Regularized set operations in solid modeling revisited

K. M. Yu, K. M. Lee, K. M. Au

Research output: Journal article publicationJournal articleAcademic researchpeer-review

1 Citation (Scopus)


The seminal works of Tilove and Requicha first introduced the use of general topology concepts in solid modeling. However, their works are brute-force approach from mathematicians’ perspective and are not easy to be comprehended by engineering trained personnels. This paper reviewed the point set topological approach using operational formulation and provided an alternate method to check the correctness of regularized set operations that was difficult to be formulated or ignored in various research work or literature study of geometric modeling. The results simply provide an alternate approach that easier to check the correctness for future research and development in geometric modeling. Essential topological concepts are described and visualized in easy to understand directed graphs. These facilitate subtle differentiation of key concepts to be recognized. In particular, some results are restated in a more mathematically correct version. Examples to use the prefix unary operators are demonstrated in solid modeling properties derivations and proofs as well as engineering applications.

Original languageEnglish
Pages (from-to)1084-1100
Number of pages17
JournalComputer-Aided Design and Applications
Issue number5
Publication statusPublished - 2020


  • Constructive Solid Geometry
  • General Topology
  • Manufacturing
  • Regularised Set Operations
  • Solid Modeling

ASJC Scopus subject areas

  • Computational Mechanics
  • Computer Graphics and Computer-Aided Design
  • Computational Mathematics


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