Data structures and algorithms 3: multi-dimensional searching and computational geometry
Data structures and algorithms 3: multi-dimensional searching and computational geometry
Computational geometry: an introduction
Computational geometry: an introduction
Intersection of convex objects in two and three dimensions
Journal of the ACM (JACM)
Visibility and intersectin problems in plane geometry
SCG '85 Proceedings of the first annual symposium on Computational geometry
A Characterization of Ten Hidden-Surface Algorithms
ACM Computing Surveys (CSUR)
An optimal real-time algorithm for planar convex hulls
Communications of the ACM
A Two-Space Solution to the Hidden Line Problem for Plotting Functions of Two Variables
IEEE Transactions on Computers
ACM SIGACT News
Intersecting line segments in parallel with an output-sensitive number of processors
SPAA '89 Proceedings of the first annual ACM symposium on Parallel algorithms and architectures
Computation of the axial view of a set of isothetic parallelepipeds
ACM Transactions on Graphics (TOG)
Generalized sweep methods for parallel computational geometry
SPAA '90 Proceedings of the second annual ACM symposium on Parallel algorithms and architectures
Parallel object-space hidden surface removal
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Hidden surface removal with respect to a moving view point
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Efficient hidden surface removal for objects with small union size
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
A simple output-sensitive algorithm for hidden surface removal
ACM Transactions on Graphics (TOG)
Hardware antialiasing of lines and polygons
I3D '92 Proceedings of the 1992 symposium on Interactive 3D graphics
Generalized hidden surface removal
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
On lines missing polyhedral sets in 3-space
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Algorithms for visibility computation on digital terrain models
SAC '93 Proceedings of the 1993 ACM/SIGAPP symposium on Applied computing: states of the art and practice
Visibility with a moving point of view
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Finite-resolution hidden surface removal
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
An Improved Output-size Sensitive Parallel Algorithm for Hidden-Surface Removal for Terrains
IPPS '98 Proceedings of the 12th. International Parallel Processing Symposium on International Parallel Processing Symposium
Computing the visibility map of fat objects
Computational Geometry: Theory and Applications
An optimal hidden-surface algorithm and its parallelization
ICCSA'11 Proceedings of the 2011 international conference on Computational science and its applications - Volume Part III
An efficient output-sensitive hidden-surface removal algorithm for polyhedral terrains
Mathematical and Computer Modelling: An International Journal
Computing the visibility map of fat objects
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
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In this paper we present an algorithm for hidden surface removal for a class of polyhedral surfaces which have a property that they can be ordered relatively quickly like the terrain maps. A distinguishing feature of this algorithm is that its running time is sensitive to the actual size of the visible image rather than the total number of intersections in the image plane which can be much larger than the visible image. The time complexity of this algorithm is &Ogr;((k +n)lognloglogn) where n and k are respectively the input and the output sizes. Thus, in a significant number of situations this will be faster than the worst case optimal algorithms which have running time &OHgr;(n2) irrespective of the output size (where as the output size k is &Ogr;(n2) only in the worst case). We also present a parallel algorithm based on a similar approach which runs in time &Ogr;(log4(n+k)) using &Ogr;((n + k)/log(n+k)) processors in a CREW PRAM model. All our bounds are obtained using ammortized analysis.