Skip to main content
SpringerLink
Log in

A combinatorial algorithm to compute set operations on simple isothetic polygons

  • Published:
Multimedia Tools and Applications Aims and scope Submit manuscript

Abstract

A combinatorial algorithm is presented in this work to compute different set operations such as union, intersection, and difference on isothetic polygons. The algorithm constructs an interval tree and formulates a set of combinatorial rules to find the intersection points between two isothetic polygons and then perform the set operations respectively. The running time of the proposed algorithm is found to be \(\mathcal {O}(n\log {}n)\).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

Code Availability

Not applicable.

References

  1. Biswas A, Bhowmick P, Bhattacharya BB (2010) Construction of isothetic covers of a digital object: a combinatorial approach. J Vis Commun Image Represent 21:295–310

    Article  Google Scholar 

  2. Chazelle B (1992) An optimal algorithm for intersecting three-dimensional convex polyhedra. SIAM J Comput 21:671–696

    Article  MATH  Google Scholar 

  3. Chazelle B, Dobkin DP (1987) Intersection of convex objects in two and three dimensions. J ACM (JACM) 34:1–27

    Article  Google Scholar 

  4. Cyrus M, Beck J (1978) Generalized two-and three-dimensional clipping. J Comput Graph 3:23–28

    Article  Google Scholar 

  5. Dobkin DP, Kirkpatrick DG (1985) A linear algorithm for determining the separation of convex polyhedra. J Algor 6:381–392

    Article  MATH  Google Scholar 

  6. Dobkin DP, Souvaine DL (1991) Detecting the intersection of convex objects in the plane. Comput Aided Geom Des 8:181–199

    Article  MATH  Google Scholar 

  7. Muller DE, Preparata FP (1978) Finding the intersection of two convex polyhedra. Theor Comput Sci 7:217–236

    Article  MATH  Google Scholar 

  8. O’Rourke J, Chien CB, Olson T, Naddor D (1982) A new linear algorithm for intersecting convex polygons. Comput Graph Image Process 19:384–391

    Article  MATH  Google Scholar 

  9. Rivero M, Feito FR (2000) Boolean operations on general planar polygons. Comput Graph 24:881–896

    Article  Google Scholar 

  10. Shamos MI (1975) Geometric complexity. In: Proceedings of the seventh annual ACM symposium on theory of computing, pp 224–233

  11. Shamos MI, Hoey D (1976) Geometric intersection problems. In: 17th Annual symposium on foundations of computer science (sfcs 1976). IEEE, pp 208–215

Download references

Funding

Not applicable.

Author information

Authors and Affiliations

  1. Department of Computer Science and Technology, Indian Institute of Engineering Science and Technology, Shibpur, India

    Raina Paul, Md Abdul Aziz Al Aman & Apurba Sarkar

  2. Department of Information Technology, Indian Institute of Engineering Science and Technology, Shibpur, India

    Arindam Biswas

Authors
  1. Raina Paul
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Md Abdul Aziz Al Aman
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Apurba Sarkar
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Arindam Biswas
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

There is equal contribution from each author.

Corresponding author

Correspondence to Raina Paul.

Ethics declarations

Ethics approval and consent to participate

Not applicable.

Consent for Publication

We give the permission for publication if accepted.

Conflict of interest/Competing interests

We affirm that this manuscript is original, has not been published before. It is not currently being considered for publication elsewhere and has no potential conflict of interest to declare.

Additional information

Availability of data and materials

Data sharing not applicable to this article as no data sets were generated or analyzed during the current study.

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Paul, R., Aman, M.A.A.A., Sarkar, A. et al. A combinatorial algorithm to compute set operations on simple isothetic polygons. Multimed Tools Appl 82, 6647–6666 (2023). https://doi.org/10.1007/s11042-022-13579-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11042-022-13579-4

Keywords

Search

Navigation