Arbitrary shape reconstruction from NC sectional data and applications in space cutter compensation and interference detection

This paper proposes an efficient shape reconstruction method from sectional data in 3-axis Numerical Control (NC) machining. A Merge-Divide algorithm is proposed to construct triangle meshes for machined surfaces with arbitrary shape and genus. The algorithm is of linear complexity due to the special property of the NC data. The method is used to interference detection and space cutter compensation in 3-axis NC machining. Experimental results verify that our method gives efficient and valid solutions to these important problems in NC machining.

[1]  Alan C. Lin,et al.  Probe-radius compensation for 3D data points in reverse engineering , 2002, Comput. Ind..

[2]  Guido Brunnett,et al.  Geometric Modeling for Scientific Visualization , 2010 .

[3]  Baining Guo,et al.  Surface reconstruction: from points to splines , 1997, Comput. Aided Des..

[4]  Mark Meyer,et al.  Discrete Differential-Geometry Operators for Triangulated 2-Manifolds , 2002, VisMath.

[5]  T. Roche,et al.  Industry , 1995 .

[6]  Tae-wan Kim,et al.  Moving parabolic approximation of point clouds , 2007, Comput. Aided Des..

[7]  Francis Schmitt,et al.  Intrinsic Surface Properties from Surface Triangulation , 1992, ECCV.

[8]  Averill M. Law,et al.  Simulation Modeling and Analysis , 1982 .

[9]  Kenneth R. Sloan,et al.  Surfaces from contours , 1992, TOGS.

[10]  Remco C. Veltkamp,et al.  Closed Object Boundaries from Scattered Points , 1994, Lecture Notes in Computer Science.

[11]  Matthias Eck,et al.  Automatic reconstruction of B-spline surfaces of arbitrary topological type , 1996, SIGGRAPH.

[12]  Joe Warren,et al.  Approximation of dense scattered data using algebraic surfaces , 1991, Proceedings of the Twenty-Fourth Annual Hawaii International Conference on System Sciences.

[13]  David P. Dobkin,et al.  Contour tracing by piecewise linear approximations , 1990, TOGS.

[14]  Marc Alexa,et al.  Computing and Rendering Point Set Surfaces , 2003, IEEE Trans. Vis. Comput. Graph..

[15]  Marie-Paule Cani,et al.  Automatic Reconstruction of Unstructured 3D Data: Combining a Medial Axis and Implicit Surfaces , 1995, Comput. Graph. Forum.

[16]  D. Levin,et al.  Mesh-Independent Surface Interpolation , 2004 .

[17]  T. A. Foley.  Interpolation of scattered data on a spherical domain , 1990 .

[18]  Hans-Christian Hege,et al.  Visualization and Mathematics III , 2011 .

[19]  Anil K. Jain,et al.  On reliable curvature estimation , 1989, CVPR.