Design of developable surfaces using optimal control

Journal of Mechanical Design

Volumn 124, Issue 4, 2002, Pages 602-608

  Park, F C ^a   Yu, Junghyun ^a   Chun, Changmook ^a   Ravani, Bahram ^b  

^a Seoul National University   (South Korea)

^b University of California   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; BOUNDARY CONDITIONS; DESIGN; DIFFERENTIATION (CALCULUS); FUNCTIONS; INTEGRATION; MATRIX ALGEBRA; OPTIMAL CONTROL SYSTEMS; REGRESSION ANALYSIS; THEOREM PROVING;

BASE CURVE; DEVELOPABLE SURFACE DESIGN; OBJECTIVE FUNCTIONS;

SURFACES;

EID: 0036936809     PISSN: 10500472     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.1515795     Document Type: Article

References (22)

1. do Carmo, M. P., 1976, Differential Geometry of Curves and Surfaces. Prentice-Hall, Englewood Cliffs, New Jersey.
2. Bodduluri, R. M. C., and Ravani, B., 1992, "Geometric Design and Fabrication of Bézier Developable Surfaces," Proc. ASME Design Automation Conf., 2, pp. 243-250.
3. Bodduluri, R. M. C., and Ravani, B., 1993, "Design of Developable Surfaces Using Duality between Plane and Point Geometries," Comput.-Aided Des., 25(10), pp. 621-632.
4. Lang, J., and Roschel, O., 1992, "Developable (1,n) Bezier Surfaces," Comput.-Aided Geom. Des., 9, pp. 291-298.
5. Hoschek, J., and Pottmann, H., 1995, "Interpolation and Approximation with Developable B-Spline Surfaces," Mathematical Methods in CAGD III, M. Daehlen, T. Lyche, and L. Schumaker, eds., Vanderbilt Univ. Press.
6. Pottmann, H., and Farin, G., 1995, "Developable Rational Bézier and B-Spline Surfaces," Computer-Aided Geometric Design, 12, pp. 513-531.
7. Aumann, G., 1991, "Interpolation with Developable Bézier Patches," Comput.-Aided Geom. Des., 23, pp. 409-420.
8. Ravani, B., and Ku, T. S., 1991, "Bertrand Offsets of Ruled and Developable Surfaces," Comput.-Aided Des., 23(2), pp. 145-152.
9. Redont, P., 1989, "Representation and Deformation of Developable Surfaces," Comput.-Aided Des., 21(1), pp. 13-20.
10. Maekawa, T., and Chalfant, J., 1998, "Design and Tessellation of B-Spline Developable Surfaces," ASME J. Mech. Des., 120(3), pp. 453-461.
11. Azariadis, P., and Aspragathos, N., 1997, "Design of Plane Developments of Doubly Curved Surfaces," Comput.-Aided Des., 29(10), pp. 675-685.
12. Elber, G., 1995, "Model Fabrication Using Surface Layout Projection," Comput.-Aided Des., 27(4), pp. 283-291.
13. Hoschek, J., and Schneider, M., 1997, "Interpolation and Approximation with Developable Surfaces," Curves and Surfaces with Applications in CAGD, A. LeMehaute, C. Rabut, L. L. Schumaker, eds., Vanderbilt Univ. Press, Nashville, pp. 185-202.
14. Chen, H.-Y., et al., 1999, "On Surface Approximation Using Developable Surfaces," Graph. Models Image Process., 61(3), pp. 110-124.
15. Pottman, H., and Wallner, M., 1999, "Approximation Algorithms for Developable Surfaces," Computer-Aided Geometric Design, 16(6), pp. 539-556.
16. Hoschek, J., and Seeman, G., 1992, "Spherical Splines," Math. Modell. Numer. Anal., 26(1), pp. 1-22.
17. Chirikjian, G. S., and Burdick, J. W., 1995, "Kinematically Optimal Hyper-Redundant Manipulator Configurations," IEEE Trans. Rob. Autom., 11(6), pp. 794-806.
18. Unger, D. J., 1991, "Developable Surfaces in Elastoplastic Fracture Mechanics," Int. J. Fract., 50(3), pp. 33-38.
19. Lu, H. Q., Todhunter, J. S., and Sze, T. W., 1993, "Congruence Conditions for Nonplanar Developable Surfaces and Their Application to Surface Recognition," CVGIP: Image Understand., 56(3), pp. 265-285.
20. Brockett, R., 1970, Finite Dimensional Linear Systems, John Wiley, New York.
21. Sternberg, S., 1964, Lectures on Differential Geometry, Prentice-Hall, Englewood Cliffs, New Jersey.
22. Kokotovic, P., and Khalil, K. H., 1986, Singular Perturbation Methods in Control: Analysis and Design, Academic Press, London.