Abstract
Techniques to combine implicit surfaces have been widely used in the context of blending surfaces, but not for making n-sided patches. This is mainly due to the lack of proper control for the interior of complex shapes and control of separate branches. The main attraction of implicit formulations is, however, that they represent a general paradigm based on distance functions. This property motivates our scheme, wherein classical implicit techniques are mixed with new features. Several examples are given to prove the feasibility of I-patches for shape design.
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Bajaj, C., Ihm, I.: C1 Smoothing of polyhedra with implicit algebraic splines. Comput. Graphics 11, 61–91 (1992).
Charrot, P., Gregory, J. A.: A pentagonal surface patch for computer aided design. Comput. Aided Geom. Des. 1, 87–94 (1984).
Hartmann, E.: Blending implicit surfaces with functional splines. Comput. Aided Des. 22, 500506 (1990).
Hartmann, E.: On the convexity of functional splines. Comput. Aided Geom. Des. 10, 127–142 (1993).
Hoffmann, C. M., Hoperoft, J.: Quadratic blending surfaces. Comput. Aided Des. 18, 301–306 (1986).
Hoffmann, C. M., Hoperoft, J.: The potential method for blending surfaces and corners. In: Geometric modelling, algorithms and new trends (Farin, G., ed.), pp. 347–365. Philadelphia: SIAM, 1987.
Holmström, L.: Piecewise quadratic blending of implicitly defined surfaces. Comput. Aided Geom. Des. 4, 171–189 (1987).
Hoschek, J., Lasser, D.: Fundamentals of computer aided geometric design. Wellesley: A. K. Peters, 1993.
Bloomenthal, J. (ed.): Introduction to implicit surfaces. San Francisco: Morgan Kaufman, 1997.
Li, J., Hoschek, J., Hartmann, E.: G’ functional splines for interpolation and approximation of curves, surfaces and solids. Comput. Aided Geom. Des. 7, 209–220 (1990).
Liming, R. A.: Practical analytical geometry with applications to aircraft. New York: Macmillan, 1944.
Loop, C., DeRose, T. D.: Generalised B-spline surfaces of arbitrary topological type. SIGGRAPH’90, 347–356 (1990).
Malraison, P.: A bibliography for n-sided surfaces. In: The mathematics of surfaces VIII (Cripps, R., ed.), pp. 419–430. Information Geometers, 1998.
Middleditch, A. E., Sears, K. H.: Blend surfaces for set theoretic volume modelling systems. SIGGRAPH’85. Comput. Graphics 19, 161–170 (1985).
Rockwood, A. P., Owen, J.: Blending surfaces in solid modelling. In: Geometric modelling, algorithms and new trends (Farin, G., ed.), pp. 367–384. Philadelphia: SIAM, 1987.
Rockwood, A. P.: The displacement method for implicit blending surfaces in solid models. ACM Trans. Graphics 8, 279–297 (1989).
Sederberg, T.: Piecewise algebraic surface patches. Comput. Aided Geom. Des. 2, 53–59 (1985).
Taubin, G.: Estimation of planar curves, surfaces and nonplanar space curves defined by implicit equations with applications to edge and range image segmentation. IEEE PAMI 13, 1115–1138 (1991).
Vaishnav, H., Rockwood, A. P.: Blending parametric objects by implicit techniques. In: 2nd Symposium on Solid Modeling and Applications (Rossignac, J., Turner, J., Allen, G., eds.), pp. 165–168. ACM SIGGRAPH (1993).
Várady, T.: Overlap patches: a new scheme for interpolating curve networks with n-sided regions. Comput. Aided Geom. Des. 1, 7–27 (1991).
Várady, T., Rockwood, A.: A geometric construction for setback vertex blending. Comput. Aided Des. 29, 413–425 (1997).
Vida, J., Martin, R. R., Várady, T.: A survey of blending methods that use parametric patches. Comput. Aided Des. 26, 341–365 (1994).
Warren, J.: Blending algebraic surfaces. ACM Trans. Graphics 8, 263–278 (1989).
Woodwark, J. R.: Blends in geometric modelling. In: The mathematics of surfaces II (Martin, R. R., ed.), pp. 255–297. Oxford University Press: OUP, 1987.
Zhang, D.: CSG Solid modelling and automatic NC machining of blend surfaces. PhD Dissertation, University of Bath, 1986.
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© 2001 Springer-Verlag Wien
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Várady, T., Benkö, P., Kós, G., Rockwood, A. (2001). Implicit Surfaces Revisited — I-Patches. In: Brunnett, G., Bieri, H., Farin, G. (eds) Geometric Modelling. Computing, vol 14. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6270-5_19
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DOI: https://doi.org/10.1007/978-3-7091-6270-5_19
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-83603-3
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