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On the Construction of Planar Embedding for a Class of Orthogonal Polyhedra

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Combinatorial Image Analysis (IWCIA 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13348))

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Abstract

2D-representations of 3D digital objects find versatile applications to computer vision, robotics, medical imaging, and in discrete geometry. This work presents an algorithm for constructing a planar embedding with only straight-line edges for a general non-intersecting orthogonal polyhedron that has genus 0. We discover certain characterizations of vertices and edges of a polyhedron that lead to efficient graph-drawing on the 2D plane. The original orthogonal polyhedron can be fully reconstructed from this graph provided the information regarding the coordinates of vertices, are preserved. The time complexity of the proposed embedding is linear in the number of edges of the orthogonal polyhedron.

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Author information

Authors and Affiliations

  1. Department of Information Technology, St. Thomas’ College of Engineering and Technology, Kolkata, India

    Nilanjana Karmakar

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

    Arindam Biswas

  3. Advanced Computing and Microelectronics Unit, Indian Statistical Institute, Kolkata, India

    Subhas C. Nandy

  4. Department of Computer Science and Engineering, Indian Institute of Technology Kharagpur, Kharagpur, India

    Bhargab B. Bhattacharya

Authors
  1. Nilanjana Karmakar
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  2. Arindam Biswas
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  3. Subhas C. Nandy
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  4. Bhargab B. Bhattacharya
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Corresponding author

Correspondence to Arindam Biswas .

Editor information

Editors and Affiliations

  1. State University of New York at Fredonia, Fredonia, NY, USA

    Reneta P. Barneva

  2. SUNY Buffalo State College, Buffalo, NY, USA

    Valentin E. Brimkov

  3. University of Messina, Messina, Italy

    Giorgio Nordo

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Karmakar, N., Biswas, A., Nandy, S.C., Bhattacharya, B.B. (2023). On the Construction of Planar Embedding for a Class of Orthogonal Polyhedra. In: Barneva, R.P., Brimkov, V.E., Nordo, G. (eds) Combinatorial Image Analysis. IWCIA 2022. Lecture Notes in Computer Science, vol 13348. Springer, Cham. https://doi.org/10.1007/978-3-031-23612-9_6

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  • DOI: https://doi.org/10.1007/978-3-031-23612-9_6

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  • Print ISBN: 978-3-031-23611-2

  • Online ISBN: 978-3-031-23612-9

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