O. Nurmi. A fast line sweep algorithm for hidden line elimination. BIT, 25(3):466-472, 1985.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....[CEGS89, CEG 92] All calculations are made in object space; therefore the image precision can be arbitrary, i.e. independent of the resolution of the computer display. Object space algorithms based on this method include: octree [Hun78, RR78, JT80, Mea82a, Mea82b] visibility map [Sch81, Nur85, GO87, McK87, Ber90, PVY90, OS91, Goo92, dB93] and many others (for an extensive overview see the books [FvDFH90, dB93] Most of these object space algorithms [dB93] are complicated and difficult to implement. Instead of comparing objects directly with each other as described above, we can ....

O. Nurmi. A fast line-sweep algorithm for hidden line elimination. BIT, 25:466--472, 1985.

....to) those by Louttel [11] Fuchs et al. [8] Weiler and Atherton [18] Sechrest and Greenberg [15] and Franklin [1,2] Various analyses of the hidden surface problem from the viewpoint of computational complexity can be found in F.F. Yao [19] Schmitt [14] Ottmann and Widmayer [13] and Nurmi [12]. In this paper, we present an algorithm, at object space, for reconstructing the visible regions in a polyhedral scene, i.e. joining the visible edge segnmnts output from a hidden line program to find the visible regions. Such an algorithm is used by e.g. lranklin s hidden surface algorithm [2] ....

O. Nurmi, "A fast line-sweep algorithm for hidden line elimination," B/T 25 pp. 466-4,72 (1985).

....polygonal boundaries that are visible) These algorithms are worstcase optimal, because there are problem instances that have Theta(n 2 ) output size (e.g. see Figure 2a) Unfortunately, these algorithms always take Theta(n 2 ) time [8, 16] even if the size of the output is very small. In [19] Nurmi gives an algorithm for general hidden line elimination that runs in O( n I) log n) time, where I is the number of pairs of line segments whose projections on intersect (I is O(n 2 ) Schmitt [25] also achieves this bound. If I is o(n 2 = log n) then these algorithms clearly run ....

O. Nurmi, "A Fast Line-Sweep Algorithm For Hidden Line Elimination," BIT, Vol. 25, 1985, 466--472.

....Conference on Communication, Control, and Computing, Allerton, IL, 1987, 849 858. y Research supported by the National Science Foundation under Grants CCR 8810568 and CCR9003299. 1 1 Introduction The hidden line and hidden surface elimination problems are well known in computer graphics [9, 15, 16, 19, 22, 23, 28, 29, 30, 31]. In the hidden line elimination problem one is given a set of simple, non intersecting planar polygons in 3 dimensional space, and a projection plane , and wishes to determine which portions of the polygonal boundaries are visible when viewed in a direction normal to , assuming all the polygons ....

....elimination in these same bounds. Both of these algorithms are optimal in the worst case, because there are problem instances that have Omega Gamma n 2 ) output size [9, 19] However, these algorithms always take O(n 2 ) time, even if the size of the output is small (e.g. O(1) In [22] Nurmi gives an algorithm for hidden line elimination that runs in O( n k) log n) time and O( n k) log n) space, where k is the number of intersecting pairs of line segments in (k is at most O(n 2 ) Schmitt [28] is able to achieve this same bound using only O(n k) space. When the number of ....

O. Nurmi, "A Fast Line-Sweep Algorithm For Hidden Line Elimination," BIT, Vol. 25, 1985, 466--472. 24

....to design a fast output sensitive (we will often use output sensitive instead of output size sensitive) parallel algorithmfor terrains, which computes a description of the output in a device independent manner. 1.2. Sequential algorithms Several sequential algorithms exist for the problem. See [13, 5, 14, 22, 7, 8, 2, 11, 19, 18, 15, 4, 16]) For the class of polyhedral terrains, Reif and Sen [19] designed the first efficient algorithm whose running time is O##k n# log 2 n# where k is the output size. 1.3. Parallel algorithms Relatively little work has been done in the context of parallel algorithms for hidden surface ....

O. Nurmi. A fast line-sweep algorithm for hidden-line elimination. BIT, 25:466 -- 472, 1985.

....modified for the hidden line elimination case. There are algorithms for hidden line elimination in literature whose running time is sensitive to the number of intersections, k, of the projection of the segments) in the image plane, typically of the order of O( n k) log n) for example see Nurmi [14] and Schmitt [20] Very recently this was improved to O(n log n k t) by Goodrich [7] where t is number of intersecting polygons on the image plane. However, in practice, the size of a displayed image can be far less than the number of intersections in the image plane. By size, we mean the number ....

O. Nurmi. A fast line-sweep algorithm for hidden line elimination. BIT, 25:466 -- 472, 1985.

....in O(n 2 ) time, and hence, are worst case optimal. There are algorithms for hidden line elimination whose running times are sensitive to the number of intersections, I , of the projections of the segments) in the projection plane, typically of the order of O( n I) log n) for example see [Nur85, Sch81] This was improved to O(n log n I t) by Goodrich [Goo92] where t is the number of intersecting polygons in the image plane. The first known efficient output sensitive algorithms were designed for the restricted input class consisting of iso oriented rectangles in R 3 [GO85, Ber88, ....

O. Nurmi. A fast line-sweep algorithm for hidden-line elimination. BIT, 25:466 -- 472, 1985.

....a major part of the rendering process. Various hidden surface algorithms have been proposed in the computational geometry literature. Worst case optimal algorithms are presented in [Dev, McK] Algorithms sensitive to the number of intersections of the objects on the viewing plane are presented in [Goo, Nur, Sch]. More recently, algorithms have been output sensitive; that is, the running time of these algorithms depends on the input size and some feature of the output, typically the scene complexity, which is the number of visible line segments in the final rendered scene. Such algorithms are found in ....

O. Nurmi, "A Fast Line Sweep Algorithm for Hidden Line Elimination," BIT 25 (1985), 466--472.

....the algorithms will run more efficiently. Early object space methods have a running time of O(n 2 ) independent of the complexity of the resulting visibility map [9, 17] Other implementations run in time O( n I) log n) where I denotes the number of intersections between the projected edges [10, 12, 19, 27], which may also be insensitive to the output size (there are easy examples where I = Theta(n 2 ) but k is a constant) Another recent technique [18] uses a randomized incremental approach, leading to expected running time that is expressed as a weighted sum over the I intersection points; ....

O. Nurmi, A fast line-sweep algorithm for hidden line elimination, BIT 25 (1985), 466--472.

....are rounded to the next integer. From the examples we conclude that, indeed, the number of contour edges is small and the number of intersections of contour edges appears to be even more favorable. The latter is particularly interesting for object space methods based on the line sweep algorithm, [7, 18, 15]. As a specific application we describe the computation of the silhouette of a polyhedral object. This presentation is a preliminary report from a project called CEBaP(Contour Edge Based Polyhedron Visualization) A brief description of the project and its goals is given in Section 6. 2 Contour ....

....considering all projected edges was studied by Hamlin and Gear [7] They analyzed possible types of intersection between edges to reduce the number of depth comparisons during the sweep. S equin and Wensley [18] extended this work to a broader class of input geometries including segments. Nurmi [15] studied the slightly different problem of hidden line elimination. He described a data structure for the sweep line status that supports the depth comparisons efficiently such that the running time is the well known bound for a Bentley Ottmann line sweep, i.e. O(n k) log n) where n is the ....

Otto Nurmi. A fast line-sweep algorithm for hidden line elimination. BIT, 25:466--472, 1985.

.... of the union of the projections of the faces processed so far) When a new face is projected onto the viewplane, its edges are Algorithm Approach Input sortable [Ede89] Divide and conquer Triangles No [Kat91] Divide and conquer, front to back Polygons Yes [Pre92, Rei88] Front to back PTM Yes [Nur85, Sch81] Sweep line Polygons No [Goo92b] Sweep line Polygons Yes [deB93] Sweep line, ray shooting Polygons No [Ove92] Back to front, incremental Triangles Yes [Dob93] On line Triangles No [deB93] On line, ray shooting Polygons No Table 2: Major existing algorithms for region visibility computation. tested ....

....output size. Sweep line algorithms first project the whole scene onto the viewplane, and then traverse it by moving a vertical line from left to right. The time complexity is equal to O( n k) log n) where k is the number of intersection points between terrain edges projected onto the viewplane [Goo92b, Nur85, Sch81]. The algorithm by de Berg [deB93] computes the viewshed on a TIN in an output sensitive way, by combining a sweeping technique with the use of efficient data structure for answering ray shooting queries. On line incremental algorithms operate on a generic set of polygons or triangles, without ....

Nurmi, O., A fast line-sweep algorithm for hidden line elimination, BIT, 25, 1985, pp.466-472.

.... computer in O(n log n) time [7] and hidden surface and line elimination problems can be solved in O(n 2 ) worst case optimal time [19] Hidden line and surface elimination problems can also be solved in a manner dependent on k, where k is the number of intersections between projected edges [6, 24, 8, 26]. Besides objectspace algorithms as above, many image space algorithms for raster graphics are known [5] The visibility problem for disjoint edges in the plane has been solved in O(log n) time on a PRAM model using O(n) processors [1, 2] Hidden surface removal and its parallelization is studied ....

O. Nurmi. A fast line-sweep algorithm for hidden line elimination. BIT, 25:466--472, 1985.

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O. Nurmi. A fast line sweep algorithm for hidden line elimination. BIT, 25(3):466-472, 1985.

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Nurmi O 1985 A Fast Line-Sweep Algorithm for Hidden Line Elimination. BIT 25: 466-472.

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