Convolution Filtering of Continuous Signed Distance Fields for Polygonal Meshes
Signed distance fields obtained from polygonal meshes are commonly used in various applications. However, they can have C1 discontinuities causing creases to appear when applying operations such as blending or metamorphosis. The focus of this work is to efficiently evaluate the signed distance funct...
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| Vydané v: | Computer Graphics Forum Ročník 34; číslo 6; s. 277 - 288 |
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| Hlavní autori: | , , , |
| Médium: | Journal Article |
| Jazyk: | English |
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Oxford
Blackwell Publishing Ltd
01.09.2015
Wiley |
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| ISSN: | 0167-7055, 1467-8659 |
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| Abstract | Signed distance fields obtained from polygonal meshes are commonly used in various applications. However, they can have C1 discontinuities causing creases to appear when applying operations such as blending or metamorphosis. The focus of this work is to efficiently evaluate the signed distance function and to apply a smoothing filter to it while preserving the shape of the initial mesh. The resulting function is smooth almost everywhere, while preserving the exact shape of the polygonal mesh. Due to its low complexity, the proposed filtering technique remains fast compared to its main alternatives providing C1‐continuous distance field approximation. Several applications are presented such as blending, metamorphosis and heterogeneous modelling with polygonal meshes.
Signed distance fields obtained from polygonal meshes are commonly used in various applications. However, they can have C1 discontinuities causing creases to appear when applying operations such as blending or metamorphosis. The focus of this work is to efficiently evaluate the signed distance function and to apply a smoothing filter to it while preserving the shape of the initial mesh. The resulting function is smooth almost everywhere, while preserving the exact shape of the polygonal mesh. Due to its low complexity, the proposed filtering technique remains fast compared to its main alternatives providing C1‐continuous distance field approximation. Several applications are presented such as blending, metamorphosis and heterogeneous modelling with polygonal meshes. |
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| AbstractList | Signed distance fields obtained from polygonal meshes are commonly used in various applications. However, they can have C super(1) discontinuities causing creases to appear when applying operations such as blending or metamorphosis. The focus of this work is to efficiently evaluate the signed distance function and to apply a smoothing filter to it while preserving the shape of the initial mesh. The resulting function is smooth almost everywhere, while preserving the exact shape of the polygonal mesh. Due to its low complexity, the proposed filtering technique remains fast compared to its main alternatives providing C super(1)-continuous distance field approximation. Several applications are presented such as blending, metamorphosis and heterogeneous modelling with polygonal meshes. Signed distance fields obtained from polygonal meshes are commonly used in various applications. However, they can have C super(1) discontinuities causing creases to appear when applying operations such as blending or metamorphosis. The focus of this work is to efficiently evaluate the signed distance function and to apply a smoothing filter to it while preserving the shape of the initial mesh. The resulting function is smooth almost everywhere, while preserving the exact shape of the polygonal mesh. Due to its low complexity, the proposed filtering technique remains fast compared to its main alternatives providing C super(1)-continuous distance field approximation. Several applications are presented such as blending, metamorphosis and heterogeneous modelling with polygonal meshes. Signed distance fields obtained from polygonal meshes are commonly used in various applications. However, they can have C 1 discontinuities causing creases to appear when applying operations such as blending or metamorphosis. The focus of this work is to efficiently evaluate the signed distance function and to apply a smoothing filter to it while preserving the shape of the initial mesh. The resulting function is smooth almost everywhere, while preserving the exact shape of the polygonal mesh. Due to its low complexity, the proposed filtering technique remains fast compared to its main alternatives providing C 1 ‐continuous distance field approximation. Several applications are presented such as blending, metamorphosis and heterogeneous modelling with polygonal meshes. Signed distance fields obtained from polygonal meshes are commonly used in various applications. However, they can have C1 discontinuities causing creases to appear when applying operations such as blending or metamorphosis. The focus of this work is to efficiently evaluate the signed distance function and to apply a smoothing filter to it while preserving the shape of the initial mesh. The resulting function is smooth almost everywhere, while preserving the exact shape of the polygonal mesh. Due to its low complexity, the proposed filtering technique remains fast compared to its main alternatives providing C1-continuous distance field approximation. Several applications are presented such as blending, metamorphosis and heterogeneous modelling with polygonal meshes. Signed distance fields obtained from polygonal meshes are commonly used in various applications. However, they can have C1 discontinuities causing creases to appear when applying operations such as blending or metamorphosis. The focus of this work is to efficiently evaluate the signed distance function and to apply a smoothing filter to it while preserving the shape of the initial mesh. The resulting function is smooth almost everywhere, while preserving the exact shape of the polygonal mesh. Due to its low complexity, the proposed filtering technique remains fast compared to its main alternatives providing C1‐continuous distance field approximation. Several applications are presented such as blending, metamorphosis and heterogeneous modelling with polygonal meshes. Signed distance fields obtained from polygonal meshes are commonly used in various applications. However, they can have C1 discontinuities causing creases to appear when applying operations such as blending or metamorphosis. The focus of this work is to efficiently evaluate the signed distance function and to apply a smoothing filter to it while preserving the shape of the initial mesh. The resulting function is smooth almost everywhere, while preserving the exact shape of the polygonal mesh. Due to its low complexity, the proposed filtering technique remains fast compared to its main alternatives providing C1‐continuous distance field approximation. Several applications are presented such as blending, metamorphosis and heterogeneous modelling with polygonal meshes. |
| Author | Fryazinov, Oleg Pasko, Alexander Sanchez, Mathieu Fayolle, Pierre-Alain |
| Author_xml | – sequence: 1 givenname: Mathieu surname: Sanchez fullname: Sanchez, Mathieu email: msanchez@bournemouth.ac.uk organization: The National Centre for Computer Animation, Bournemouth University, Poole, UK – sequence: 2 givenname: Oleg surname: Fryazinov fullname: Fryazinov, Oleg email: ofryazinov@bournemouth.ac.uk organization: The National Centre for Computer Animation, Bournemouth University, Poole, UK – sequence: 3 givenname: Pierre-Alain surname: Fayolle fullname: Fayolle, Pierre-Alain email: fayolle@u-aizu.ac.jp organization: Division of Information and Systems, University of Aizu, Aizu-Wakamatsu city, Japan – sequence: 4 givenname: Alexander surname: Pasko fullname: Pasko, Alexander email: apasko@bournemouth.ac.uk organization: The National Centre for Computer Animation, Bournemouth University, Poole, UK |
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| References | [COSL98] Cohen-Or D., Solomovic A., Levin D.: Three-dimensional distance field metamorphosis. ACM Transactions on Graphics 17 (Apr. 1998), 116-141. [CT11] Calakli F., Taubin G.: SSD: Smooth signed distance surface reconstruction. Computer Graphics Forum 30, 7 (2011), 1993-2002. [JBS06] Jones M. W., Baerentzen J. A., Sramek M.: 3D distance fields: A survey of techniques and applications. IEEE Transactions on Visualization and Computer Graphics 12 (July 2006), 581-599. [GS99] Gagvani N., Silver D.: Parameter-controlled volume thinning. Graphical Models and Image Processing 61, 3 (May 1999), 149-164. [Req96] Requicha A.: Geometric Modeling: A First Course. University of South California. 1996. [BFP13] Belyaev A., Fayolle P.-A., Pasko A.: Signed Lp-distance fields. Computer Aided Design 45, 2 (Feb. 2013), 523-528. [PASS95] Pasko A., Adzhiev V., Sourin A., Savchenko V.: Function representation in geometric modeling: Concepts, implementation and applications. The Visual Computer 11, 8 (1995), 429-446. [GBF03] Guendelman E., Bridson R., Fedkiw R.: Nonconvex rigid bodies with stacking. ACM Transactions on Graphics 22 (July 2003), 871-878. [MdGD*10] Mullen P., deGoes F., Desbrun M., Cohen-Steiner D., Alliez P.: Signing the unsigned: Robust surface reconstruction from raw pointsets. Computer Graphics Forum 29 (2010), 1733-1741. [PT92] Payne B. A., Toga A. W.: Distance field manipulation of surface models. IEEE Computer Graphics and Applications 12 (January 1992), 65-71. [PK08] Pavic D., Kobbelt L.: High-resolution volumetric computation of offset surfaces with feature preservation. Computer Graphics Forum 27, 2 (2008), 165-174. [CWW13] Crane K., Weischedel C., Wardetzky M.: Geodesics in heat: A new approach to computing distance based on heat flow. ACM Transactions on Graphics 32, 5 (Oct. 2013), 152:1-152:11. [BST04] Biswas A., Shapiro V., Tsukanov I.: Heterogeneous material modeling with distance fields. 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A., Adzhiev V.: BSP-fields: An exact representation of polygonal objects by differentiable scalar fields based on binary space partitioning. Computer-Aided Design 43, 3 (2011), 265-277. [WK03] Wu J., Kobbelt L.: Piecewise linear approximation of signed distance fields. In Proceedings of Vision, Modeling and Visualization 03 (2003), pp. 513-520. [GBC*13] Gourmel O., Barthe L., Cani M.-P., Wyvill B., Bernhardt A., Paulin M., Grasberger H.: A gradient-based implicit blend. ACM Transactions on Graphics 32, 2 (Apr. 2013), 12:1-12:12. [OBA*03] Ohtake Y., Belyaev A., Alexa M., Turk G., Seidel H.-P.: Multi-level partition of unity implicits. ACM Transactions on Graphics 22 (July 2003), 463-470. [Har96] Hart J. C.: Sphere tracing: A geometric method for the antialiased ray tracing of implicit surfaces. The Visual Computer 12, 10 (1996), 527-545. [JSW05] Ju T. Schaefer S., Warren J.: Mean value coordinates for closed triangular meshes. ACM Transactions on Graphics 24 (July 2005), 561-566. [YT02] Yngve G., Turk G.: Robust creation of implicit surfaces from polygonal meshes. IEEE Transactions on Visualization and Computer Graphics 8 (October 2002), 346-359. [JKSH13] Jacobson A., Kavan L., Sorkine-Hornung O.: Robust inside-outside segmentation using generalized winding numbers. ACM Transactions on Graphics 32, 4 (July 2013), 33:1-33:12. [RP66] Rosenfeld A., Pfaltz J. L.: Sequential operations in digital picture processing. Journal of ACM 13 (Oct. 1966), 471-494. [SOS04] Shen C., O'Brien J. F., Shewchuk J. R.: Interpolating and approximating implicit surfaces from polygon soup. ACM Transactions on Graphics 23 (Aug. 2004), 896-904. 2004; 21 2010 2013; 45 1995; 11 1998 2011; 30 2008 1996 2006 2005 2004 2003 1992 1999; 61 2002 2011; 8 1996; 12 2001 2000 2013; 32 2008; 27 2011; 43 2001; 18 2013 2014; 33 1966 e_1_2_9_31_1 e_1_2_9_11_1 e_1_2_9_34_1 e_1_2_9_10_1 e_1_2_9_13_1 e_1_2_9_32_1 e_1_2_9_12_1 e_1_2_9_33_1 Wu J. (e_1_2_9_35_1) 2003 Rosenfeld A. 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| References_xml | – reference: [PT92] Payne B. A., Toga A. W.: Distance field manipulation of surface models. IEEE Computer Graphics and Applications 12 (January 1992), 65-71. – reference: [CB14] Calderon S., Boubekeur T.: Point morphology. ACM Transactions on Graphics (2014). (Proc. SIGGRAPH 2014), 33, 45:1-45:13. – reference: [GBC*13] Gourmel O., Barthe L., Cani M.-P., Wyvill B., Bernhardt A., Paulin M., Grasberger H.: A gradient-based implicit blend. ACM Transactions on Graphics 32, 2 (Apr. 2013), 12:1-12:12. – reference: [PASS95] Pasko A., Adzhiev V., Sourin A., Savchenko V.: Function representation in geometric modeling: Concepts, implementation and applications. The Visual Computer 11, 8 (1995), 429-446. – reference: [FPA11] Fryazinov O., Pasko A. A., Adzhiev V.: BSP-fields: An exact representation of polygonal objects by differentiable scalar fields based on binary space partitioning. Computer-Aided Design 43, 3 (2011), 265-277. – reference: [BFP13] Belyaev A., Fayolle P.-A., Pasko A.: Signed Lp-distance fields. Computer Aided Design 45, 2 (Feb. 2013), 523-528. – reference: [LW11] Liu S., Wang C. C.: Fast intersection-free offset surface generation from freeform models with triangular meshes. IEEE Transactions on Automation Science and Engineering 8, 2 (2011), 347-360. – reference: [SOS04] Shen C., O'Brien J. F., Shewchuk J. R.: Interpolating and approximating implicit surfaces from polygon soup. ACM Transactions on Graphics 23 (Aug. 2004), 896-904. – reference: [YT02] Yngve G., Turk G.: Robust creation of implicit surfaces from polygonal meshes. IEEE Transactions on Visualization and Computer Graphics 8 (October 2002), 346-359. – reference: [JKSH13] Jacobson A., Kavan L., Sorkine-Hornung O.: Robust inside-outside segmentation using generalized winding numbers. ACM Transactions on Graphics 32, 4 (July 2013), 33:1-33:12. – reference: [BST04] Biswas A., Shapiro V., Tsukanov I.: Heterogeneous material modeling with distance fields. Computer Aided Geometric Design 21, 3 (Mar. 2004), 215-242. – reference: [Ju04] Ju T.: Robust repair of polygonal models. ACM Transactions on Graphics 23 (Aug. 2004), 888-895. – reference: [JSW05] Ju T. Schaefer S., Warren J.: Mean value coordinates for closed triangular meshes. ACM Transactions on Graphics 24 (July 2005), 561-566. – reference: [OBA*03] Ohtake Y., Belyaev A., Alexa M., Turk G., Seidel H.-P.: Multi-level partition of unity implicits. ACM Transactions on Graphics 22 (July 2003), 463-470. – reference: [JBS06] Jones M. W., Baerentzen J. A., Sramek M.: 3D distance fields: A survey of techniques and applications. IEEE Transactions on Visualization and Computer Graphics 12 (July 2006), 581-599. – reference: [VBG*13] Vaillant R., Barthe L., Guennebaud G., Cani M.-P., Rohmer D., Wyvill B., Gourmel O., Paulin M.: Implicit skinning: Real-time skin deformation with contact modeling. ACM Transactions on Graphics 32, 4 (July 2013), 125:1-125:12. – reference: [WK03] Wu J., Kobbelt L.: Piecewise linear approximation of signed distance fields. In Proceedings of Vision, Modeling and Visualization 03 (2003), pp. 513-520. – reference: [CWW13] Crane K., Weischedel C., Wardetzky M.: Geodesics in heat: A new approach to computing distance based on heat flow. ACM Transactions on Graphics 32, 5 (Oct. 2013), 152:1-152:11. – reference: [GS99] Gagvani N., Silver D.: Parameter-controlled volume thinning. Graphical Models and Image Processing 61, 3 (May 1999), 149-164. – reference: [GBF03] Guendelman E., Bridson R., Fedkiw R.: Nonconvex rigid bodies with stacking. ACM Transactions on Graphics 22 (July 2003), 871-878. – reference: [BA05] Baerentzen J. A., Aanaes H.: Signed distance computation using the angle weighted pseudonormal. IEEE Transactions on Visualization and Computer Graphics 11 (May 2005), 243-253. – reference: [COSL98] Cohen-Or D., Solomovic A., Levin D.: Three-dimensional distance field metamorphosis. ACM Transactions on Graphics 17 (Apr. 1998), 116-141. – reference: [Req96] Requicha A.: Geometric Modeling: A First Course. University of South California. 1996. – reference: [CT11] Calakli F., Taubin G.: SSD: Smooth signed distance surface reconstruction. Computer Graphics Forum 30, 7 (2011), 1993-2002. – reference: [PK08] Pavic D., Kobbelt L.: High-resolution volumetric computation of offset surfaces with feature preservation. Computer Graphics Forum 27, 2 (2008), 165-174. – reference: [MdGD*10] Mullen P., deGoes F., Desbrun M., Cohen-Steiner D., Alliez P.: Signing the unsigned: Robust surface reconstruction from raw pointsets. 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| Snippet | Signed distance fields obtained from polygonal meshes are commonly used in various applications. However, they can have C1 discontinuities causing creases to... Signed distance fields obtained from polygonal meshes are commonly used in various applications. However, they can have C 1 discontinuities causing creases to... Signed distance fields obtained from polygonal meshes are commonly used in various applications. However, they can have C super(1) discontinuities causing... |
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| SubjectTerms | Analysis Approximation Blending distance function Filtering Filtration Finite element method geometric modelling I.3.5 [Computer Graphics]: Computational Geometry and Object Modelling-Geometric algorithms Image processing systems implicit surfaces languages and systems Mathematical analysis Mathematical models polygonal modelling Preserving signed distance fields Studies Topological manifolds |
| Title | Convolution Filtering of Continuous Signed Distance Fields for Polygonal Meshes |
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