Cyclides in pure blending II. (English) Zbl 0900.68416
Summary: In this the second of a two part paper, we continue our study of pure blends between natural quadrics using both Dupin ring cyclides and parabolic cyclides. Note, we make a distinction between blends and joins. If and only if conditions for the existence of cyclide blends and constructive proofs of their correctness are given in each quadric/quadric case. Easily implementable tests are given for these conditions. The relationship of the existence of cyclide blends to the common inscribed sphere condition is examined. Finally, an example that contains at least one of each type of cyclide blend is presented.
MSC:
| 68U05 | Computer graphics; computational geometry (digital and algorithmic aspects) |
References:
| [1] | Allen, S.; Dutta, D., Cyclides in pure blending I, Computer Aided Geometric Design, 13, 51-75 (1996) · Zbl 0900.68415 |
| [2] | Johnstone, J. K.; Shene, C.-K., Dupin cyclides as blending surfaces for cones, (Fisher, R. B., Mathematics of Surfaces V (1994), Oxford University Press), 3-29 · Zbl 0813.65022 |
| [3] | Pratt, M. J., Cyclides in computer aided geometric design, Computer Aided Geometric Design, 7, 221-242 (1990) · Zbl 0712.65008 |
| [4] | Shene, C.-K., Planar intersection and blending of natural quadrics, (Ph.D. Thesis (1992), Department of Computer Science, Johns Hopkins University) · Zbl 0951.68161 |
| [5] | Srinivas, Y. L.; Dutta, D., Blending and joining using cyclides, ASME Trans. Journal of Mechanical Design, 116, 1034-1041 (1994) |
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