SOME NEW RESULTS ON MOVING POLYGONS IN THE PLANE.

Godfried Toussaint, Jorg R. Sack

    Research output: Contribution to conferencePaper

    Abstract

    Let P equals (p//1,p//2,. . . , p//n) and Q equals (q//1,q//2,. . . ,q//m) be two non-intersecting polygons in the plane specified by their cartesian coordinates in order. Given a direction d we can ask whether P can be translated an arbitrary distance in direction d without colliding with Q. An algorithm is presented for answering the above translation query in O(n plus m) time. It is also shown that all the directions of movability (translation) of P with respect to Q can be computed in O(nm) time. For the more general case of a set of M non-intersecting n-gons P equals (P//1,P//2,. . . ,P//M) we say that it exhibits the translation ordering property if for all fixed directions there exists an ordering for translating the polygons by a single common vector without any collisions occurring with those polygons not yet moved. It is shown that for a given collection P, the translation ordering property query can be answered in O(Mn plus M**2log n) time.

    Original languageEnglish (US)
    Pages158-163
    Number of pages6
    StatePublished - Dec 1 1983

    ASJC Scopus subject areas

    • Engineering(all)

    Cite this

    Toussaint, G., & Sack, J. R. (1983). SOME NEW RESULTS ON MOVING POLYGONS IN THE PLANE.. 158-163.

    SOME NEW RESULTS ON MOVING POLYGONS IN THE PLANE. / Toussaint, Godfried; Sack, Jorg R.

    1983. 158-163.

    Research output: Contribution to conferencePaper

    Toussaint, G & Sack, JR 1983, 'SOME NEW RESULTS ON MOVING POLYGONS IN THE PLANE.' pp. 158-163.
    Toussaint, Godfried ; Sack, Jorg R. / SOME NEW RESULTS ON MOVING POLYGONS IN THE PLANE. 6 p.
    @conference{b11443c695b84b979aeeb1342d2cb54a,
    title = "SOME NEW RESULTS ON MOVING POLYGONS IN THE PLANE.",
    abstract = "Let P equals (p//1,p//2,. . . , p//n) and Q equals (q//1,q//2,. . . ,q//m) be two non-intersecting polygons in the plane specified by their cartesian coordinates in order. Given a direction d we can ask whether P can be translated an arbitrary distance in direction d without colliding with Q. An algorithm is presented for answering the above translation query in O(n plus m) time. It is also shown that all the directions of movability (translation) of P with respect to Q can be computed in O(nm) time. For the more general case of a set of M non-intersecting n-gons P equals (P//1,P//2,. . . ,P//M) we say that it exhibits the translation ordering property if for all fixed directions there exists an ordering for translating the polygons by a single common vector without any collisions occurring with those polygons not yet moved. It is shown that for a given collection P, the translation ordering property query can be answered in O(Mn plus M**2log n) time.",
    author = "Godfried Toussaint and Sack, {Jorg R.}",
    year = "1983",
    month = "12",
    day = "1",
    language = "English (US)",
    pages = "158--163",

    }

    TY - CONF

    T1 - SOME NEW RESULTS ON MOVING POLYGONS IN THE PLANE.

    AU - Toussaint, Godfried

    AU - Sack, Jorg R.

    PY - 1983/12/1

    Y1 - 1983/12/1

    N2 - Let P equals (p//1,p//2,. . . , p//n) and Q equals (q//1,q//2,. . . ,q//m) be two non-intersecting polygons in the plane specified by their cartesian coordinates in order. Given a direction d we can ask whether P can be translated an arbitrary distance in direction d without colliding with Q. An algorithm is presented for answering the above translation query in O(n plus m) time. It is also shown that all the directions of movability (translation) of P with respect to Q can be computed in O(nm) time. For the more general case of a set of M non-intersecting n-gons P equals (P//1,P//2,. . . ,P//M) we say that it exhibits the translation ordering property if for all fixed directions there exists an ordering for translating the polygons by a single common vector without any collisions occurring with those polygons not yet moved. It is shown that for a given collection P, the translation ordering property query can be answered in O(Mn plus M**2log n) time.

    AB - Let P equals (p//1,p//2,. . . , p//n) and Q equals (q//1,q//2,. . . ,q//m) be two non-intersecting polygons in the plane specified by their cartesian coordinates in order. Given a direction d we can ask whether P can be translated an arbitrary distance in direction d without colliding with Q. An algorithm is presented for answering the above translation query in O(n plus m) time. It is also shown that all the directions of movability (translation) of P with respect to Q can be computed in O(nm) time. For the more general case of a set of M non-intersecting n-gons P equals (P//1,P//2,. . . ,P//M) we say that it exhibits the translation ordering property if for all fixed directions there exists an ordering for translating the polygons by a single common vector without any collisions occurring with those polygons not yet moved. It is shown that for a given collection P, the translation ordering property query can be answered in O(Mn plus M**2log n) time.

    UR - http://www.scopus.com/inward/record.url?scp=0020861207&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=0020861207&partnerID=8YFLogxK

    M3 - Paper

    SP - 158

    EP - 163

    ER -