Skip to main content

Interpolation regions for convex cubic curve segments

Abstract

Given a family of planar, convex, cubic curve segments with fixed end points and tangents, subregions of the plane are characterized in which additional points can be interpolated by at least one member of the family. The region for a second additional point is a remarkably thin double crescent.

This is a preview of subscription content, access via your institution.

References

  1. C. de Boor, K. Höllig and M. Sabin, High accuracy geometric Hermite interpolation, Comput. Aided Geom. Design 4 (1987) 269–278.

    Article  Google Scholar 

  2. C. Hoffmann and J. Peters, Geometric constraints for CAGD, in:Mathematical Methods in Computer-Aided Gemetric Design III, eds. M. Dahlen, T. Lyche and L. L. Schumaker (Vanderbilt Press, Nashville, 1995).

    Google Scholar 

  3. K. Höllig and J. Koch, Geometric Hermite interpolation with maximal order and smoothness, Preprint 95-9, Math. Inst. A, University of Stuttgart, Germany (1995).

    Google Scholar 

  4. M. A. Lachance and A. J. Schwartz, Four-point parabolic interpolation, Comput. Aided Geom. Design 9 (1991) 143–149.

    Article  Google Scholar 

  5. H. Pottmann and T. D. DeRose, Classification using normal curves, in:Curves and Surfaces in Computer Vision and Graphics II, SPIE Vol. 1610 (1991) pp. 217–228.

    Google Scholar 

  6. M. C. Stone and T. D. DeRose, A geometric characterization of cubic curves, ACM TOG 8(3) (1989) 143–163.

    Google Scholar 

  7. B. Su and D. Liu, An affine invariant theory and its application in computational geometry, Scientia Sinica A 26(3) (1983) 259–272.

    Google Scholar 

  8. C. Y. Wang, Shape classification of the parametric cubic curve and parametric B-spline cubic curve, Computer Aided Design 13(4) (1981) 199–206.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by L.L. Schumaker

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Peters, J. Interpolation regions for convex cubic curve segments. Adv Comput Math 6, 87–96 (1996). https://doi.org/10.1007/BF02127698

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02127698

Keywords

  • Additional Point
  • Curve Segment
  • Interpolation Region