Four-dimensional geometric element definitions and interferences via five-dimensional homogeneous

Yukihito Sakai, Shuji Hashimoto

    Research output: Contribution to journalArticle

    5 Citations (Scopus)

    Abstract

    We have systematized various studies on 4-D visualization and interaction thus far, and we proposed 4-D geometric algorithms via 5-D homogeneous processing. Our framework uses 5 × 5 matrices and 5 × 5 determinants to express various types of transformations, and it simplifies geometric operations without the use of division operations. Using the proposed scheme, we developed an interactive 4-D space display system. The simplicity, generality, and duality of 5-D homogeneous processing are effective not only for 4-D geometric operations but also for interference problems among various 4-D objects. However, the processing regarding geometric characteristics of 4-D objects was not considered in our previous works. In this paper, we describe 4-D geometric elements, in general, and we discuss 4-D computational geometry via 5-D homogeneous processing. Unified geometric operations without the use of division operations constitute the most important part of 5-D homogeneous processing. We systematize the methods for 4-D geometric element definitions and interferences via 5-D homogeneous processing. In the field of 4-D visualization, the proposed algorithms can be potentially used in a user interface for feature detection of a 4-D object and collision detection of several 4-D objects. We comprehensively develop and advance the theoretical framework in the field of 4-D graphics. It is expected that this method of processing will be useful for the performance improvement of 4-D graphics systems.

    Original languageEnglish
    Pages (from-to)129-139
    Number of pages11
    JournalJournal of Visualization
    Volume14
    Issue number2
    DOIs
    Publication statusPublished - 2011

    Fingerprint

    interference
    Processing
    division
    computational geometry
    Visualization
    Computational geometry
    display devices
    determinants
    User interfaces
    Display devices
    collisions
    matrices
    interactions

    Keywords

    • 4-D Euclidean space
    • 4-D geometric element definitions
    • 4-D geometric element interferences
    • 5-D homogeneous processing

    ASJC Scopus subject areas

    • Condensed Matter Physics
    • Electrical and Electronic Engineering

    Cite this

    Four-dimensional geometric element definitions and interferences via five-dimensional homogeneous. / Sakai, Yukihito; Hashimoto, Shuji.

    In: Journal of Visualization, Vol. 14, No. 2, 2011, p. 129-139.

    Research output: Contribution to journalArticle

    Sakai, Yukihito ; Hashimoto, Shuji. / Four-dimensional geometric element definitions and interferences via five-dimensional homogeneous. In: Journal of Visualization. 2011 ; Vol. 14, No. 2. pp. 129-139.
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