Sage Journals: Discover world-class research

Abstract

This paper presents an approach for identification and reconstruction of surfaces from unorganized three-dimensional data. The concepts of distance function and free differential motion are introduced to characterize the kinematic properties of some kinds of surfaces, including simple surfaces and kinematic surfaces generated by a generatrix undergoing a screw motion. Then, a method is proposed automatically to identify the type of the surface and roughly estimate the location of the screw axis as well as the profile of the generatrix from the discrete measurement points. Based on the differential property of the signed distance function, a least-squares surface fitting algorithm is developed to finely tune the location and shape parameters of the reconstructed surface. This algorithm is also applicable to the reconstruction of implicit surfaces such as quadratic surfaces. Examples are provided to investigate the efficiency and precision of the developed method.

Keywords

distance function kinematic surface screw motion surface identification surface reconstruction surface fitting

References

Hevert

Ponce

, ‘A new method for segmenting 3-D scenes into primitive’ Proceedings of Sixth International Conference on Pattern recognition, Munich, (1982), pp. 836–838.

Peternell

Pottmann

Steiner

, ‘Hough transform and Laguerre geometry for the recognition and reconstruction of special 3D shapes’ Technical report 100, Institute of Geometry, April 2003.

Flynn

P. J.

Jain

A. K.

, ‘Surface classification: Hypothesis testing and parameter estimation’ Proceedings of IEEE Conference on Computer vision and pattern recognition, (1988), pp. 261–267 (Ann Arbor).

Lai

J.-Y.

Ueng

W.-D.

, ‘Reconstruction of surfaces of revolution from measured points’ Computers in Ind. 41 (2000): 147–161.

Huang

J. B.

Meng

C. H.

, ‘Identification and characterization of regular surfaces from unorganized points by normal sensitivity analysis’ ASME J. Computing and Inf. Sci. Engng 2 (2002): 115–123.

Pottmann

Randrup

, ‘Rotational and helical surface reconstruction for reverse engineering’ Computing 60 (4) (1998): 307–322.

Pottmann

Peternell

Ravani

, ‘An introduction to line geometry with applications’ Computer Aided Des. 31 (1999): 3–16.

Pottmann

Hofer

Odehnal

Wallner

Pajdla

Matas

, ‘Line geometry for 3D shape understanding and reconstruction’ Computer vision | ECCV 2004, Part I, Lecture Notes in Computer Science (New york: Springer Verlag 2004): Pp. 297–309.

Pottmann

Wallner

, Computational line geometry (Berlin: Springer Verlag 2001).

10.

Lee

I.-K.

Wallner

Pottmann

, ‘Scattered data approximation with kinematic surfaces’ (1999).

11.

Liu

Pottmann

Wang

, ‘Constrained 3D shape reconstruction using a combination of surface fitting and registration’ Computer-Aided Des. 38 (2006): 572–583.

12.

Zhu

L. M.

Ding

, ‘A unified approach for least-squares surface fitting’ Sci. China (Ser. G) 47(S1) (2004): 72–78.

13.

Zhu

L. M.

, Distance function based models and algorithms for fitting of geometric elements to measured coordinate points. Postdoctoral technical report, School of Mechanical Science and Engineering, Huazhong University of Science and Technology, China, 2002.

14.

Zhu

L. M.

Xiong

Z. H.

Ding

Xiong

Y. L.

, ‘A distance function based approach for localization and profile error evaluation of complex surface’ Trans. ASME J. Mfg Sci. Engng 126 (2004): 484–501.

15.

Selig

J. M.

Rooney

, ‘Reuleaux pairs and surfaces that cannot be gripped’ Int. J. Robotics Res. 8 (5) (1989): 79–87.

16.

Pauly

Kobbelt

Gross

, Multiresolution modeling of point-sampled geometry. ETH Zurich Technical report, 2002.

17.

Ball

R. S.

, A treatise on the theory of screws (Cambridge University Press 1998).

18.

Murray

R. M.

Sastry

S. S.

, A mathematical introduction to robotic manipulation (Boca Raton: CRC Press 1994).

19.

Patrikalakis

M. N.

Maekawa

, Shape interrogation for computer aided design and manufacturing (Berlin, Heidelberg: Springer-Verlag 2002).

20.

Huang

J. B.

Meng

C. H.

, ‘Automatic data segmentation for geometric feature extraction from unorganized point cloud’ IEEE Trans. Robotics Automa. 17 (3) (2001): 268–279.

Identification and reconstruction of surfaces based on distance function

Abstract

Abstract

Keywords

References