This paper describes a new algorithm for solving the hidden surface (or line) problem, to more rapidly generate realistic images of 3-D scenes composed of polygons, and presents the development of theoretical foundations in the area as well as additional related algorithms. As in many applications the environment to be displayed consists of polygons many of whose relative geometric relations are static, we attempt to capitalize on this by preprocessing the environment's database so as to decrease the run-time computations required to generate a scene. This preprocessing is based on generating a “binary space partitioning” tree whose in order traversal of visibility priority at run-time will produce a linear order, dependent upon the viewing position, on (parts of) the polygons, which can then be used to easily solve the hidden surface problem. In the application where the entire environment is static with only the viewing-position changing, as is common in simulation, the results presented will be sufficient to solve completely the hidden surface problem.

In many scientific and technical endeavors, a three-dimensional solid must be reconstructed from serial sections, either to aid in the comprehension of the object's structure or to facilitate its automatic manipulation and analysis. This paper presents a general solution to the problem of constructing a surface over a set of cross-sectional contours. This surface, to be composed of triangular tiles, is constructed by separately determining an optimal surface between each pair of consecutive contours. Determining such a surface is reduced to the problem of finding certain minimum cost cycles in a directed toroidal graph. A new fast algorithm for finding such cycles is utilized. Also developed is a closed-form expression, in terms of the number of contour points, for an upper bound on the number of operations required to execute the algorithm. An illustrated example which involves the construction of a minimum area surface describing a human head is included.

In many scientific and technical endeavors, a three-dimensional solid must be reconstructed from serial sections, either to aid in the comprehension of the object's structure or to facilitate its automatic manipulation and analysis. This paper presents a general solution to the problem of constructing a surface over a set of crosssectional contours. This surface, to be composed of triangular tiles, is constructed by separately determining an optimal surface between each pair of consecutive contours. Determining such a surface is reduced to the problem of finding certain minimum cost cycles in a directed toroidal graph.A new fast algorithm for finding such cycles is utilized. Also developed is a closed-form expression, in terms of the number of contour points, for an upper bound on the number of operations required to execute the algorithm.An illustrative example which involves the construction of a minimum area surface describing a human head is included.

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A parallel computing system becomes increasingly prone to failure as the number of processing elements in it increases. In this paper, we describe a completely general strategy that takes an arbitrary step of an ideal CRCW PRAM and automatically translates it to run efficiently and robustly on a PRAM in which processors are prone to failure. The strategy relies on efficient robust algorithms for solving a core problem, the Certified Write-All Problem. This problem characterizes the core of robustness, because, as we show, its complexity is equal to that of any general strategy for realizing robustness in the model. We analyze the expected parallel time and work of various algorithms for solving this problem. Our results are a non-trivial generalization of Brent's *Permission to copy without fee all or part of this material is granted provided that the copies are not made or distn'buted for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Association for Computing Machinery. To copy otherwise, or to republish, requires a fee and/or specific permission.Lemma. We consider the case where the number of the available processors decreases dynamically over time, whereas Brent's Lemma is only applicable in the case where the processor availability pattern is static.

We present a general and efficient strategy for computing mtustly on unreliable parallel machines. The model of a parallel machine that we use is a CRCW PRAM with dynamic resource fluctuations: processors can fail during the computation, and may possibly bc restored later.We first introduce the notions of dejinite and tentatitie algorithms for executing a single parallel step of an ideal parallel machine on the unreliable machine.A definite algorithm is one that guarantees a correct "