On the polynomial time computability of abstract ray-tracing problems

Shuji Isobe, Tetsuo Kuriyama, Masahiro Mambo, Hiroki Shizuya

    Research output: Contribution to journalArticlepeer-review


    The abstract ray-tracing problem asks, for a given scene consisting of a light source, a light receiver and finitely many obstacles in a space, and a given positive integer ε +~ 0, whether a ray going out from the light source could reach the light receiver with intensity at least ε. The problem is known to be PSPACE-hard, and it is very unlikely that there exists an efficient algorithm to solve the problem without adding any restriction. In this paper, we show that the problem can be solved in polynomial time under some weak practical restrictions.

    Original languageEnglish
    Pages (from-to)1209-1213
    Number of pages5
    JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
    Issue number5
    Publication statusPublished - 2005 Jan 1


    • Abstract ray-tracing problem (ARTP)
    • PSPACE-hard/complete
    • Ray-tracing problem
    • Scene

    ASJC Scopus subject areas

    • Signal Processing
    • Computer Graphics and Computer-Aided Design
    • Electrical and Electronic Engineering
    • Applied Mathematics


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