Abstract
We introduce a novel continuous surface deformation method which relies on a time-dependent vector field over a triangular mesh. For every time step the piecewise linear vector field is obtained by least-squares minimization of the metric distortion induced by integration subject to boundary conditions. As an integral part of the approach, we introduce a new measure to describe local metric distortion which is invariant to the particular triangulation of the surface and which can incorporate smoothness of the field. Neither of these properties are met by previous work. A GPU implementation of the proposed algorithm enables fast deformations. The resulting deformations have lower metric distortions than deformations by existing (linear or non-linear) methods. This is shown for a number of representative test data sets.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alexa, M., Cohen-Or, D., Levin, D.: As-rigid-as-possible shape interpolation. In: Proc. SIGGRAPH, pp. 157–164 (2000)
Angelidis, A., Cani, M.P., Wyvill, G., King, S.: Swirling-sweepers: Constant volume modeling. In: Pacific Graphics (2004)
Au, O.K.C., Tai, C.L., Liu, L., Fu, H.: Dual laplacian editing for meshes. IEEE TVCG 12(3), 386–395 (2006)
Botsch, M., Kobbelt, L.: An intuitive framework for real-time freeform modeling. ACM Trans. Graphics 23(3), 630–634 (2004)
Botsch, M., Pauly, M., Gross, M., Kobbelt, L.: Primo: coupled prisms for intuitive surface modeling. In: SGP, pp. 11–20 (2006)
Botsch, M., Sorkine, O.: On linear variational surface deformation methods. IEEE Transactions on Visualization and Computer Graphics 14(1), 213–230 (2008)
Botsch, M., Sumner, R., Pauly, M., Gross, M.: Deformation transfer for detail-preserving surface editing. In: Proc. of VMV, pp. 357–364 (2006)
do Carmo, M.P.: Riemannian Geometry. Birkhäuser, Boston (1992)
Davis, T.A.: Direct Methods for Sparse Linear Systems. SIAM, Philadelphia (2006)
Du, H., Qin, H.: Direct manipulation and interactive sculpting of PDE surfaces. CGF (Proc. Eurographics) 19(3), 261–270 (2000)
Eckstein, I., Pons, J.P., Tong, Y., Kuo, C.C.J., Desbrun, M.: Generalized surface flows for mesh processing. In: SGP, pp. 183–192 (2007)
Efimow, N.: Flaechenverbiegungen in Grossen. Akadmie-Verlag (1957) (German)
English, E., Bridson, R.: Animating developable surfaces using nonconforming elements. ACM Trans. Graphics 27, 1–5 (2008)
von Funck, W., Theisel, H., Seidel, H.P.: Vector field based shape deformations. In: Proc. SIGGRAPH, pp. 1118–1125 (2006)
von Funck, W., Theisel, H., Seidel, H.P.: Explicit control of vector field based shape deformations. In: Proc. Pacific Graphics, pp. 291–300 (2007)
Huang, J., Shi, X., Liu, X., Zhou, K., Wei, L.Y., Teng, S.H., Bao, H., Guo, B., Shum, H.Y.: Subspace gradient domain mesh deformation. ACM Trans. Graphics 25(3), 1126–1134 (2006)
Kilian, M., Flöry, S., Chen, Z., Mitra, N.J., Sheffer, A., Pottmann, H.: Curved folding. ACM Trans. Graphics 27(3), 1–9 (2008)
Kilian, M., Mitra, N.J., Pottmann, H.: Geometric modeling in shape space. ACM Trans. Graphics 26(3) (2007); Proc. SIGGRAPH
Lipman, Y., Sorkine, O., Levin, D., Cohen-Or, D.: Linear rotation-invariant coordinates for meshes. In: Proc. SIGGRAPH, pp. 479–487. ACM Press, New York (2005)
Nealen, A., Mueller, M., Keiser, R., Boxerman, E., Carlson, M.: Physically based deformable models in computer graphics. CGF 25, 809–836 (2006)
Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes: The Art of Scientific Computing. Cambridge University Press, Cambridge (2007)
Qin, H., Mandal, C., Vemuri, B.C.: Dynamic catmull-clark subdivision surfaces. IEEE Transactions on Visualization and Computer Graphics 4(3) (1998)
Sengupta, S., Harris, M., Zhang, Y., Owens, J.D.: Scan primitives for gpu computing. In: GH 2007: Proc. of the 22nd ACM SIGGRAPH/EUROGRAPHICS Symposium on Graphics Hardware (2007)
Sorkine, O., Cohen-Or, D., Lipman, Y., Alexa, M., Rössl, C., Seidel, H.P.: Laplacian surface editing. In: SGP, pp. 175–184 (2004)
Sumner, R.W., Schmid, J., Pauly, M.: Embedded deformation for shape manipulation. ACM Trans. Graphics 26(3), 80:1–80:7 (2007)
Xu, W., Wang, J., Yin, K., Zhou, K., van de Panne, M., Chen, F., Guo, B.: Joint-aware manipulation of deformable models. In: Proc. SIGGRAPH (2009)
Zayer, R., Rössl, C., Karni, Z., Seidel, H.P.: Harmonic guidance for surface deformation. CGF (Proc. EUROGRAPHICS) 24(3), 601–609 (2005)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Martinez Esturo, J., Rössl, C., Theisel, H. (2012). Continuous Deformations by Isometry Preserving Shape Integration. In: Boissonnat, JD., et al. Curves and Surfaces. Curves and Surfaces 2010. Lecture Notes in Computer Science, vol 6920. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27413-8_29
Download citation
DOI: https://doi.org/10.1007/978-3-642-27413-8_29
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-27412-1
Online ISBN: 978-3-642-27413-8
eBook Packages: Computer ScienceComputer Science (R0)