An efficient output-sensitive hidden-surface removal algorithm for polyhedral terrains
TL;DR: An algorithm for hidden surface removal for a class of polyhedral surfaces which have a property that they can be ordered relatively quickly is presented, which will be faster than the worst case optimal algorithms which have running time of @W(n^2) irrespective of the output size.
About: This article is published in Mathematical and Computer Modelling.The article was published on 1995-03-01 and is currently open access. It has received 7 citations till now. The article focuses on the topics: Output-sensitive algorithm & Hidden surface determination.
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TL;DR: The P-buffer algorithm introduced in this paper is a method for rendering line-drawing images with dashed hidden-lines that can be used as a compromise approach that reveals the concealed information of hidden-surface-removed views for time-critical rendering.
7 citations
20 Jun 2011
TL;DR: A new optimal sequential algorithm is proposed, which is amenable to parallelization and might also have practical significance in its own right, for the problems called hidden-line and hidden-surface removal in computer graphics.
Abstract: Given a collection of non-intersecting simple polygons possibly with holes and with a total of n edges in three-dimensional space; parallel algorithms are given for the problems called hidden-line and hidden-surface removal in computer graphics. More precisely, algorithms are proposed to find the portions of the edges visible from (0, 0, ∞) and to find the upper envelope (i.e., the pointwise maximum) of the polygons. The proposed solution for the hidden-line problem is the parallelization of the optimal sequential algorithm given by Devai in 1986. As the optimal sequential algorithm for the hidden-surface problem given by McKenna in 1987 is rather involved, a new optimal sequential algorithm is proposed, which is amenable to parallelization and might also have practical significance in its own right. Both of the parallel hiddenline and hidden-surface algorithms take Θ(log n) time using n2/ log n CREW PRAM processors.
6 citations
Cites background from "An efficient output-sensitive hidde..."
...Since then spectacular progress has been reported in the computational-geometry literature [6,7,12,15,22,25,30,38,39,43,45] mainly about solutions which are output-size sensitive, i....
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..., when each edge of the input polygons is parallel to one of the coordinate axes [22,39] or the input is fat objects [6] or objects with small union size [30] or a terrain [12,43]....
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30 Mar 1998
TL;DR: An efficient parallel algorithm for hidden-surface removal for terrain maps on the CREW PRAM model with a work bound of O((n+k) \polylog ( n)) where n and k are the input and output sizes, respectively.
Abstract: We describe an efficient parallel algorithm for hidden-surface removal for terrain maps. The algorithm runs in O(log/sup 4/ n) steps on the CREW PRAM model with a work bound of O((n+k)polylog(n)) where n and k are the input and output sizes respectively. In order to achieve the work bound we use a number of techniques, among which our use of persistent data-structures is somewhat novel in the context of parallel algorithms. To the best of our knowledge this is the most efficient parallel algorithm for hidden-surface removal for an important class of 3-D scenes.
3 citations
30 Sep 2004
TL;DR: The goal of this work is to establish an algorithm to efficiently preprocess a hierarchical height field model that enables the real-time culling of occluded geometry while still allowing for classic terrain-rendering frameworks.
Abstract: Hierarchical Occlusion Culling for Arbitrarily-Meshed Height Fields. (May 2004) Paul Michael Edmondson, B.S., Texas A&M University Chair of Advisory Committee: Dr. John Keyser Many graphics applications today have need for high-speed 3-D visualization of height fields. Most of these applications deal with the display of digital terrain models characterized by a simple, but vast, non-overlapping mesh of triangles. A great deal of research has been done to find methods of optimizing such systems. The goal of this work is to establish an algorithm to efficiently preprocess a hierarchical height field model that enables the real-time culling of occluded geometry while still allowing for classic terrain-rendering frameworks. By exploiting the planarmonotone characteristics of height fields, it is possible to create a unique and efficient occlusion culling method that is optimized for terrain rendering and similar applications. Previous work has shown that culling is possible with certain regularly-gridded height field models, but not until now has a system been shown to work with all height fields, regardless of how their meshes are constructed. By freeing the system of meshing restrictions, it is possible to incorporate a number of broader height field algorithms with widely-used applications such as flight simulators, GIS systems, and computer games.
Cites background from "An efficient output-sensitive hidde..."
...With that crucial restriction taken into account, there is little that their viewshed model adds over and above the HSR systems that their paper references, like those of Reif and Sen [31] and Katz et al....
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...It has also been pointed out that a characteristic of height fields is that the upper boundary of their projection on the y z plane is monotone with respect to increasing x values [31]....
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...With that crucial restriction taken into account, there is little that their viewshed model adds over and above the HSR systems that their paper references, like those of Reif and Sen [31] and Katz et al. [25]....
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References
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Book•
01 Jan 1983TL;DR: The basis of this book is the material contained in the first six chapters of the earlier work, The Design and Analysis of Computer Algorithms, and has added material on algorithms for external storage and memory management.
Abstract: From the Publisher:
This book presents the data structures and algorithms that underpin much of today's computer programming. The basis of this book is the material contained in the first six chapters of our earlier work, The Design and Analysis of Computer Algorithms. We have expanded that coverage and have added material on algorithms for external storage and memory management. As a consequence, this book should be suitable as a text for a first course on data structures and algorithms. The only prerequisite we assume is familiarity with some high-level programming language such as Pascal.
2,690 citations
TL;DR: The paper shows that the order of sorting and the types of sorting used form differences among the existing hidden-surface algorithms.
Abstract: : The paper asserts that the hidden-surface problem is mainly one of sorting. The various surfaces of an object to be shown in hidden-surface or hidden-line form must be sorted to find out which ones are visible at various places on the screen. Surfaces may be sorted by lateral position in the picture (XY), by depth (Z), or by other criteria. The paper shows that the order of sorting and the types of sorting used form differences among the existing hidden-surface algorithms. (Modified author abstract)
793 citations
Book•
01 Jan 1996TL;DR: Object-oriented purists may view this book as one on object-based programming, using object-oriented analysis and design with implementation in Ada 95, and the approach transcends the specifics in any particular programming language.
Abstract: I m p 1 e m e n t a t i o n development process. In basic physics, there are two primitives, force and mass. Force acts on mass and mass is changed by the force. In software development, the analogy to mass is objects and the analogy to force is operations, or algorithms. The term "object-oriented" means various things to different groups of software developers. To some it may imply the use of a particular object-oriented programming language, like Smalltalk, Actor, or C++. To others it could mean the step before system implementation, or coding, in the software development process, an object-oriented approach to design. Object-oriented purists may view this book as one on object-based programming, using object-oriented analysis and design with implementation in Ada 95. In any case, whether we call it objectoriented or object-based, the approach transcends the specifics in any particular programming language. During the analysis phase, solution details are not important; the overriding concern is understanding the problem. An object-based approach to analysis
690 citations
TL;DR: A fully dynamic maintenance algorithm for convex hulls that can process insertions and deletions of single points in only O(log* n) steps per transaction, where n is the number of points currently in the set.
505 citations
03 Nov 1982
TL;DR: It is proved that it is possible, in O(N) time, to find two vertices a,b in P, such that the segment ab lies entirely inside the polygon P and partitions it into two polygons, each with a weight not exceeding 2C/3.
Abstract: Let P be a simple polygon with N vertices, each being assigned a weight ∈ {0,1}, and let C, the weight of P, be the added weight of all vertices. We prove that it is possible, in O(N) time, to find two vertices a,b in P, such that the segment ab lies entirely inside the polygon P and partitions it into two polygons, each with a weight not exceeding 2C/3. This computation assumes that all the vertices have been sorted along some axis, which can be done in O(Nlog N) time. We use this result to derive a number of efficient divide-and-conquer algorithms for: 1. Triangulating an N-gon in O(Nlog N) time. 2. Decomposing an N-gon into (few) convex pieces in O(Nlog N) time. 3. Given an O(Nlog N) preprocessing, computing the shortest distance between two arbitrary points inside an N-gon (i.e., the internal distance), in O(N) time. 4. Computing the longest internal path in an N-gon in O(N2) time. In all cases, the algorithms achieve significant improvements over previously known methods, either by displaying better performance or by gaining in simplicity. In particular, the best algorithms for Problems 2,3,4, known so far, performed respectively in O(N2), O(N2), and O(N4) time.
294 citations