{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T11:55:29Z","timestamp":1759838129595},"publisher-location":"Berlin, Heidelberg","reference-count":32,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540792451"},{"type":"electronic","value":"9783540792468"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"DOI":"10.1007\/978-3-540-79246-8_25","type":"book-chapter","created":{"date-parts":[[2008,4,29]],"date-time":"2008-04-29T04:11:48Z","timestamp":1209442308000},"page":"329-343","source":"Crossref","is-referenced-by-count":7,"title":["Parametric Polynomial Minimal Surfaces of Degree Six with Isothermal Parameter"],"prefix":"10.1007","author":[{"given":"Gang","family":"Xu","sequence":"first","affiliation":[]},{"given":"Guozhao","family":"Wang","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"25_CR1","unstructured":"Bletzinger, K.-W.: Form finding of membrane structures and minimal surfaces by numerical continuation. In: Proceeding of the IASS Congress on Structural Morphology: Towards the New Millennium, Nottingham, pp. 68\u201375 (1997) ISBN 0-85358-064-2"},{"key":"25_CR2","doi-asserted-by":"publisher","first-page":"231","DOI":"10.4007\/annals.2006.164.231","volume":"164","author":"A.I. Bobenko","year":"2006","unstructured":"Bobenko, A.I., Hoffmann, T., Springborn, B.A.: Minimal surfaces from circle patterns: Geometry from combinatorics. Annals of Mathematics\u00a0164, 231\u2013264 (2006)","journal-title":"Annals of Mathematics"},{"key":"25_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1007\/3-540-46080-2_8","volume-title":"Computational Science - ICCS 2002","author":"C. Cos\u00edn","year":"2002","unstructured":"Cos\u00edn, C., Monterde, J.: B\u00e9zier Surfaces of Minimal Area. In: Sloot, P.M.A., Tan, C.J.K., Dongarra, J., Hoekstra, A.G. (eds.) ICCS-ComputSci 2002. LNCS, vol.\u00a02330, pp. 72\u201381. Springer, Heidelberg (2002)"},{"key":"25_CR4","doi-asserted-by":"crossref","unstructured":"Desbrun, M., Grinspun, E., Schroder, P.: Discrete differential geometry: an applied introduction. In: SIGGRAPH Course Notes (2005)","DOI":"10.1145\/1198555.1198660"},{"key":"25_CR5","volume-title":"Differential geometry of curves and surfaces","author":"M. Carmo Do","year":"1976","unstructured":"Do Carmo, M.: Differential geometry of curves and surfaces. Prentice-Hall, Englewood Cliffs (1976)"},{"key":"25_CR6","unstructured":"Grandine, S., Del Valle, T., Moeller, S.K., Natarajan, G., Pencheva, J., Sherman, S.: Wise. Designing airplane struts using minimal surfaces IMA Preprint 1866 (2002)"},{"key":"25_CR7","doi-asserted-by":"crossref","unstructured":"Gu, X., Yau, S.: Surface classification using conformal structures. ICCV, 701-708 (2003)","DOI":"10.1109\/ICCV.2003.1238416"},{"key":"25_CR8","unstructured":"Gu, X., Yau, S.: Computing conformal structure of surfaces CoRR cs.GR\/0212043 (2002)"},{"key":"25_CR9","doi-asserted-by":"publisher","first-page":"580","DOI":"10.1016\/0010-4485(90)90043-C","volume":"9","author":"J. Hoscheck","year":"1990","unstructured":"Hoscheck, J., Schneider, F.: Spline conversion for trimmed rational Bezier and B-spline surfaces. Computer Aided Design\u00a09, 580\u2013590 (1990)","journal-title":"Computer Aided Design"},{"key":"25_CR10","doi-asserted-by":"publisher","first-page":"663","DOI":"10.1016\/j.cad.2007.05.006","volume":"8","author":"M. Jin","year":"2007","unstructured":"Jin, M., Luo, F., Gu, X.F.: Computing general geometric structures on surfaces using Ricci flow. Computer-Aided Design\u00a08, 663\u2013675 (2007)","journal-title":"Computer-Aided Design"},{"key":"25_CR11","doi-asserted-by":"publisher","first-page":"711","DOI":"10.1016\/j.jcp.2006.10.007","volume":"2","author":"K. Jung","year":"2007","unstructured":"Jung, K., Chu, K.T., Torquato, S.: A variational level set approach for surface area minimization of triply-periodic surfaces. Journal of Computational Physics\u00a02, 711\u2013730 (2007)","journal-title":"Journal of Computational Physics"},{"key":"25_CR12","doi-asserted-by":"crossref","unstructured":"Li, X., Guo, X.H., Wang, H.Y., He, Y., Gu, X.F., Qin, H.: Harmonic volumetric mapping for solid modeling applications. In: Symposium on Solid and Physical Modeling, pp. 109\u2013120 (2007)","DOI":"10.1145\/1236246.1236263"},{"key":"25_CR13","doi-asserted-by":"publisher","first-page":"681","DOI":"10.1145\/1141911.1141941","volume":"3","author":"Y. Liu","year":"2006","unstructured":"Liu, Y., Pottmann, H., Wallner, J., Yang, Y.L., Wang, W.P.: Geometric modeling with conical meshes and developable surfaces. ACM Trans. Graphics\u00a03, 681\u2013689 (2006)","journal-title":"ACM Trans. Graphics"},{"key":"25_CR14","first-page":"824","volume":"4","author":"J.J. Man","year":"2003","unstructured":"Man, J.J., Wang, G.Z.: Approximating to nonparameterzied minimal surface with B-spline surface. Journal of Software\u00a04, 824\u2013829 (2003)","journal-title":"Journal of Software"},{"key":"25_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"262","DOI":"10.1007\/978-3-540-39422-8_18","volume-title":"Mathematics of Surfaces","author":"J. Monterde","year":"2003","unstructured":"Monterde, J.: The Plateau-B\u00e9zier Problem. In: Wilson, M.J., Martin, R.R. (eds.) Mathematics of Surfaces. LNCS, vol.\u00a02768, pp. 262\u2013273. Springer, Heidelberg (2003)"},{"key":"25_CR16","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1016\/j.cagd.2003.07.009","volume":"1","author":"J. Monterde","year":"2004","unstructured":"Monterde, J.: B\u00e9zier surfaces of minimal area: The Dirichlet approach. Computer Aided Geometric Design\u00a01, 117\u2013136 (2004)","journal-title":"Computer Aided Geometric Design"},{"key":"25_CR17","doi-asserted-by":"publisher","first-page":"697","DOI":"10.1016\/j.cagd.2004.07.003","volume":"7","author":"J. Monterde","year":"2004","unstructured":"Monterde, J., Ugail., H.: On harmonic and biharmonic B\u00e9zier surfaces. Computer Aided Geometric Design\u00a07, 697\u2013715 (2004)","journal-title":"Computer Aided Geometric Design"},{"key":"25_CR18","doi-asserted-by":"publisher","first-page":"208","DOI":"10.1016\/j.cagd.2005.09.001","volume":"2","author":"J. Monterde","year":"2006","unstructured":"Monterde, J., Ugail, H.: A general 4th-order PDE method to generate B\u00e9zier surfaces from boundary. Computer Aided Geometric Design\u00a02, 208\u2013225 (2006)","journal-title":"Computer Aided Geometric Design"},{"key":"25_CR19","volume-title":"Lectures on minimal surfaces","author":"J.C.C. Nitsche","year":"1989","unstructured":"Nitsche, J.C.C.: Lectures on minimal surfaces, vol.\u00a01. Cambridge Univ. Press, Cambridge (1989)"},{"key":"25_CR20","volume-title":"A survey of minimal surfaces","author":"R. Osserman","year":"1986","unstructured":"Osserman, R.: A survey of minimal surfaces, 2nd edn. Dover publ., New York( (1986)","edition":"2"},{"key":"25_CR21","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1080\/10586458.1993.10504266","volume":"1","author":"U. Pinkall","year":"1993","unstructured":"Pinkall, U., Polthier, K.: Computing discrete minimal surface and their conjugates. Experiment Mathematics\u00a01, 15\u201336 (1993)","journal-title":"Experiment Mathematics"},{"key":"25_CR22","doi-asserted-by":"crossref","unstructured":"Polthier, K.: Polyhedral surface of constant mean curvature. Habilitationsschrift TU Berlin (2002)","DOI":"10.1515\/crll.2002.066"},{"key":"25_CR23","doi-asserted-by":"crossref","unstructured":"Pottmann, H., Liu, Y.: Discrete surfaces in isotropic geometry. In: Mathematics of Surfaces, vol. XII, pp. 341-363 (2007)","DOI":"10.1007\/978-3-540-73843-5_21"},{"key":"25_CR24","first-page":"1","volume":"3","author":"H. Pottmann","year":"2007","unstructured":"Pottmann, H., Liu, Y., Wallner, J., Bobenko, A., Wang, W.P.: Geometry of multi-layer freeform structures for architecture. ACM Transactions on Graphics\u00a03, 1\u201311 (2007)","journal-title":"ACM Transactions on Graphics"},{"key":"25_CR25","doi-asserted-by":"crossref","first-page":"737","DOI":"10.1016\/j.cad.2004.08.011","volume":"7","author":"C.H.. S\u00e9quin","year":"2005","unstructured":"S\u00e9quin, C.H.: CAD Tools for Aesthetic Engineering. Computer Aided Design\u00a07, 737\u2013750 (2005)","journal-title":"Computer Aided Design"},{"key":"25_CR26","first-page":"547","volume-title":"The Visual Mind II","author":"J.. Sullivan","year":"2005","unstructured":"Sullivan, J.: The aesthetic value of optimal geometry. In: Emmer, M. (ed.) The Visual Mind II, pp. 547\u2013563. MIT Press, Cambridge (2005)"},{"key":"25_CR27","doi-asserted-by":"crossref","unstructured":"Wallner, J., Pottmann, H.: Infinitesimally flexible meshes and discrete minimal surfaces. Monatsh. Math (to appear, 2006)","DOI":"10.1007\/s00605-007-0502-4"},{"key":"25_CR28","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1016\/j.cad.2006.09.005","volume":"3","author":"Y. Wang","year":"2007","unstructured":"Wang, Y.: Periodic surface modeling for computer aided nano design. Computer Aided Design\u00a03, 179\u2013189 (2007)","journal-title":"Computer Aided Design"},{"key":"25_CR29","first-page":"2180","volume":"12","author":"G. Xu","year":"2006","unstructured":"Xu, G., Wang, G.Z.: Harmonic B-B surfaces over triangular domain. Journal of Computers\u00a012, 2180\u20132185 (2006)","journal-title":"Journal of Computers"},{"key":"25_CR30","doi-asserted-by":"publisher","first-page":"342","DOI":"10.1016\/j.cad.2007.02.007","volume":"5","author":"G.L. Xu","year":"2007","unstructured":"Xu, G.L., Zhang, Q.: G 2 surface modeling using minimal mean-curvature-variation flow. Computer-Aided Design\u00a05, 342\u2013351 (2007)","journal-title":"Computer-Aided Design"},{"key":"25_CR31","doi-asserted-by":"publisher","first-page":"767","DOI":"10.1016\/j.cagd.2004.07.007","volume":"10","author":"G.L. Xu","year":"2004","unstructured":"Xu, G.L.: Discrete Laplace-Beltrami operators and their convergence. Computer Aided Geometric Design\u00a010, 767\u2013784 (2004)","journal-title":"Computer Aided Geometric Design"},{"key":"25_CR32","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1016\/j.cagd.2005.07.002","volume":"2","author":"G.L. Xu","year":"2006","unstructured":"Xu, G.L.: Convergence analysis of a discretization scheme for Gaussian curvature over triangular surfaces. Computer Aided Geometric Design\u00a02, 193\u2013207 (2006)","journal-title":"Computer Aided Geometric Design"}],"container-title":["Lecture Notes in Computer Science","Advances in Geometric Modeling and Processing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-540-79246-8_25.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,27]],"date-time":"2021-04-27T11:15:02Z","timestamp":1619522102000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-540-79246-8_25"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[null]]},"ISBN":["9783540792451","9783540792468"],"references-count":32,"URL":"https:\/\/doi.org\/10.1007\/978-3-540-79246-8_25","relation":{},"subject":[]}}