Rotational and Helical Surface Approximation for Reverse Engineering

Computing (Vienna/New York)

Volumn 60, Issue 4, 1998, Pages 307-322

  Pottmann, H ^a   Randrup, T ^b  

^a VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

^b Odense Steel Shipyard Ltd   (Denmark)

Author keywords

Computer aided design; Computer aided manufacturing; Helical surface; Line geometry; Reverse engineering; Surface approximation; Surface of revolution

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTATIONAL GEOMETRY; COMPUTER AIDED DESIGN; COMPUTER AIDED MANUFACTURING; DATA REDUCTION;

ROTATIONAL/HELICAL SURFACE APPROXIMATION; SURFACE OF REVOLUTION;

REVERSE ENGINEERING;

EID: 0031645991     PISSN: 0010485X     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02684378     Document Type: Article

References (22)

1. Chen, H. Y., Pottmann, H.: Approximation by ruled surfaces. J. Comput. Appl. Math. (submitted).
2. Eckhardt, U., Maderlechner, G.: Thinning of binary images. Hamburger Beiträge zur Angewandten Mathematik, Reihe B, Bericht 11, 1989.
3. Eckhardt, U., Maderlechner, G.: Invariant thinning. Int. J. Pattern Rec. Art. Intell. 7, 1115-1144 (1993).
4. Eiber, G., Kim, M.-S.: Geometric shape recognition of freeform curves and surfaces. Grap. Models Image Proc. 60 (to appear).
5. Elsässer, G., Hoschek, J.: Approximation of digitized points by surfaces of revolution. Comput. Graphics 20, 85-94 (1996).
6. Gander, W., Golub, G.H., Strebel, R.: Least-squares fitting of circles and ellipses. BIT 34, 558-578 (1994).
7. Hoschek, J., Lasser, D.: Fundamentals of computer aided geometric design. Wellesley Massachusetts: A. K. Peters, 1993.
8. Klein, F.: Die allgemeine lineare Transformation der Linienkoordinaten. In: Gesammelte math. Abhandlungen I. Berlin: Springer, 1921.
9. Kraus, K.: Photogrammetrie, Vol. 2. Bonn: Dümmler, 1996.
10. Leonardis, A., Gupta, A., Bajcsy, R.: Segmentation of range images as the search for parametric geometric models. Int. J. Comput. Vision 14, 253-277 (1995).
11. Lukács, G., Marshall, A. D., Martin, R. R.: Geometric least-squares fitting of spheres, cylinders, cones and tori. Preprint, University of Wales, Cardiff, 1997.
12. Martin, R. R., Stroud, I. A., Marshall, A. D.: Data reduction for reverse engineering. In: Goodman, T. N. T. (ed.) Mathematics of Surfaces VII, pp. 85-100. Information Geometers, 1997.
13. Meer, P., Mintz, D., Rosenfeld, A., Kim, D. V.: Robust regression methods for computer vision: A review. Int. J. Comput. Vision 6, 59-70 (1991).
14. Müller, H. R.: Kinematik. Berlin: Walter de Gruyter, 1963.
15. Piegl, L., Tiller, W.: The NURBS book. Berlin Heidelberg New York Tokyo: Springer 1995.
16. Pottmann, H., Chen, H. Y., Lee, I. K.: Approximation by profile surfaces, Preprint, 1998.
17. Randrup, T.: Approximation by cylinder surfaces. Comput. Aided Des. (submitted).
18. Rousseeuw, P. J., Leroy, A. M.: Robust regression and outlier detection. New York: Wiley, 1987.
19. Rosenfeld, A.: Digital topology. Am. Math. Monthly 86, 621-630 (1979).
20. Sapidis, N. S., Besl, P. J.: Direct construction of polynomial surfaces from dense range images through region growing. ACM Trans. Graphics 14, 171-200 (1995).
21. Varady, T., Martin, R. R., Cox J.: Reverse engineering of geometric models - an introduction. Comput. Aided Des. 29, 255-268 (1997).
22. Wunderlich, W.: Zyklische Strahlkomplexe und geodätische Linien auf euklidischen und nichteuklidischen Dreh- und Schraubflächen. Math. Z. 55, 407-418 (1964).