. – reference: Botsch M., Kobbelt L.: Multiresolution surface representation based on displacement volumes. Comput. Graph. Forum 22, 3 (2003), 483-492. 3. – reference: Do Carmo M.P.: Riemannian Geometry, 1st ed. Birkhäuser, 1992. 4. – reference: Moon H. P.: Equivolumetric offsets for 2d machining with constant material removal rate. Computer Aided Geometric Design 25, 6 (2008), 397-410. 3. – reference: Harris J. W., Stocker H.: The Handbook of Mathematics and Computational Science, 1st ed. Springer-Verlag New York, Inc., Secaucus , NJ , USA , 1997. 2. – reference: Capell S., Burkhart M., Curless B., Duchamp T., Popović Z.: Physically based rigging for deformable characters. Graph. Models 69, 1 (2007), 71-87. 3. – reference: Farouki R. T., Han C. Y.: Rational approximation schemes for rotation-minimizing frames on pythagorean-hodograph curves. Computer Aided Geometric Design 20, 7 (2003), 435-454. 4. – reference: Rossignac J., Requicha A.: Piecewise-circular curves for geometric modeling. IBM Journal of Research and Development 3 (1987), 129-148. 4. – reference: Zhuo W., Rossignac J.: Curvature-based offset distance: Implementations and applications. Computers & Graphics 36, 5 (2012), 445-454. 2, 3. – reference: Chirikjian G. S.: Closed-form primitives for generating locally volume preserving deformations. Journal of Mechanical Design 117, 3 (1995), 347-354. 3. – volume: 26 issue: 3 year: 2007 article-title: Simulation of bubbles in foam with the volume control method publication-title: ACM Trans. Graph. – volume: 26 start-page: 17 year: 2009 end-page: 36 article-title: Equivolumetric offset surfaces publication-title: Computer Aided Geometric Design – volume: 27 start-page: 1919 issue: 7 year: 2008 end-page: 1927 article-title: Local volume preservation for skinned characters publication-title: Comput. Graph. Forum – year: 2009 – start-page: 114 year: 1840 end-page: 118 – volume: 25 start-page: 397 issue: 6 year: 2008 end-page: 410 article-title: Equivolumetric offsets for 2d machining with constant material removal rate publication-title: Computer Aided Geometric Design – start-page: 10 year: 2004 end-page: 15 – volume: 22 start-page: 483 issue: 3 year: 2003 end-page: 492 article-title: Multiresolution surface representation based on displacement volumes publication-title: Comput. Graph. Forum – volume: 69 start-page: 71 issue: 1 year: 2007 end-page: 87 article-title: Physically based rigging for deformable characters publication-title: Graph. Models – volume: 79 start-page: 289 year: 2006 end-page: 297 article-title: The volume swept out by a moving planar region publication-title: Mathematics Magazine – year: 2007 – start-page: 39 year: 2007 end-page: 46 – year: 2006 – volume: 36 start-page: 445 issue: 5 year: 2012 end-page: 454 article-title: Curvature‐based offset distance: Implementations and applications publication-title: Computers & Graphics – volume: 117 start-page: 347 issue: 3 year: 1995 end-page: 354 article-title: Closed‐form primitives for generating locally volume preserving deformations publication-title: Journal of Mechanical Design – year: 1997 – year: 2000 – volume: 20 start-page: 435 issue: 7 year: 2003 end-page: 454 article-title: Rational approximation schemes for rotation‐minimizing frames on pythagorean‐hodograph curves publication-title: Computer Aided Geometric Design – start-page: 21 year: 1984 end-page: 30 – year: 1992 – volume: 3 start-page: 129 year: 1987 end-page: 148 article-title: Piecewise‐circular curves for geometric modeling publication-title: IBM Journal of Research and Development – year: 1999 – ident: e_1_2_8_19_2 doi: 10.1111/j.1467-8659.2008.01340.x – ident: e_1_2_8_9_2 doi: 10.1145/311535.311576 – ident: e_1_2_8_11_2 doi: 10.2307/27642954 – ident: e_1_2_8_22_2 doi: 10.1007/978-1-4612-1504-2 – ident: e_1_2_8_20_2 doi: 10.1145/1599470.1599481 – ident: e_1_2_8_24_2 doi: 10.1145/267734.267771 – ident: e_1_2_8_8_2 doi: 10.1007/978-1-4757-2201-7 – ident: e_1_2_8_5_2 doi: 10.1111/1467-8659.00696 – ident: e_1_2_8_2_2 doi: 10.1109/PCCGA.2004.1348329 – ident: e_1_2_8_18_2 doi: 10.1016/j.cagd.2008.01.003 – ident: e_1_2_8_7_2 doi: 10.1115/1.2826687 – ident: e_1_2_8_25_2 doi: 10.1145/1179352.1142002 – ident: e_1_2_8_23_2 – ident: e_1_2_8_10_2 doi: 10.1016/S0167-8396(03)00095-5 – ident: e_1_2_8_17_2 doi: 10.1016/j.cagd.2007.08.002 – volume-title: The Handbook of Mathematics and Computational Science year: 1997 ident: e_1_2_8_13_2 – ident: e_1_2_8_16_2 doi: 10.1145/344779.344862 – ident: e_1_2_8_6_2 doi: 10.1016/j.gmod.2006.09.001 – volume: 3 start-page: 129 year: 1987 ident: e_1_2_8_21_2 article-title: Piecewise‐circular curves for geometric modeling publication-title: IBM Journal of Research and Development – ident: e_1_2_8_3_2 – ident: e_1_2_8_15_2 doi: 10.1145/1276377.1276500 – ident: e_1_2_8_14_2 doi: 10.1145/1230100.1230107 – ident: e_1_2_8_4_2 doi: 10.1145/964965.808573 – ident: e_1_2_8_26_2 doi: 10.1016/j.cag.2012.03.013 – ident: e_1_2_8_12_2 doi: 10.1145/304012.304036 |
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| SubjectTerms | 3-D graphics Analysis Deformation Digital simulation Exact solutions F.2.2 [Theory of Computation]: Nonnumerical Algorithms and Problems-Geometrical problems and computations I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling-Geometric transformations Image processing systems Preservation Proxy client servers Spine Studies Three dimensional Three dimensional models |
| Title | Fleshing: Spine-driven Bending with Local Volume Preservation |
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