Four-dimensional collision detection via five-dimensional homogeneous processing

Yuki Nakai, Takanobu Miwa, Hiroki Shigemune, Shuji Hashimoto, Hideyuki Sawada

Research output: Chapter in Book/Report/Conference proceedingConference contribution


For the visualization of a 4-D object, information in 4-D space is obtained by projecting a 4-D space onto a 3-D space. Previous researches mainly paid attention to the geometrical information of a single 4-D object in 4-D space. Our research aims to develop a visualization system for physical phenomena in 4-D space and to study the human spatial cognition of the 4-D space through the projected 3-D space. In this research, we focus on a collision of two 4-D objects in 4-D space and develop an algorithm for the collision detection between two 4-D objects to be displayed in 3-D space. In our developed algorithm, a 4-D object is defined as a mesh data of tetrahedrons, and a tetrahedron-based collision detection algorithm is performed by a combination of half-space tests with the use of 5-D homogeneous processing to enhance the calculation accuracy of the collision detection. The results of the collision detection between the 4-D objects are presented.

Original languageEnglish
Title of host publicationEleventh International Conference on Graphics and Image Processing, ICGIP 2019
EditorsZhigeng Pan, Xun Wang
ISBN (Electronic)9781510635234
Publication statusPublished - 2020
Event11th International Conference on Graphics and Image Processing, ICGIP 2019 - Hangzhou, China
Duration: 2019 Oct 122019 Oct 14

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
ISSN (Print)0277-786X
ISSN (Electronic)1996-756X


Conference11th International Conference on Graphics and Image Processing, ICGIP 2019


  • 4-D space
  • 4-D visualization
  • Collision detection
  • Information perception

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering


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