×

Skeleton-based 3D surface parameterization applied on texture mapping. (English) Zbl 1277.68280

Summary: Assume a 2D manifold surface topologically equivalent to a sphere with handles. We propose a novel 3D surface parametrization along the surface skeleton. First, we use a global mapping of the surface vertices onto a computed skeleton. Second, we use local mapping of the surrounding area of each skeleton segment into a small rectangle whose size is derived based on the surface properties around the segment. Each rectangle can be textured by assigning the local \(u\), \(v\) texture coordinates. Furthermore, these rectangles are packed into a large squared texture called skeleton texture map (STM) by approximately solving a palette loading problem.
Our technique enables the mapping of a texture onto the surface without necessity to store texture coordinates together with the model data. In other words it is enough to store the geometry data with STM and the coordinates are calculated on the fly.

MSC:

68U05 Computer graphics; computational geometry (digital and algorithmic aspects)
65D17 Computer-aided design (modeling of curves and surfaces)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] AU, O. K.-C., TAI, C.-L., CHU, H.-K., COHEN-OR, D., AND LEE, T.-Y. 2008. Skeleton extraction by mesh contraction. In ACM SIGGRAPH 2008 papers. 1-10.
[2] AUJAY, G., HÉTROY, F., LAZARUS, F., AND DEPRAZ, C. 2007. Harmonic skeleton for realistic character animation. In Proceedings of the 2007 ACM SIGGRAPH. 151-160.
[3] BEN-CHEN, M., GOTSMAN, C., AND BUNIN, G. 2008. Conformal flattening by curvature prescription and metric scaling. Computer Graphics Forum 27, 2, 449-458.
[4] BENSON, D. AND DAVIS, J. 2002. Octree textures. ACM Trans. Graph. 21, 785-790.
[5] BIER, E. AND SLOAN, K. 1986. Two-part texture mappings. IEEE Computer Graphics and Applications 6, 40-53. · doi:10.1109/MCG.1986.276545
[6] BIRGIN, E. G., LOBATO, R. D., AND MORABITO, R. 2010. Generating unconstrained two-dimensional nonguillotine cutting patterns by a recursive partitioning algorithm.
[7] CAO, J., TAGLIASACCHI, A., OLSON, M., ZHANG, H., AND SU, Z. 2010. Point cloud skeletons via laplacian based contraction. In Proceedings of the 2010 SMI Conf. 187-197.
[8] CARR, N. A. AND HART, J. C. 2002. Meshed atlases for real-time procedural solid texturing. ACM Transactions on Graphics 21, 106-131. · Zbl 05457187 · doi:10.1145/508357.508360
[9] CORNEA, N. D., SILVER, D., AND MIN, P. 2007. Curve-skeleton properties, applications, and algorithms. IEEE Transactions on Visualization and Computer Graphics 13, 3, 530-548. · Zbl 05339873 · doi:10.1109/TVCG.2007.1002
[10] DEBRY, D., GIBBS, J., DELEON, D., AND ROBINS, P. N. 2002. Painting and rendering textures on unparameterized models.
[11] DEY, T. K. AND SUN, J. 2006. Defining and computing curve-skeletons with medial geodesic function. In Proceedings of the 4th EG symposium on Geom. processing. 143-152.
[12] FLOATER, M. S. 2003. Mean value coordinates. Computer Aided Geometric Design 20, 2003. · Zbl 1069.65553 · doi:10.1016/S0167-8396(03)00002-5
[13] GARLAND, M. AND HECKBERT, P. S. 1997. Surface simplification using quadric error metrics. In SIGGRAPH ’97: Proceedings of the 24th annual conference on Computer graphics and interactive techniques. ACM Press/Addison-Wesley Publishing Co., New York, NY, USA, 209-216.
[14] GU, X. AND YAU, S.-T. 2003. Global conformal surface parameterization. In Proceedings of the 2003 Eurographics/ ACM SIGGRAPH symposium on Geometry processing. SGP ’03. Eurographics Association, Aire-la- Ville, Switzerland, Switzerland, 127-137.
[15] HAKER, S., ANGENENT, S., TANNENBAUM, A., KIKINIS, R., SAPIRO, G., AND HALLE, M. 2000. Conformal surface parameterization for texture mapping. IEEE Transactions on Visualization and Computer Graphics 6, 181-189. · Zbl 05108174 · doi:10.1109/2945.856998
[16] HE, Y., WANG, H., FU, C.-W., AND QIN, H. 2009. A divide-and-conquer approach for automatic polycube map construction. Computers & Graphics, 369-380.
[17] HILAGA, M., SHINAGAWA, Y., KOHMURA, T., AND KUNII, T. L. 2001. Topology matching for fully automatic similarity estimation of 3d shapes. In Proceedings of the 28th annual conference on Computer graphics and interactive techniques. SIGGRAPH ’01. ACM, New York, NY, USA, 203-212.
[18] HORMANN, K. AND GREINER, G. 2000. MIPS: An Efficient Global Parametrization Method. Vanderbilt University Press.
[19] JIN, M., KIM, J., LUO, F., AND GU, X. 2008. Discrete surface ricci flow. IEEE Transactions on Visualization and Computer Graphics 14, 1030-1043. · Zbl 05340049 · doi:10.1109/TVCG.2008.57
[20] KHAREVYCH, L., SPRINGBORN, B., AND SCHRÖ DER, P. 2006. Discrete conformal mappings via circle patterns. ACM Trans. Graph. 25, 412-438.
[21] LEE, A. W. F., SWELDENS, W., SCHRÖDER, P., COWSAR, L., AND DOBKIN, D. 1998. MAPS: multiresolution adaptive parameterization of surfaces. In Proceedings of the 25th annual conference on Computer graphics and interactive techniques. SIGGRAPH ’98. ACM, New York, NY, USA, 95-104.
[22] LEFEBVRE, S. AND DACHSBACHER, C. 2007. Tiletrees. In Proceedings of the ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games.
[23] LÉVY, B. AND MALLET, J.-L. 1998. Non-distorted texture mapping for sheared triangulated meshes. In Proceedings of the 25th annual conf. on CG and interactive techniques. 343-352.
[24] LÉVY, B., PETITJEAN, S., RAY, N., AND MAILLOT, J. 2002. Least squares conformal maps for automatic texture atlas generation. ACM Trans. Graph. 21, 362-371.
[25] LIN, J., JIN, X., FAN, Z., AND WANG, C. C. L. 2008. Automatic polycube-maps. In Proceedings of the 5th international conference on Advances in geometric modeling and processing. GMP’08. Springer-Verlag, Berlin, Heidelberg, 3-16.
[26] LIU, P.-C., WU, F.-C., MA, W.-C., LIANG, R.-H., AND OUHYOUNG, M. 2003. Automatic animation skeleton construction using repulsive force field. In Proceedings of the 11th Pacific Conference on CG and Applications. 409-413.
[27] MAILLOT, J., YAHIA, H., AND VERROUST, A. 1993. Interactive texture mapping. In Proceedings of the 20th annual conference on Computer graphics and interactive techniques. 27-34.
[28] PATANE, G., SPAGNUOLO, M., AND FALCIDIENO, B. 2004. Para-graph: Graph-based parameterization of triangle meshes with arbitrary genus. Comput. Graph. Forum, 783-797.
[29] PIPONI, D. AND BORSHUKOV, G. 2000. Seamless texture mapping of subdivision surfaces by model pelting and texture blending. In Proceedings of the 27th annual conference on Computer graphics and interactive techniques. SIGGRAPH ’00. ACM Press/Addison-Wesley Publishing Co., New York, NY, USA, 471-478.
[30] PRAUN, E. AND HOPPE, H. 2003. Spherical parametrization and remeshing. ACM Trans. Graph. 22, 340-349.
[31] PURNOMO, B., COHEN, J. D., AND KUMAR, S. 2004. Seamless texture atlases. In ACM SIGGRAPH symposium on Geometry processing. 65-74.
[32] RAY, N., LI, W. C., LÉVY, B., SHEFFER, A., AND ALLIEZ, P. 2006. Periodic global parameterization. ACM Trans. Graph. 25, 1460-1485.
[33] SANDER, P. V., GORTLER, S. J., SNYDER, J., AND HOPPE, H. 2002. Signal-specialized parametrization. In Proceedings of the 13th Eurographics workshop on Rendering. EGRW ’02. Eurographics Association, Airela- Ville, Switzerland, Switzerland, 87-98.
[34] SANDER, P. V., SNYDER, J., GORTLER, S. J., AND HOPPE, H. 2001. Texture mapping progressive meshes. In Proceedings of the 28th annual conf. on CG and inter. techn. 409-416.
[35] SHAPIRA, L., SHAMIR, A., AND COHEN-OR, D. 2008. Consistent mesh partitioning and skeletonisation using the shape diameter function. Vis. Comput. 24, 249-259.
[36] SHARF, A., LEWINER, T., SHAMIR, A., AND KOBBELT, L. 2007. On-the-fly curve-skeleton computation for 3D shapes. Computer Graphics Forum, (Proceedings Eurographics 2007) 26, 3, 323-328. · Zbl 05653174 · doi:10.1111/j.1467-8659.2007.01054.x
[37] SHEFFER, A. AND HART, J. C. 2002. Seamster: Inconspicuous low-distortion texture seam layout. In IEEE Visualization. 291-298.
[38] SHEFFER, A. AND STURLER, E. D. 2000. Surface parameterization for meshing by triangulation flattening. In Proc. 9th International Meshing Roundtable. 161-172.
[39] TARINI, M., HORMANN, K., CIGNONI, P., AND MONTANI, C. 2004. Polycube-maps. In In Proceedings of SIGGRAPH 2004. 853-860.
[40] TEICHMANN, M. AND TELLER, S. 1998. Assisted articulation of closed polygonal models. In SIGGRAPH ’98: ACM SIGGRAPH 98 Conference abstracts and applications. ACM, New York, NY, USA, 254.
[41] WANG, H., HE, Y., LI, X., GU, X., AND QIN, H. 2007. Polycube splines. In Proceedings of the 2007 ACM symposium on Solid and physical modeling. SPM ’07. ACM, New York, NY, USA, 241-251. · Zbl 1206.65038
[42] YUKSEL, C., KEYSER, J., AND HOUSE, D. H. 2010. Mesh colors. ACM Trans. Graph. 29, 15:1-15:11.
[43] ZHANG, E., MISCHAIKOW, K., AND TURK, G. 2005. Feature-based surface parameterization and texture mapping. ACM Trans. Graph. 24, 1-27.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.