Abstract
When interpolating a network of curves to create a C 1 surface from smooth patches, the network has to satisfy an algebraic condition, called the vertex enclosure constraint. We show the existence of an additional constraint that governs the admissibility of curve networks for G 2 interpolation by smooth patches.
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Du, W.-H., Schmitt, F.J.M.: G 1 smooth connection between rectangular and triangular Bézier patches at a common corner. In: Laurent, P.-J., Le Méhauté, A., Schumaker, L.L. (eds.) Curves and Surfaces, pp. 161–168. Academic Press, London (1991)
Du, W.-H., Schmitt, F.J.M.: On the G 2 continuity of piecewise parametric surfaces. In: Lyche, S. (ed.) Mathematical Methods in CAGD II, pp. 197–207 (1992)
Grimm, C.M., Hughes, J.F.: Modeling surfaces of arbitrary topology using manifolds. In: Computer Graphics. Annual Conference Series, vol. 29, pp. 359–368 (1995)
Gregory, J.A.: Smooth interpolation without twist constraints. In: Barnhill, R.E., Riesenfeld, R.F. (eds.) Computer Aided Geometric Design, pp. 71–87. Academic Press, London (1974)
Hahn, J.: Filling polygonal holes with rectangular patches. In: Theory and practice of geometric modeling (Blaubeuren, 1988), pp. 81–91. Springer, Berlin (1989)
Hermann, T.: G 2 interpolation of free form curve networks by biquintic Gregory patches. Computer Aided Geometric Design 13, 873–893 (1996)
Hermann, T., Lukács, G., Wolter, F.E.: Geometrical criteria on the higher order smoothness of composite surfaces. Computer Aided Geometric Design 17, 907–911 (1999)
Hermann, T., Peters, J., Strotman, T.: A geometric criterion for smooth interpolation of curve networks. In: Keyser, J. (ed.) SPM 2009: 2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling, pp. 169–173. ACM, New York (2009)
Karčiauskas, K., Peters, J.: Guided spline surfaces. Computer Aided Geometric Design 26(1), 105–116 (2009)
Loop, C.T., Schaefer, S.: G 2 tensor product splines over extraordinary vertices. Comput. Graph. Forum 27(5), 1373–1382 (2008)
Miura, K.T., Wang, K.K.: C 2 Gregory patch. In: Post, F.H., Barth, W. (eds.) EUROGRAPHICS 1991, pp. 481–492. North-Holland, Amsterdam (1991)
Prautzsch, H., Boehm, W., Paluzny, M.: Bézier and B-Spline Techniques. Springer, Heidelberg (2002)
Peters, J.: Smooth interpolation of a mesh of curves. Constructive Approximation 7, 221–246 (1991)
Peters, J.: Joining smooth patches at a vertex to form a C k surface. Computer-Aided Geometric Design 9, 387–411 (1992)
Peters, J.: Geometric continuity. In: Handbook of Computer Aided Geometric Design, pp. 193–229. Elsevier, Amsterdam (2002)
Prautzsch, H.: Freeform splines. Computer Aided Geometric Design 14(3), 201–206 (1997)
Reif, U.: TURBS—topologically unrestricted rational B-splines. Constructive Approximation 14(1), 57–77 (1998)
Ye, X.: Curvature continuous interpolation of curve meshes. Computer Aided Geometric Design 14(2), 169–190 (1997)
Ying, L., Zorin, D.: A simple manifold-based construction of surfaces of arbitrary smoothness. ACM TOG 23(3), 271–275 (2004)
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Hermann, T., Peters, J., Strotman, T. (2010). Constraints on Curve Networks Suitable for G 2 Interpolation. In: Mourrain, B., Schaefer, S., Xu, G. (eds) Advances in Geometric Modeling and Processing. GMP 2010. Lecture Notes in Computer Science, vol 6130. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13411-1_6
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DOI: https://doi.org/10.1007/978-3-642-13411-1_6
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