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  • 1
    Electronic Resource
    Electronic Resource
    Chemical dynamics of the reaction between chlorine atoms and deuterated cyclohexane (1992)
    s.l. : American Chemical Society
    Journal of the American Chemical Society 114 (1992), S. 58-63 
    Details
    ISSN: 1520-5126
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/ja00027a008
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  • 2
    Electronic Resource
    Electronic Resource
    Implicitly representing arrangements of lines or segments (1989)
    Springer
    Discrete & computational geometry 4 (1989), S. 433-466 
    Details
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Anarrangement ofn lines (or line segments) in the plane is the partition of the plane defined by these objects. Such an arrangement consists ofO(n 2) regions, calledfaces. In this paper we study the problem of calculating and storing arrangementsimplicitly, using subquadratic space and preprocessing, so that, given any query pointp, we can calculate efficiently the face containingp. First, we consider the case of lines and show that with Λ(n) space1 and Λ(n 3/2) preprocessing time, we can answer face queries in Λ(√n)+O(K) time, whereK is the output size. (The query time is achieved with high probability.) In the process, we solve three interesting subproblems: (1) given a set ofn points, find a straight-edge spanning tree of these points such that any line intersects only a few edges of the tree, (2) given a simple polygonal path Γ, form a data structure from which we can find the convex hull of any subpath of Γ quickly, and (3) given a set of points, organize them so that the convex hull of their subset lying above a query line can be found quickly. Second, using random sampling, we give a tradeoff between increasing space and decreasing query time. Third, we extend our structure to report faces in an arrangement of line segments in Λ(n 1/3)+O(K) time, givenΛ(n 4/3) space and Λ(n 5/3) preprocessing time. Lastly, we note that our techniques allow us to computem faces in an arrangement ofn lines in time Λ(m 2/3 n 2/3+n), which is nearly optimal.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02187742
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  • 3
    Electronic Resource
    Electronic Resource
    On arrangements of Jordan arcs with three intersections per pair (1989)
    Springer
    Discrete & computational geometry 4 (1989), S. 523-539 
    Details
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Motivated by a number of motion-planning questions, we investigate in this paper some general topological and combinatorial properties of the boundary of the union ofn regions bounded by Jordan curves in the plane. We show that, under some fairly weak conditions, a simply connected surface can be constructed that exactly covers this union and whose boundary has combinatorial complexity that is nearly linear, even though the covered region can have quadratic complexity. In the case where our regions are delimited by Jordan acrs in the upper halfplane starting and ending on thex-axis such that any pair of arcs intersect in at most three points, we prove that the total number of subarcs that appear on the boundary of the union is only Θ(nα(n)), whereα(n) is the extremely slowly growing functional inverse of Ackermann's function.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02187745
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  • 4
    Electronic Resource
    Electronic Resource
    Visibility of disjoint polygons (1986)
    Springer
    Algorithmica 1 (1986), S. 49-63 
    Details
    ISSN: 1432-0541
    Keywords: Computational geometry ; Computer graphics ; Robotics ; Visibility ; Hidden-line Elimination ; Visibility graph ; Shortest path
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Consider a collection of disjoint polygons in the plane containing a total ofn edges. We show how to build, inO(n 2) time and space, a data structure from which inO(n) time we can compute the visibility polygon of a given point with respect to the polygon collection. As an application of this structure, the visibility graph of the given polygons can be constructed inO(n 2) time and space. This implies that the shortest path that connects two points in the plane and avoids the polygons in our collection can be computed inO(n 2) time, improving earlierO(n 2 logn) results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01840436
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  • 5
    Electronic Resource
    Electronic Resource
    An efficient algorithm for finding the CSG representation of a simple polygon (1993)
    Springer
    Algorithmica 10 (1993), S. 1-23 
    Details
    ISSN: 1432-0541
    Keywords: Constructive solid geometry ; Computational geometry ; Boundary representation ; Monotone boolean formulae ; Incremental convex hull
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Modeling two-dimensional and three-dimensional objects is an important theme in computer graphics. Two main types of models are used in both cases: boundary representations, which represent the surface of an object explicitly but represent its interior only implicitly, and constructive solid geometry representations, which model a complex object, surface and interior together, as a boolean combination of simpler objects. Because neither representation is good for all applications, conversion between the two is often necessary. We consider the problem of converting boundary representations of polyhedral objects into constructive solid geometry (CSG) representations. The CSG representations for a polyhedronP are based on the half-spaces supporting the faces ofP. For certain kinds of polyhedra this problem is equivalent to the corresponding problem for simple polygons in the plane. We give a new proof that the interior of each simple polygon can be represented by a monotone boolean formula based on the half-planes supporting the sides of the polygon and using each such half-plane only once. Our main contribution is an efficient and practicalO(n logn) algorithm for doing this boundary-to-CSG conversion for a simple polygon ofn sides. We also prove that such nice formulae do not always exist for general polyhedra in three dimensions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01908629
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  • 6
    Electronic Resource
    Electronic Resource
    Computing the intersection-depth of polyhedra (1993)
    Springer
    Algorithmica 9 (1993), S. 518-533 
    Details
    ISSN: 1432-0541
    Keywords: Intersection ; Minkowski sum ; Plane sweep ; Ray shooting ; Polyhedral hierarchy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Given two intersecting polyhedraP, Q and a directiond, find the smallest translation ofQ alongd that renders the interiors ofP andQ disjoint. The same problem can also be posed without specifying the direction, in which case the minimum translation over all directions is sought. These are fundamental problems that arise in robotics and computer vision. We develop techniques for implicitly building and searching convolutions and apply them to derive efficient algorithms for these problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01190153
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  • 7
    Electronic Resource
    Electronic Resource
    An optimal visibility graph algorithm for triangulated simple polygons (1989)
    Springer
    Algorithmica 4 (1989), S. 141-155 
    Details
    ISSN: 1432-0541
    Keywords: Simple polygon ; Visibility graph ; Triangulation ; Shortest path ; Shortest-path map
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract LetP be a triangulated simple polygon withn sides. The visibility graph ofP has an edge between every pair of polygon vertices that can be connected by an open segment in the interior ofP. We describe an algorithm that finds the visibility graph ofP inO(m) time, wherem is the number of edges in the visibility graph. Becausem can be as small asO(n), the algorithm improves on the more general visibility algorithms of Asanoet al. [AAGHI] and Welzl [W], which take Θ(n 2) time, and on Suri'sO(m logn) visibility graph algorithm for simple polygons [S].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01553883
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  • 8
    Electronic Resource
    Electronic Resource
    Quantum state-resolved study of pure rotational excitation of CO2 by hot atoms (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 91 (1989), S. 4636-4642 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Rotationally inelastic scattering of carbon dioxide by translationally hot H, D, and Cl atoms was studied by time-resolved diode laser absorption. The high J rotational distribution falls off quite rapidly between J=60 and J=80. D atom collisions have roughly twice the excitation cross section versus H atom collisions, with the H*/D* ratio decreasing with increasing J. These results are consistent with a constraint on the total reagent orbital angular momentum available for rotational excitation. Transient Doppler profiles measured immediately after hot atom/CO2 collisions indicate that CO2 molecules excited to high J levels have a larger recoil velocity than molecules excited to lower J levels. This result is consistent with predictions based on a simple model which treats the CO2 potential as a hard shell ellipsoid.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.456753
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  • 9
    Electronic Resource
    Electronic Resource
    Rotationally and translationally resolved hot atom collisional excitation of the CO2 Fermi mixed bend/stretch vibrational levels by time-dependent diode laser spectroscopy (1990)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 93 (1990), S. 4922-4937 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: High resolution IR diode laser absorption spectroscopy is employed to monitor the nascent rotational population distributions and transient linewidths in the Fermi mixed symmetric stretch/overtone bend vibrational mode of CO2 (1000/0200) following collisions with translationally hot hydrogen and deuterium atoms, produced from the 193 nm excimer laser photolysis of H2S or D2S. The nascent 1000/0200 rotational distribution produced by H* atom collisional excitation peaks at J∼26 and is well fit by a 747 K Boltzmann distribution. The transient linewidths are 1.5–3 times the ambient, room temperature CO2 Doppler linewidths, are∼0.002 cm−1 larger for D* atom collisions than H* atom collisions, and increase with increasing rotational quantum number. The experimentally determined relative cross sections for H* atom collisional excitation of CO2 vibrational states are as follows: 0001 antisymmetric stretch: 1000 Fermi mixed upper level: 0200 Fermi mixed lower level: 0220 bend≈1.0 : 0.6 : 0.6 : 0.4. The absolute cross section for inelastic collisional scattering of CO2 by H* atoms into 1000 J=38 is (1.4±0.8)×10−2 A(ring)2, and the total excitation cross section for the 1000 vibrational state is 0.37±0.21 A(ring)2. A statistical model and a simple quantized Landau–Teller model are unable to explain qualitatively the observed data; however, a breathing ellipsoid model, coupled with an IOS quantum scaling relation, reproduces the major features in the experimental data for both the 1000/0200 and 0001 states. The differences in the experimental data for distinct vibrational motions can be attributed to hot atoms sampling different regions of the potential surface.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.458681
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  • 10
    Electronic Resource
    Electronic Resource
    Diode laser probing of the low frequency vibrational modes of baths of CO2 and N2O excited by relaxation of highly excited NO2 (1990)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 93 (1990), S. 8474-8481 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Quenching of highly excited vibrational states of NO2 in baths of CO2 and N2O has been investigated. Dilute NO2 mixtures were excited by a pulse from an excimer pumped dye laser operating at 495 nm. Various vibrational modes of the bath gases were probed with continuous wave IR diode lasers. Less than 20% of the energy initially placed in the NO2 by the dye laser is taken up by the vibrational degrees of freedom of the CO2 or N2O baths. For N2O, the three different vibrational modes (ν1=1285 cm−1, ν2=589 cm−1, ν3=2223 cm−1) take up almost equal amounts of energy from NO2, but the number of vibrational quanta produced in the bath is found to increase with decreasing vibrational frequency. Similar results are found for CO2 except that the ν1 and ν2 modes cannot be studied separately for this bath gas due to rapid ν1↔ν2 intermode equilibration.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.459286
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