Abstract
Combining classical line geometry with techniques from numerical approximation, we develop algorithms for approximation in line space. In particular, linear complexes, linear congruences and reguli are fitted to given sets of lines or line segments. The results are applied to computationally robust detection of special robot configurations and to reconstruction of fundamental surface shapes from scattered points.
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References
Bottema, O. and Roth, B., (1990), Theoretical Kinematics, Dover Publ., New York.
Chazelle, B., Edelsbrunner, H., Guibas, L.J., Sharir, M. and Stolfi, J., (1996), Lines in space: combinatorics and algorithms, Algorithmica 15, 428–447.
Chen, H.Y. and Pottmann, H., (1997), Approximation by ruled surfaces, J. of Computational and Applied Math., submitted.
Ge, Q.J. and Ravani, B., (1994), On representation and interpolation of line segments for computer aided geometric design, ASME Design Automation Conf., vol. 96-1, 191–198.
Hlavaty, V., (1953), Differential Line Geometry, P. Nordhoff Ltd., Groningen.
Hoschek, J., (1971), Liniengeometrie, Bibliograph. Institut, Zürich.
Hoschek, J. and Lasser, D., (1993), Fundamentals of Computer Aided Geometric Design, A. K. Peters, WeUesley, MA.
Hunt, K.H., (1978), Kinematic geometry of mechanisms, Clarendon Press, Oxford.
Hunt, K.H., (1986), Special configurations of robot-arms via screw theory, Robotica 4, 171–179.
Husty, M., Karger, A., Sachs, H. and Steinhilper, W., (1997), Kinematik und Robotik, Springer.
Klein, F., (1921), Die allgemeine lineare Transformation der Linienkoordinaten, in: Gesammelte math. Abhandlungen I, Berlin, Springer.
Leonardis, A., Gupta, A. and Bajcsy, R. (1995), Segmentation of range images as the search for parametric geometric models, Intl. Journal of Computer Vision 14, 253–277s.
Lukács, G., Marshall, A.D. and Martin, R.R., (1997), Geometric least-squares fitting of spheres, cylinders, cones and tori, Preprint, University of Wales, Cardiff.
Martin, R.R., Stroud, I.A., Marshall, A.D., (1997), Data reduction for reverse engineering, in: The Mathematics of Surfaces VII, eds. T.N.T. Goodman, Information Geometers.
Merlet, J.-P., (1992), Singular Configurations of Parallel Manipulators and Grassmann Geometry, Int. Journal of Robotics Research, vol. 8, no. 5, 45–56.
Pottmann, H. and Randrup, T., (1997), Rotational and helical surface reconstruction for reverse engineering, Computing, submitted.
Randrup, T., (1997), Approximation by cylinder surfaces, Computer Aided Design, submitted.
Ravani, B. and Wang, J.W., (1991), Computer aided design of line constructs, ASME J. Mechanical Design 113, 363–371.
Sapidis, N.S. and Besl, P.J., (1995), Direct construction of polynomial surfaces from dense range images through region growing, ACM Trans. on Graphics 14, 171–200.
Varady, T., Martin, R. R. and Cox, J., (1997), Reverse engineering of geometric models — an introduction, Computer Aided Design 29, 255–268.
Wunderlich, W., (1964), Zyklische Strahlkomplexe und geodätische Linien auf euklidischen und nichteuklidischen Dreh-und Schraubflächen. Math. Zeitschr. 85, 407–418.
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Pottmann, H., Peternell, M., Ravani, B. (1998). Approximation in Line Space — Applications in Robot Kinematics and Surface Reconstruction. In: Lenarčič, J., Husty, M.L. (eds) Advances in Robot Kinematics: Analysis and Control. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9064-8_41
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DOI: https://doi.org/10.1007/978-94-015-9064-8_41
Publisher Name: Springer, Dordrecht
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