Influence of data points density on geometrical accuracy of interpolation surface

  • 1 Faculty of Mechanical Engineering, Czech Technical University in Prague, Czech Republic


Interpolation is one of widely used methods reconstructing the shape of a freeform surface from data points obtained by measurement. The geometrical accuracy of the resulting reconstructed surface is expressed as a range of normal deviations of the surface from the original shape and depends mainly on the density of the input data points. In the paper, a method to determine the g eometrical accuracy of the interpolation surface fitted through a set of definition points arranged in a structured quadrilateral mesh with a given density is described. Practical application of this method is demonstrated on the processing of experimental data mathematically generated from a known CAD model of suitably chosen freeform surface



  1. A. Manor, A. Fischer, Reverse Engineering of 3D Models Based on Image Processing and 3D scanning Techniques, (342-356, 2001)
  2. Y. Liu, M. Yen, Optimized triangle mesh reconstruction from unstructured points. The visual Computer, 19:23-37, 03 (2003)
  3. G. Mansour, A developed algorithm for simulation of blades to reduce the measurement points and time on coordinate measuring machine. Measurement, 54:51-57 (2014)
  4. E. Savio, L. Chiffre, R. Smith, Metrology of freeform shaped parts. CIRP annals – Manufacturing technology, 56:810-835, 12 (2007)
  5. L. Beiser, Unified Optical Scanning Technology, (John Wiley & Sons, Ltd, 2003)
  6. V. Mehrad, D. Xue, P. Gu, Prediction of surface reconstruction uncerntainties for freeform surface inspection. Measurement, 46:2682-2694, 10 (2013)
  7. L. Piegl, W. Tiller, The NURBS Book, (Springer, 1997)
  8. P. Skalník, V. Zelený, I. Linkeová, Calibration of freeform standard. In Proceedings of the 15th international conference of the European society for precision engineering and technologies euspen, 147-148 (2015)
  9. V. Zelený, I. Linkeová, P. Skalník, Calibrated cad model of freeform standard. In XXI IMEKO World Congress Measurement in Research and Industry, 1423-1428 (2015)
  10. International vocabulary of metrology – Basic and general and associated terms (VIM, Standard, BIMP, 2012)
  11. S. Hyde, B. W. Ninham, S. Andersson, K. Larsson, T. Landh, Z. Blum, S. Lidin, Chapter I – the mathematics of curvature, The Language of Shape, (Elsevier Science B. V., 1997)
  12. K. Tapp, Differential Geometry of Curves and Surfaces, (Springer International Publishing, 2016)

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