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A combinatorial algorithm is presented here which partitions a given orthogonal polyhedron, P, (genus zero and non-self-intersecting) into approximately minimum number of cuboids in \(O(n \log n)\) time where n is the number of vertices of P. The proposed cuboidization algorithm may start from any rectangular face. The combinatorial rules are formed to determine a cuboid from a given rectangular face. The generated cuboid is removed from the polyhedron, the new faces are created thereof are inserted in a queue. The next rectangular faces of traversal is selected from the queue. If cuboid extraction disconnects the input polyhedron, all the disconnected parts will be tracked through the queue as it stores newly generated faces. The cuboidization algorithm has various applications in 3D modelling and 3D shape analysis.

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Approximate Cuboidization of an Orthogonal Polyhedron: A Combinatorial Approach

  • 会议论文

  • 发表日期：

    2025年

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  • Anukul Maity,
  • Mousumi Dutt,
  • Arindam Biswas,
  • Bhargab B. Bhattacharya

摘要

A combinatorial algorithm is presented here which partitions a given orthogonal polyhedron, P, (genus zero and non-self-intersecting) into approximately minimum number of cuboids in \(O(n \log n)\) time where n is the number of vertices of P. The proposed cuboidization algorithm may start from any rectangular face. The combinatorial rules are formed to determine a cuboid from a given rectangular face. The generated cuboid is removed from the polyhedron, the new faces are created thereof are inserted in a queue. The next rectangular faces of traversal is selected from the queue. If cuboid extraction disconnects the input polyhedron, all the disconnected parts will be tracked through the queue as it stores newly generated faces. The cuboidization algorithm has various applications in 3D modelling and 3D shape analysis.