Advertisement

Geometrically Constrained Surface (Re)Construction

  • Gudrun Albrecht
  • Franca Caliò
  • Edie Miglio
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 809)

Abstract

We consider the reverse engineering problem to construct a \(G^1\) continuous interpolant to a triangulated set of 3D points and corresponding normals by fitting a composite surface consisting of rational triangular Bézier patches by using the so–called rational blend technique. The proposed method gives a solution depending on free shape parameters which are fixed by minimizing different functionals linked to suitable surface metrics. It is illustrated by significant application examples.

Keywords

Reverse engineering Fairing Rational Bézier patches 

References

  1. 1.
    Caliò, F., Miglio, E.: Constrained reconstruction of 3d curves and surfaces using integral spline operators. CAIM 74, 29–49 (2013)zbMATHGoogle Scholar
  2. 2.
    Mann, S., Loop, C., Lounsbery, Meyers, D., Painter, J., Derose, T., Sloan, K.: A survey of parametric scattered data fitting using triangular interpolants. In: Curve and Surface Design, pp. 145–172. SIAM (1992)CrossRefGoogle Scholar
  3. 3.
    Boschiroli, M., Fünfzig, C., Romani, L., Albrecht, G.: \(g^{1}\) rational blend interpolary schemes: a comparative study. Graph. Models 74, 29–49 (2012)CrossRefGoogle Scholar
  4. 4.
    Boschiroli, M.: Local parametric Bézier interpolants for triangular meshes: from polynomial to rational schemes. Ph.D. Thesis, University of Valenciennes, Valenciennes, Fr (2012)Google Scholar
  5. 5.
    Walton, D., Meek, D.: A triangular \(g^{1}\) patch from boundary curves. Comput. Aided Des. 28(2), 113–123 (1996)CrossRefGoogle Scholar
  6. 6.
    Walton, D., Yeung, M.: Geometric modelling from CT scans for stereolithography apparatus. In: New Advances in CAD & Computer Graphics, pp. 417–422 (1993)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Escuela de MatemáticasUniversidad Nacional de ColombiaMedellínColombia
  2. 2.Department of MathematicsPolitecnico di MilanoMilanItaly
  3. 3.MOX, Department of MathematicsPolitecnico di MilanoMilanItaly

Personalised recommendations