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Field functions for implicit surfaces. (English) Zbl 0668.65015

A technique of building 3D models from an iso-surface in a scalar field is discussed. One of the characteristics of this method - referred as the soft object of implicit surface method - is that a few primitives blend to form a complex surface. The shape of these primitives is given by a field function. A new family of field functions is introduced which have to be more useful for modelling than previous field functions.
It is shown that the new field functions are useful for modelling and some of the problems appearing in using this technique are examined: primitive shape, undesirable blending and under sampling effects. The use of several field functions simultaneously and the manner in which the soft object system has been integrated into an animation system are also discussed. Further investigation domains are also mentioned.
Reviewer: O.Brudaru

MSC:

65D15 Algorithms for approximation of functions
51N05 Descriptive geometry
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[1] Barr A (1981) Superquadrics and angle preserving transformations. IEEE Comput Graph Appl (January 1981), pp 11–23
[2] Blinn J (1982) A generalization of algebraic surface drawing. ACM Trans Graph 1:235 · doi:10.1145/357306.357310
[3] Bloomenthal J (1987) Boundary representation of implicit surfaces. Res Rep CSL-87-2, Xerox PARC
[4] Bloomenthal J (1988) Polygonization of implicit surfaces. Computer Aided Geometric Design 5:341–355 · Zbl 0659.65013 · doi:10.1016/0167-8396(88)90013-1
[5] Gardner M (1965) Mathematical games. Sci Am (July)
[6] Jevans D, Wyvill B, Wyvill G (1988) Speeding up 3 D animation for simulation. Proc MAPCON IV, Soc Comput Simulation, pp 94–100
[7] Lorensen W, Cline H (1987) Marching cubes: a high resolution 3D surface construction algorithm. Comput Graph (Proc SIGGRAPH 87) 21(4):163–169 · doi:10.1145/37402.37422
[8] Middleditch A, Sears K (1985) Blend surfaces for set theoretic volume modelling systems. Comput Graph (Proc SIGGRAPH 85) 19(3):161–170 · doi:10.1145/325165.325231
[9] Nishimura H, Hirai A, Kawai T, Kawata T, Shirakawa I, Omura K (1985) Object modeling by distribution function and a method of image generation. Journal of papers given at the Electronics Communication Conference ’85 (in Jpn) J68-D(4)
[10] Reeves W (1983) Particle systems – a technique for modeling a class of fuzzy objects. ACM Trans Graph 2 (April):91–108 · doi:10.1145/357318.357320
[11] Von Herzen B, Barr A (1987) Accurate triangulations of deformed, intersecting surfaces. Comput Graph (Proc SIGGRAPH 87) 21(4):103–110 · doi:10.1145/37402.37415
[12] Wyvill B, mcPheeters C, Garbutt R (1986a) The University of Calgary 3D computer animation system. J Soc Motion Picture Television Engin 95(6):629–636
[13] Wyvill G, Wyvill B, McPheeters C (1986b) Data structures for soft objects. The Visual Computer 2:227–234 · doi:10.1007/BF01900346
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