Principles of interactive computer graphics (2nd ed.)
Principles of interactive computer graphics (2nd ed.)
Fundamentals of interactive computer graphics
Fundamentals of interactive computer graphics
Quadratic bounds for hidden line elimination
SCG '86 Proceedings of the second annual symposium on Computational geometry
One, two, three . . . infinity: lower bounds for parallel computation
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
Worst-case optimal hidden-surface removal
ACM Transactions on Graphics (TOG)
A Characterization of Ten Hidden-Surface Algorithms
ACM Computing Surveys (CSUR)
On the complexity of computing the measure of ∪[ai,bi]
Communications of the ACM
An algorithm for hidden line elimination
Communications of the ACM
Hidden surface removal using polygon area sorting
SIGGRAPH '77 Proceedings of the 4th annual conference on Computer graphics and interactive techniques
Introduction to VLSI Systems
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Bounds on the time for parallel RAM's to compute simple functions
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
The notion of quantitative invisibility and the machine rendering of solids
ACM '67 Proceedings of the 1967 22nd national conference
Parallel processing techniques for hidden surface removal
SIGGRAPH '79 Proceedings of the 6th annual conference on Computer graphics and interactive techniques
A linear time exact hidden surface algorithm
SIGGRAPH '80 Proceedings of the 7th annual conference on Computer graphics and interactive techniques
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Line/Polygon Classification: A Study of the Complexity of Geometric Computation
IEEE Computer Graphics and Applications
A Solution to the Hidden-Line Problem for Computer-Drawn Polyhedra
IEEE Transactions on Computers
Parallel computational geometry
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
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Parallel algorithms are given for the exact solution of the hidden-line problem. Most of the parallel algorithms proposed for visibility problems in the literature give approximate solutions. and thus cannot yield an upper bound on the complexity of the particular problem. The first algorithm proposed here is worth mentioning not only for its simplicity. but also from a practical point of view: a speed up of a factor P is achieved by using P processors. 1≤P≤N, where N is the number of edges used to describe a polygonal scene. Additionally. the problem of aliasing inherent with approximation methods is avoided. The significance of the second algorithm, which is based on the first one, is mainly on the theoretical level: it is used to establish the parallel complexity of the hidden-line problem. The sequential complexity of this problem has recently been proved to be Θ(N2), and now we can prove that in the parallel case the problem is in the complexity class NC, i.e., it can be solved in time polynomial in log N by using a number of processors polynomial in N, assuming any reasonable model of parallel computation. More particularly, an O (log N) parallel time solution is given which cannot be further improved even if arbitrarily many processors of a concurrent read, exclusive write parallel RAM model are available.