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Finding the limbs and cusps of generalized cylinders

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Abstract

This paper addresses the problem of finding analytically the limbs and cusps of generalized cylinders. Orthographic projections of generalized cylinders whose axis is straight and whose axis is an arbitrary 3D curve are considered in turn. In both cases, the general equations of the limbs and cusps are given. They are solved for three classes of generalized cylinders: solids of revolution, straight homogeneous generalized cylinders whose scaling sweeping rule is a polynomial of degree less than or equal to 5 and generalized cylinders whose axis is an arbitrary 3D curve but the cross section is circular and constant. Examples of limbs and cusps found for each class are given. Applications and extensions to perspective projection and completely general straight generalized cylinders are discussed.

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References

  1. T.O. Binford, “Visual perception by computer,” in PROC. IEEE CONF. Systems and Control, Miami, December 1971.

  2. T.O. Binford, “Inferring surfaces from images,” Artificial Intelligence, vol. 17, pp. 205–244, 1981.

    Google Scholar 

  3. R.A. Brooks, “Symbolic reasoning among 3D models and 2D images,” Artificial Intelligence, vol. 17, pp. 285–348, 1981.

    Google Scholar 

  4. J.J. Koenderink and A.J. Van Doorn, “The singularities of the visual mapping,” Biological Cybernetics, vol. 24, pp. 51–59, 1976.

    Google Scholar 

  5. J. Malik, “Labelling line drawings of curved objects,” in PROC. IU WORKSHOP, Miami Beach, Fla., 1985, pp. 209–218.

  6. D. Marr, “Analysis of occluding contour,” in PROC. ROY. SOC. (London) B-197, pp. 441–475, 1977.

  7. D. Marr and K. Nishihara, “Representation and recognition of the spatial organization of three dimensional shapes,” in PROC. ROY. SOC. (London), B-200, pp. 269–294, 1977.

  8. R. Nevatia, Machine perception. Prentice-Hall: Englewood Cliffs, N.J., 1982.

    Google Scholar 

  9. J. Ponce and D. Chelberg, “Localized intersections computation for solid modeling with straight homogeneous generalized cylinders,” in PROC. FOURTH IEEE ROBOTICS CONF., Raleigh, N.C., April 1987.

  10. J. Ponce, D. Chelberg, and W. Mann, “Analytical properties of generalized cylinders and their projections,” in PROC. FIRST INT. CONF. ON COMPUTER VISION, London, U.K., June 1987.

  11. J. Ponce and D. Chelberg, “Finding the limbs and cusps of generalized cylinders,” to appear as a CS Technical Report, Stanford University, 1987.

  12. S.A. Shafer and T. Kanade, “The theory of straight homogeneous generalized cylinders,” Tech. Rep. CMU-CS083-105, Computer Science Department, Carnegie Mellon University, 1983.

  13. R. Scott, “Graphics and prediction from models,” in PROC. IU WORKSHOP, pp. 98–106, 1984.

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This work was supported by the Air Force Office of Scientific Research under contract F33615-85-C-5106 and the Advanced Research Agency under Knowledge Based Vision contract AIADS S1093-S-1.

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Ponce, J., Chelberg, D. Finding the limbs and cusps of generalized cylinders. Int J Comput Vision 1, 195–210 (1988). https://doi.org/10.1007/BF00127820

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  • DOI: https://doi.org/10.1007/BF00127820

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