course

Directional field synthesis, design, and processing

Authors:

Klaus Hildebrandt,

Mirela Ben-Chen Technion,

Daniele PanozzoAuthors Info & Claims

SIGGRAPH '17: ACM SIGGRAPH 2017 Courses

Article No.: 12, Pages 1 - 30

https://doi.org/10.1145/3084873.3084921

Published: 30 July 2017 Publication History

Abstract

Direction fields and vector fields play an increasingly important role in computer graphics and geometry processing. The synthesis of directional fields on surfaces, or other spatial domains, is a fundamental step in numerous applications, such as mesh generation, deformation, texture mapping, and many more. The wide range of applications resulted in definitions for many types of directional fields: from vector and tensor fields, over line and cross fields, to frame and vector-set fields. Depending on the application at hand, researchers have used various notions of objectives and constraints to synthesize such fields. These notions are defined in terms of fairness, feature alignment, symmetry, or field topology, to mention just a few. To facilitate these objectives, various representations, discretizations, and optimization strategies have been developed. These choices come with varying strengths and weaknesses. This course provides a systematic overview of directional field synthesis for graphics applications, the challenges it poses, and the methods developed in recent years to address these challenges.

References

[1]

Adams, B., Wicke, M., Ovsjanikov, M., Wand, M., Seidel, H., and Guibas, L. J. 2010. Meshless shape and motion design for multiple deformable objects. Computer Graphics Forum 29, 1, 43--59.

[2]

Agricola, I., and Friedrich, T. 2002. Global Analysis: Differential Forms in Analysis, Geometry, and Physics. AMS.

[3]

Alliez, P., Cohen-Steiner, D., Devillers, O., Lévy, B., and Desbrun, M. 2003. Anisotropic polygonal remeshing. ACM Transactions on Graphics 22, 3.

Digital Library

[4]

An, S. S., Kim, T., and James, D. L. 2008. Optimizing cubature for efficient integration of subspace deformations. ACM Transactions on Graphics 27, 5, 1--10.

Digital Library

[5]

Arnold, D. N., Falk, R. S., and Winther, R. 2006. Finite element exterior calculus, homological techniques, and applications. Acta numerica 15, 1.

[6]

Azencot, O., Ben-Chen, M., Chazal, F., and Ovsjanikov, M. 2013. An operator approach to tangent vector field processing. Computer Graphics Forum 32, 5.

Digital Library

[7]

Azencot, O., Weissmann, S., Ovsjanikov, M., Wardetzky, M., and Ben-Chen, M. 2014. Functional fluids on surfaces. Computer Graphics Forum 33, 5.

Digital Library

[8]

Azencot, O., Ovsjanikov, M., Chazal, F., and Ben-Chen, M. 2015. Discrete derivatives of vector fields on surfaces - an operator approach. ACM Transactions on Graphics 34, 3 (May).

Digital Library

[9]

Barbič, J., and James, D. L. 2005. Real-time subspace integration for St. Venant-Kirchhoff deformable models. ACM Transactions on Graphics 24, 3, 982--990.

Digital Library

[10]

Ben-Chen, M., Butscher, A., Solomon, J., and Guibas, L. 2010. On discrete killing vector fields and patterns on surfaces. Computer Graphics Forum 29, 5.

[11]

Bommes, D., Zimmer, H., and Kobbelt, L. 2009. Mixed-integer quadrangulation. ACM Transactions on Graphics 28, 3.

Digital Library

[12]

Bommes, D., Zimmer, H., and Kobbelt, L. 2012. Practical mixed-integer optimization for geometry processing. In Proceedings of the 7th international conference on Curves and Surfaces, Springer-Verlag, Berlin, Heidelberg, 193--206.

Digital Library

[13]

Bommes, D., Campen, M., Ebke, H.-C., Alliez, P., and Kobbelt, L. 2013. Integer-grid maps for reliable quad meshing. ACM Transactions on Graphics 32, 4.

Digital Library

[14]

Bommes, D., Lévy, B., Pietroni, N., Puppo, E., Silva, C., Tarini, M., and Zorin, D. 2013. Quad-mesh generation and processing: A survey. Computer Graphics Forum 32, 6.

Digital Library

[15]

Botsch, M., and Kobbelt, L. 2001. Resampling feature regions in polygonal meshes for surface anti-aliasing. Computer Graphics Forum 20, 3.

[16]

Brambilla, A., Carnecky, R., Peikert, R., Viola, I., and Hauser, H. 2012. Illustrative Flow Visualization: State of the Art, Trends and Challenges. In Eurographics 2012 - State of the Art Reports.

[17]

Brandt, C., Scandolo, L., Eisemann, E., and Hildebrandt, K. 2016. Spectral processing of tangential vector fields. Computer Graphics Forum 35.

Digital Library

[18]

Cabral, B., and Leedom, L. C. 1993. Imaging vector fields using line integral convolution. In Proc. SIGGRAPH '93.

Digital Library

[19]

Campen, M., and Kobbelt, L. 2014. Interactive design of quad layouts using elastica strips. ACM Transactions on Graphics 33, 6.

Digital Library

[20]

Campen, M., and Kobbelt, L. 2014. Quad layout embedding via aligned parameterization. Computer Graphics Forum 33, 8.

Digital Library

[21]

Campen, M., Bommes, D., and Kobbelt, L. 2012. Dual loops meshing: quality quad layouts on manifolds. ACM Transactions on Graphics 31, 4.

Digital Library

[22]

Campen, M., Heistermann, M., and Kobbelt, L. 2013. Practical anisotropic geodesy. Computer Graphics Forum 32, 5.

Digital Library

[23]

Campen, M., Bommes, D., and Kobbelt, L. 2015. Quantized global parametrization. ACM Transactions on Graphics 34, 6.

Digital Library

[24]

Campen, M., Ibing, M., Ebke, H.-C., Zorin, D., and Kobbelt, L. 2016. Scale-invariant directional alignment of surface parametrizations. Computer Graphics Forum 35, 5.

Digital Library

[25]

Campen, M., Silva, C. T., and Zorin, D. 2016. Bijective maps from simplicial foliations. ACM Transactions on Graphics, to appear 35, 4.

Digital Library

[26]

Campen, M. 2014. Quad Layouts: Generation and Optimization of Conforming Quadrilateral Surface Partitions. Shaker Verlag.

Digital Library

[27]

Chen, G., Mischaikow, K., Laramee, R. S., Pilarczyk, P., and Zhang, E. 2007. Vector field editing and periodic orbit extraction using morse decomposition. IEEE Transactions on Visualization and Computer Graphics 13, 4.

[28]

Chen, G., Kwatra, V., Wei, L., Hansen, C. D., and Zhang, E. 2012. Design of 2d time-varying vector fields. IEEE Transactions on Visualization and Computer Graphics 18, 10.

Digital Library

[29]

Chi, M., Yao, C., Zhang, E., and Lee, T. 2014. Optical illusion shape texturing using repeated asymmetric patterns. The Visual Computer 30, 6--8.

Digital Library

[30]

Cignoni, P., Pietroni, N., Malomo, L., and Scopigno, R. 2014. Field-aligned mesh joinery. ACM Transactions on Graphics 33, 1.

Digital Library

[31]

Cohen-Steiner, D., Alliez, P., and Desbrun, M. 2004. Variational shape approximation. ACM Transactions on Graphics 23, 3.

Digital Library

[32]

Corman, E., Ovsjanikov, M., and Chambolle, A. 2015. Continuous Matching via Vector Field Flow. Computer Graphics Forum.

[33]

Crane, K., Desbrun, M., and Schröder, P. 2010. Trivial connections on discrete surfaces. Computer Graphics Forum 29, 5.

[34]

Crane, K., de Goes, F., Desbrun, M., and Schröder, P. 2013. Digital geometry processing with discrete exterior calculus. In ACM SIGGRAPH 2013 Courses, SIGGRAPH '13.

[35]

D'Azevedo, E. F. 2000. Are bilinear quadrilaterals better than linear triangles? J. Sci. Comput. 22, 1.

Digital Library

[36]

de Goes, F., Alliez, P., Owhadi, H., and Desbrun, M. 2013. On the equilibrium of simplicial masonry structures. ACM Transactions on Graphics 32, 4.

Digital Library

[37]

de Goes, F., Liu, B., Budninskiy, M., Tong, Y., and Desbrun, M. 2014. Discrete 2-tensor fields on triangulations. Computer Graphics Forum 33, 5.

Digital Library

[38]

de Goes, F., Desbrun, M., and Tong. 2016. Vector field processing on triangle meshes. SIGGRAPH 2016 Course Notes.

Digital Library

[39]

Desbrun, M., Hirani, A., Leok, M., and Marsden, J. 2005. Discrete exterior calculus. preprint, arXiv:math.DG/0508341.

[40]

Diamanti, O., Vaxman, A., Panozzo, D., and Sorkine-Hornung, O. 2014. Designing N-PolyVector fields with complex polynomials. Computer Graphics Forum 33, 5.

Digital Library

[41]

Diamanti, O., Vaxman, A., Panozzo, D., and Sorkine-Hornung, O. 2015. Integrable PolyVector fields. ACM Transactions on Graphics 34, 4.

Digital Library

[42]

do Carmo, M. P. 1992. Riemannian Geometry. Birkhäuser.

[43]

Ebke, H.-C., Campen, M., Bommes, D., and Kobbelt, L. 2014. Level-of-detail quad meshing. ACM Transactions on Graphics 33, 6.

Digital Library

[44]

Farin, G., and Hansford, D. 1999. Discrete coons patches. Computer Aided Geometric Design 16, 7, 691--700.

Digital Library

[45]

Ferreira, N., Klosowski, J. T., Scheidegger, C. E., and Silva, C. T. 2013. Vector field k-means: Clustering trajectories by fitting multiple vector fields. Computer Graphics Forum 32, 3, 201--210.

Digital Library

[46]

Fisher, M., Schröder, P., Desbrun, M., and Hoppe, H. 2007. Design of tangent vector fields. ACM Transactions on Graphics 26, 3.

Digital Library

[47]

Forsberg, A., Chen, J., and Laidlaw, D. 2009. Comparing 3d vector field visualization methods: A user study. IEEE Transactions on Visualization and Computer Graphics 15, 6.

Digital Library

[48]

Fu, L., Kara, L. B., and Shimada, K. 2014. Modeling flow features with user-guided streamline parameterization. Computer-Aided Design 46.

Digital Library

[49]

Fulton, W. 1995. Algebraic Topology: A First Course. Springer.

[50]

Garland, M., and Heckbert, P. S. 1997. Surface simplification using quadric error metrics. In Proceedings of SIGGRAPH, 209--216.

Digital Library

[51]

Giannakopoulos, A. E., and Engel, A. J. 1988. Directional control in grid generation. J. Comput. Phys. 74, 2.

Digital Library

[52]

Gortler, S. J., Gotsman, C., and Thurston, D. 2006. Discrete one-forms on meshes and applications to 3d mesh parameterization. Computer Aided Geometric Design 23, 2.

Digital Library

[53]

Granlund, G. H., and Knutsson, H. 1995. Signal Processing for Computer Vision. Kluwer Academic Publishers, Norwell, MA, USA.

[54]

Grushko, C., Raviv, D., and Kimmel, R. 2012. Intrinsic local symmetries: A computational framework. In Proceedings of the 5th Eurographics Conference on 3D Object Retrieval, Eurographics Association, EG 3DOR' 12.

[55]

Gu, X., and Yau, S.-T. 2002. Computing conformal structure of surfaces. Communications in Information and Systems 2, 2, 121--146.

[56]

Hertzmann, A., and Zorin, D. 2000. Illustrating smooth surfaces. In Proc. SIGGRAPH 2000.

Digital Library

[57]

Hildebrandt, K., Schulz, C., von Tycowicz, C., and Polthier, K. 2011. Interactive surface modeling using modal analysis. ACM Transactions on Graphics 30, 5, 119:1--119:11.

Digital Library

[58]

Hildebrandt, K., Schulz, C., von Tycowicz, C., and Polthier, K. 2012. Modal shape analysis beyond Laplacian. Computer Aided Geometric Design 29, 5, 204--218.

Digital Library

[59]

Hirani, A. N. 2003. Discrete exterior calculus. PhD thesis, California Institute of Technology.

[60]

Huang, Z., and Ju, T. 2016. Extrinsically smooth direction fields. Computers & Graphics 58, 109 -- 117.

Digital Library

[61]

Huang, J., Shi, X., Liu, X., Zhou, K., Wei, L.-Y., Teng, S.-H., Bao, H., Guo, B., and Shum, H.-Y. 2006. Subspace gradient domain mesh deformation. ACM Transactions on Graphics 25, 3.

Digital Library

[62]

Huang, J., Tong, Y., Wei, H., and Bao, H. 2011. Boundary aligned smooth 3d cross-frame field. ACM Transactions on Graphics 30, 6.

Digital Library

[63]

Iarussi, E., Bommes, D., and Bousseau, A. 2015. Bendfields: Regularized curvature fields from rough concept sketches. ACM Transactions on Graphics 34, 3.

Digital Library

[64]

Izmestiev, I., Kusner, R. B., Rote, G., Springborn, B., and Sullivan, J. M. 2012. There is no triangulation of the torus with vertex degrees 5, 6, ..., 6, 7 and related results: Geometric proofs for combinatorial theorems. ArXiv e-prints.

[65]

Jacobson, A., Baran, I., Kavan, L., Popović, J., and Sorkine, O. 2012. Fast automatic skinning transformations. ACM Transactions on Graphics 31, 4, 77:1--77:10.

Digital Library

[66]

Jaenich, K. 2013. Vector Analysis. Springer.

[67]

Jakob, W., Tarini, M., Panozzo, D., and Sorkine-Hornung, O. 2015. Instant field-aligned meshes. ACM Transactions on Graphics 34, 6 (Nov.).

Digital Library

[68]

Jiang, T., Huang, J., Wang, Y., Tong, Y., and Bao, H. 2014. Frame field singularity correctionfor automatic hexahedralization. IEEE Transactions on Visualization and Computer Graphics 20, 8.

Digital Library

[69]

Jiang, T., Fang, X., Huang, J., Bao, H., Tong, Y., and Desbrun, M. 2015. Frame field generation through metric customization. ACM Transactions on Graphics 34, 4.

Digital Library

[70]

Jost, J. 2008. Riemannian geometry and geometric analysis. Springer.

[71]

Jucovič, E., and Trenkler, M. 1973. A theorem on the structure of cell-decompositions of orientable 2-manifolds. Mathematika 20.

[72]

Kälberer, F., Nieser, M., and Polthier, K. 2007. Quadcover - surface parameterization using branched coverings. Computer Graphics Forum 26, 3.

[73]

Kim, T., and James, D. L. 2011. Physics-based character skinning using multi-domain subspace deformations. In Symposium on Computer Animation, 63--72.

Digital Library

[74]

Knöppel, F., and Pinkall, U. 2015. Complex line bundles over simplicial complexes and their applications. preprint, arXiv:1506.07853.

[75]

Knöppel, F., Crane, K., Pinkall, U., and Schröder, P. 2013. Globally optimal direction fields. ACM Transactions on Graphics 32, 4.

Digital Library

[76]

Knöppel, F., Crane, K., Pinkall, U., and Schröder, P. 2015. Stripe patterns on surfaces. ACM Transactions on Graphics 34.

Digital Library

[77]

Knupp, P. 1995. Mesh generation using vector fields. J. Comput. Phys. 119, 1.

Digital Library

[78]

Kowalski, N., Ledoux, F., and Frey, P. 2013. A PDE based approach to multidomain partitioning and quadrilateral meshing. In Proceedings of the 21st International Meshing Roundtable.

[79]

Kowalski, N., Ledoux, F., and Frey, P. 2014. Block-structured hexahedral meshes for CAD models using 3d frame fields. Procedia Engineering 82. 23rd International Meshing Roundtable (IMR23).

[80]

Kuehnel, W. 2005. Differential Geometry: Curves - Surfaces - Manifolds. AMS.

[81]

Lai, Y.-K., Jin, M., Xie, X., He, Y., Palacios, J., Zhang, E., Hu, S.-M., and Gu, X. 2010. Metric-driven rosy field design and remeshing. IEEE Transactions on Visualization and Computer Graphics 16, 1.

Digital Library

[82]

Laidlaw, D. H., and Vilanova, A. 2012. New developments in the visualization and processing of tensor fields. Springer Science & Business Media.

[83]

Laidlaw, D. H., Davidson, J. S., Miller, T. S., da Silva, M., Kirby, R. M., Warren, W. H., and Tarr, M. 2001. Quantitative comparative evaluation of 2d vector field visualization methods. In Proceedings of the Conference on Visualization '01, IEEE Computer Society, VIS '01.

Digital Library

[84]

Laidlaw, D., Kirby, R., Jackson, C., Davidson, J., Miller, T., da Silva, M., Warren, W., and Tarr, M. 2005. Comparing 2d vector field visualization methods: a user study. IEEE Transactions on Visualization and Computer Graphics 11, 1 (Jan).

Digital Library

[85]

Laramee, R. S., Hauser, H., Zhao, L., and Post, F. H. 2007. Topology-based flow visualization, the state of the art. In Topology-based Methods in Visualization, Mathematics and Visualization.

[86]

Li, W.-C., Ray, N., and Lévy, B. 2006. Automatic and interactive mesh to t-spline conversion. In Proc. SGP '06.

Digital Library

[87]

Li, W. C., Vallet, B., Ray, N., and Lévy, B. 2006. Representing Higher-Order Singularities in Vector Fields on Piecewise Linear Surfaces. IEEE Transactions on Visualization and Computer Graphics 12, 5.

Digital Library

[88]

Li, E., Lévy, B., Zhang, X., Che, W., Dong, W., and Paul, J.-C. 2011. Meshless quadrangulation by global parameterization. Computers & Graphics.

Digital Library

[89]

Li, Y., Bao, F., Zhang, E., Kobayashi, Y., and Wonka, P. 2011. Geometry synthesis on surfaces using field-guided shape grammars. IEEE Transactions on Visualization and Computer Graphics 17, 2.

[90]

Li, Y., Liu, Y., Xu, W., Wang, W., and Guo, B. 2012. All-hex meshing using singularity-restricted field. ACM Transactions on Graphics 31, 6.

Digital Library

[91]

Li, Y., Liu, Y., and Wang, W. 2015. Planar hexagonal meshing for architecture. IEEE Transactions on Visualization and Computer Graphics 21, 1 (Jan).

[92]

Liu, Y., Pottmann, H., Wallner, J., Yang, Y.-L., and Wang, W. 2006. Geometric modeling with conical meshes and developable surfaces. ACM Transactions on Graphics 25, 3.

Digital Library

[93]

Liu, Y., Xu, W., Wang, J., Zhu, L., Guo, B., Chen, F., and Wang, G. 2011. General planar quadrilateral mesh design using conjugate direction field. ACM Transactions on Graphics 30, 6.

Digital Library

[94]

Liu, B., Tong, Y., de Goes, F., and Desbrun, M. 2016. Discrete connection and covariant derivative for vector field analysis and design. ACM Transactions on Graphics 35, 3.

Digital Library

[95]

Ma, C., Wei, L.-Y., and Tong, X. 2011. Discrete element textures. ACM Transactions on Graphics 30, 4 (July).

Digital Library

[96]

Marcias, G., Pietroni, N., Panozzo, D., Puppo, E., and Sorkine-Hornung, O. 2013. Animation-aware quadrangulation. Computer Graphics Forum 32, 5.

Digital Library

[97]

Martinez Esturo, J., Rössl, C., and Theisel, H. 2014. Generalized metric energies for continuous shape deformation. In Mathematical Methods for Curves and Surfaces, vol. 8177 of Lecture Notes in Computer Science. Springer Berlin Heidelberg, 135--157.

[98]

Max, N. 1999. Weights for computing vertex normals from facet normals. J. Graphics, GPU, & Game Tools 4, 2, 1--6.

[99]

Mebarki, A., Alliez, P., and Devillers, O. 2005. Farthest point seeding for efficient placement of streamlines. In Visualization, 2005. VIS 05. IEEE.

[100]

Mehta, S. U., Ramamoorthi, R., Meyer, M., and Hery, C. 2012. Analytic tangent irradiance environment maps for anisotropic surfaces. Computer Graphics Forum 31, 4.

Digital Library

[101]

Mercat, C. 2001. Discrete Riemann surfaces and the Ising model. Communications in Mathematical Physics 218, 1, 177--216.

[102]

Morita, S. 2001. Geometry of differential forms. American Mathematical Society, Providence, R.I.

[103]

Myles, A., Pietroni, N., and Zorin, D. 2014. Robust field-aligned global parametrization. ACM Transactions on Graphics 33, 4.

Digital Library

[104]

Nieser, M., Reitebuch, U., and Polthier, K. 2011. Cube-cover - parameterization of 3d volumes. Computer Graphics Forum 30, 5.

[105]

Nieser, M., Palacios, J., Polthier, K., and Zhang, E. 2012. Hexagonal global parameterization of arbitrary surfaces. IEEE Transactions on Visualization and Computer Graphics 18, 6, 865--878.

Digital Library

[106]

Nieser, M. 2012. Parameterization and Tiling of Polyhedral Surfaces. PhD thesis, Freie Universität Berlin.

[107]

O'Neill, B. 1966. Elementary Differential Geometry. Academic Press.

[108]

Pal, K., Schüller, C., Panozzo, D., Sorkine-Hornung, O., and Weyrich, T. 2014. Content-aware surface parameterization for interactive restoration of historical documents. Computer Graphics Forum 33, 2.

Digital Library

[109]

Palacios, J., and Zhang, E. 2007. Rotational symmetry field design on surfaces. ACM Transactions on Graphics 26, 3.

Digital Library

[110]

Palacios, J., and Zhang, E. 2011. Interactive visualization of rotational symmetry fields on surfaces. IEEE Transactions on Visualization and Computer Graphics 17, 7.

Digital Library

[111]

Pan, H., Liu, Y., Sheffer, A., Vining, N., Li, C.-J., and Wang, W. 2015. Flow aligned surfacing of curve networks. ACM Transactions on Graphics 34, 4.

Digital Library

[112]

Panozzo, D., Lipman, Y., Puppo, E., and Zorin, D. 2012. Fields on symmetric surfaces. ACM Transactions on Graphics 31, 4.

Digital Library

[113]

Panozzo, D., Block, P., and Sorkine-Hornung, O. 2013. Designing unreinforced masonry models. ACM Transactions on Graphics 32, 4.

Digital Library

[114]

Panozzo, D., Puppo, E., Tarini, M., and Sorkine-Hornung, O. 2014. Frame fields: Anisotropic and non-orthogonal cross fields. ACM Transactions on Graphics 33, 4.

Digital Library

[115]

Paris, S., Chang, W., Kozhushnyan, O. I., Jarosz, W., Matusik, W., Zwicker, M., and Durand, F. 2008. Hair photo-booth: Geometric and photometric acquisition of real hairstyles. ACM Transactions on Graphics 27, 3 (Aug.).

Digital Library

[116]

Patil, S., van den Berg, J., Curtis, S., Lin, M., and Manocha, D. 2011. Directing crowd simulations using navigation fields. IEEE Transactions on Visualization and Computer Graphics 17, 2.

Digital Library

[117]

Pedersen, H. K. 1995. Decorating implicit surfaces. In Proc. SIGGRAPH '95.

Digital Library

[118]

Peng, Z., and Laramee, R. S., 2009. Higher dimensional vector field visualization: A survey.

[119]

Pietroni, N., Corsini, M., Cignoni, P., and Scopigno, R. 2011. An interactive local flattening operator to support digital investigations on artwork surfaces. IEEE Transactions on Visualization and Computer Graphics 17, 12.

Digital Library

[120]

Pietroni, N., Tarini, M., Sorkine, O., and Zorin, D. 2011. Global parametrization of range image sets. ACM Transactions on Graphics 30, 6.

Digital Library

[121]

Pietroni, N., Tonelli, D., Puppo, E., Froli, M., Scopigno, R., and Cignoni, P. 2015. Statics aware grid shells. Computer Graphics Forum.

Digital Library

[122]

Polthier, K., and Preuss, E. 2003. Identifying vector field singularities using a discrete Hodge decomposition. In Visualization and Mathematics III.

[123]

Polthier, K., and Schmies, M. 1998. Mathematical Visualization, vol. III. Springer Verlag, ch. Straightest Geodesics on Polyhedral Surfaces.

[124]

Pottmann, H., Huang, Q., Deng, B., Schiftner, A., Kilian, M., Guibas, L., and Wallner, J. 2010. Geodesic patterns. ACM Transactions on Graphics 29, 4.

Digital Library

[125]

Praun, E., Finkelstein, A., and Hoppe, H. 2000. Lapped textures. In Proc. SIGGRAPH '00.

Digital Library

[126]

Ray, N., and Sokolov, D. 2014. Robust polylines tracing for n-symmetry direction field on triangulated surfaces. ACM Transactions on Graphics 33, 3.

Digital Library

[127]

Ray, N., and Sokolov, D. 2015. On smooth 3d frame field design. CoRR.

[128]

Ray, N., Li, W. C., Lévy, B., Sheffer, A., and Alliez, P. 2006. Periodic global parameterization. ACM Transactions on Graphics 25, 4.

Digital Library

[129]

Ray, N., Vallet, B., Li, W. C., and Lévy, B. 2008. N-symmetry direction field design. ACM Transactions on Graphics 27, 2.

Digital Library

[130]

Ray, N., Vallet, B., Alonso, L., and Lévy, B. 2009. Geometry-aware direction field processing. ACM Transactions on Graphics 29, 1.

Digital Library

[131]

Ray, N., Nivoliers, V., Lefebvre, S., and Lévy, B. 2010. Invisible seams. In Proc. Eurographics Symposium on Rendering.

Digital Library

[132]

Raymond, B., Guennebaud, G., Barla, P., Pacanowski, R., and Granier, X. 2014. Optimizing BRDF orientations for the manipulation of anisotropic highlights. Computer Graphics Forum 33, 2.

Digital Library

[133]

Schwarz, G. 1995. Hodge Decomposition - A Method for Solving Boundary Value Problems. Springer.

[134]

Solomon, J., Ben-Chen, M., Butscher, A., and Guibas, L. 2011. As-killing-as-possible vector fields for planar deformation. Computer Graphics Forum 30, 5, 1543--1552.

[135]

Solomon, J., Ben-Chen, M., Butscher, A., and Guibas, L. 2011. Discovery of intrinsic primitives on triangle meshes. Computer Graphics Forum 30, 2, 365--374.

[136]

Spencer, B., Laramee, R. S., Chen, G., and Zhang, E. 2009. Evenly spaced streamlines for surfaces: An image-based approach. Computer Graphics Forum 28, 6.

[137]

Stiny, G., and Gips, J. 1971. Shape grammars and the generative specification of painting and sculpture. In IFIP Congress (2), 1460--1465.

[138]

Tarini, M., Puppo, E., Panozzo, D., Pietroni, N., and Cignoni, P. 2011. Simple quad domains for field aligned mesh parametrization. ACM Transactions on Graphics 30, 6.

Digital Library

[139]

Tewari, G., Gotsman, C., and Gortler, S. J. 2006. Meshing genus-1 point clouds using discrete one-forms. Computers & Graphics 30, 6, 917--926.

Digital Library

[140]

Tong, Y., Alliez, P., Cohen-Steiner, D., and Desbrun, M. 2006. Designing quadrangulations with discrete harmonic forms. In Eurographics Symposium on Geometry Processing, 201--210.

Digital Library

[141]

Turk, G. 2001. Texture synthesis on surfaces. In Proc. SIGGRAPH '01.

Digital Library

[142]

van Wijk, J. J. 2002. Image based flow visualization. ACM Transactions on Graphics 21, 3.

Digital Library

[143]

Vaxman, A., and Ben-Chen, M. 2015. Dupin meshing: A parameterization approach to planar hex-dominant meshing. Tech. Rep. CS-2015-01, Department of Computer Science,technion-IIT.

[144]

von Funck, W., Theisel, H., and Seidel, H.-P. 2006. Vector field based shape deformations. ACM Transactions on Graphics 25, 3.

Digital Library

[145]

von Tycowicz, C., Schulz, C., Seidel, H.-P., and Hildebrandt, K. 2013. An efficient construction of reduced deformable objects. ACM Transactions on Graphics 32, 6, 213:1--213:10.

Digital Library

[146]

von Tycowicz, C., Schulz, C., Seidel, H.-P., and Hildebrandt, K. 2015. Real-time nonlinear shape interpolation. ACM Transactions on Graphics 34, 3, 34:1--34:10.

Digital Library

[147]

Vouga, E., Höbinger, M., Wallner, J., and Pottmann, H. 2012. Design of self-supporting surfaces. ACM Transactions on Graphics 31, 4.

Digital Library

[148]

Wang, K., Tong, Y., Desbrun, M., Schröder, P., et al. 2006. Edge subdivision schemes and the construction of smooth vector fields. ACM Transactions on Graphics 25, 3.

Digital Library

[149]

Wardetzky, M., Bergou, M., Harmon, D., Zorin, D., and Grinspun, E. 2007. Discrete quadratic curvature energies. Computer Aided Geometric Design 24, 8--9.

Digital Library

[150]

Wardetzky, M. 2006. Discrete Differential Operators on Polyhedral Surfaces-Convergence and Approximation. PhD thesis, Freie Universität Berlin.

[151]

Warner, F. W. 1983. Foundations of differentiable manifolds and Lie groups. Springer.

[152]

Wei, L.-Y., and Levoy, M. 2001. Texture synthesis over arbitrary manifold surfaces. In Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH '01.

Digital Library

[153]

Weinkauf, T., Theisel, H., Hege, H.-C., and Seidel, H.-P. 2004. Topological construction and visualization of higher order 3D vector fields. Computer Graphics Forum 23, 3.

[154]

Wijk, J. J. v. 2003. Image based flow visualization for curved surfaces. In Proceedings of the 14th IEEE Visualization 2003 (VIS'03), VIS '03.

Digital Library

[155]

Wu, X., Wand, M., Hildebrandt, K., Kohli, P., and Seidel, H.-P. 2014. Real-time symmetry-preserving deformation. Computer Graphics Forum 33, 7, 229--238.

Digital Library

[156]

Yang, Y.-L., Wang, J., Vouga, E., and Wonka, P. 2013. Urban pattern: Layout design by hierarchical domain splitting. ACM Transactions on Graphics 32, 6 (Nov.).

Digital Library

[157]

Yao, C.-Y., Chi, M.-T., Lee, T.-Y., and Ju, T. 2012. Region-based line field design using harmonic functions. IEEE Transactions on Visualization and Computer Graphics 18, 6.

[158]

Zadravec, M., Schiftner, A., and Wallner, J. 2010. Designing quad-dominant meshes with planar faces. Computer Graphics Forum 29, 5.

[159]

Zhang, E., Mischaikow, K., and Turk, G. 2006. Vector field design on surfaces. ACM Transactions on Graphics 25, 4.

Digital Library

[160]

Zhang, E., Hays, J., and Turk, G. 2007. Interactive tensor field design and visualization on surfaces. IEEE Transactions on Visualization and Computer Graphics 13, 1.

Digital Library

[161]

Zhang, E., Yeh, H., Lin, Z., and Laramee, R. S. 2009. Asymmetric tensor analysis for flow visualization. IEEE Transactions on Visualization and Computer Graphics 15, 1.

Digital Library

[162]

Zhang, M., Huang, J., Liu, X., and Bao, H. 2010. A wave-based anisotropic quadrangulation method. ACM Transactions on Graphics 29, 4.

Digital Library

[163]

Zhang, E. 2013. Npr for traditional artistic genres. In Image and Video-Based Artistic Stylisation, P. Rosin and J. Collomosse, Eds., vol. 42 of Computational Imaging and Vision. Springer London.

[164]

Zheng, X., and Pang, A. 2005. 2d asymmetric tensor analysis. In 16th IEEE Visualization Conference (VIS 2005), 23--28 October 2005, Minneapolis, MN, USA, 1.

[165]

Zhuang, Y., Zou, M., Carr, N., and Ju, T. 2014. Anisotropic geodesics for live-wire mesh segmentation. Computer Graphics Forum 33, 7.

Digital Library

Cited By

Mitra RJimenez Berumen EHofmann MChien E(2024)Singular Foliations for Knit Graph DesignACM SIGGRAPH 2024 Conference Papers10.1145/3641519.3657487(1-11)Online publication date: 13-Jul-2024
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https://dl.acm.org/doi/10.1145/3641519.3657487
Eggler AFalque RLiu MVidal‐Calleja TSorkine‐Hornung OPietroni N(2024)Digital Garment AlterationComputer Graphics Forum10.1111/cgf.1524843:7Online publication date: 7-Nov-2024
https://doi.org/10.1111/cgf.15248
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https://doi.org/10.1007/s11004-023-10106-5
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