## A Hardware-Assisted Visibility-Ordering Algorithm with Applications to Volume Rendering (2000)

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Venue: | In Data Visualization (2001 |

Citations: | 14 - 3 self |

### BibTeX

@INPROCEEDINGS{Krishnan00ahardware-assisted,

author = {Shankar Krishnan and Cláudio T. Silva and Bin Wei},

title = {A Hardware-Assisted Visibility-Ordering Algorithm with Applications to Volume Rendering},

booktitle = {In Data Visualization (2001},

year = {2000},

pages = {233--242}

}

### OpenURL

### Abstract

. We propose a hardware-assisted visibility ordering algorithm. From a given viewpoint, a (back-to-front) visibility ordering of a set of objects is a partial order on the objects such that if object obstructs object , then precedes in the ordering. Such orderings are useful because they are the building blocks of other rendering algorithms such as direct volume rendering of unstructured grids. The traditional way to compute the visibility order is to build a set of visibility relations (e.g., ), and then run a topological sort on the set of relations to actually get the partial ordering. Our technique instead works by assigning a layer number to each primitive, which directly determines the visibility ordering. Objects that have the same layer number are independent, and can be placed anywhere with respect to each other. We use a simple technique which exploits a combination of the z- and stencil buffers to compute the layer number of each primitive...

### Citations

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Citation Context ... Kedem, and Naylor [9] developed the Binary Space Partitioning tree (BSP-tree), which is a data structure that represents a hierarchical convex decomposition of a given space (in our case, ��� )=-= (see [8, 9, 16]). Each node � of a BSPtree � corresponds to a c-=-onvex polyhedral region, ������������� ; the root node corresponds to all of ��� . Each non-leaf node � also corresponds to a plane, ������� , which par... |

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Citation Context ...o [14], which is based on the Cube-4 architecture of Pfister and Kaufman [15]. Another approach is to leverage existing graphics hardware, such as the texture-mapping based technique of Cabral et al. =-=[1]-=-. Although different, these two techniques have something fundamentally in common: the volumetric data model used is the same, that is, each volumetric grid is basically a regularly spaced 3D matrix o... |

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Citation Context ...n z (depth) of the primitives, then for each primitive, it fine tunes the ordering by checking whether other primitives actually precede it in the ordering. Building on [21], Fuchs, Kedem, and Naylor =-=[9] devel-=-oped the Binary Space Partitioning tree (BSP-tree), which is a data structure that represents a hierarchical convex decomposition of a given space (in our case, ��� ) (see [8, 9, 16]). Each node... |

240 | Real-Time, Continuous Level of Detail Rendering of Height Fields
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Citation Context ...tentially render several million tetrahedra per second. In the domain of rendering of digital terrain models, the trends have been towards converting the data into some form of adaptive tessellations =-=[12]-=- instead of rendering a large collection of small triangles. Extending this notion to three dimensions, PT seems like the adaptive analog for volume rendering as opposed to approaches based on texture... |

231 |
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Citation Context ...applications, it would be prudent to try and solve this problem in hardware at some pre-specified resolution. As other researchers have found (see, for instance, Hoff et al. [10], Westermann and Ertl =-=[23, 22]-=-) exploiting the ever-faster graphics hardware available in workstations and PCs, can lead to simpler, and more efficient solutions to our rendering problems. Our work is motivated by this trend. 3 Ou... |

229 | A Polygonal Approximation to Direct Scalar Volume
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Citation Context ... spaced 3D matrix of voxels.s2 Krishnan, Silva, and Wei An alternative technique for exploring graphics hardware for volume rendering is the Projected Tetrahedra (PT) algorithm of Shirley and Tuchman =-=[17]-=-, which uses the traditional 3D polygon-rendering pipeline. This technique renders a volumetric grid by breaking the volumetric grid into a collection of tetrahedra. Then, each tetrahedra is rendered ... |

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Citation Context ...the computation of the full behind relation (which is worst-case quadratic in the number of objects being ordered). Work on visibility ordering in computer graphics was pioneered by Schumacker et al. =-=[21]-=-. An earlier (complete) solution to computing a visibility-order was given by Newell, Newell, and Sancha (NNS) [13] which is the basis for several recent techniques [20]. The NNS algorithm starts with... |

193 | Fast Computation of Generalized Voronoi Diagrams Using Graphics Hardware
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Citation Context ...utmost importance in most applications, it would be prudent to try and solve this problem in hardware at some pre-specified resolution. As other researchers have found (see, for instance, Hoff et al. =-=[10]-=-, Westermann and Ertl [23, 22]) exploiting the ever-faster graphics hardware available in workstations and PCs, can lead to simpler, and more efficient solutions to our rendering problems. Our work is... |

164 | The VolumePro real-time ray-casting system
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Citation Context ...es for exploring graphics hardware in volume rendering. One approach is to build new hardware, specialized for volume rendering. Quite possibly, the most visible example of this approach is VolumePro =-=[14]-=-, which is based on the Cube-4 architecture of Pfister and Kaufman [15]. Another approach is to leverage existing graphics hardware, such as the texture-mapping based technique of Cabral et al. [1]. A... |

88 | Cube-4: A scalable architecture for real-time volume rendering
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Citation Context ... to build new hardware, specialized for volume rendering. Quite possibly, the most visible example of this approach is VolumePro [14], which is based on the Cube-4 architecture of Pfister and Kaufman =-=[15]-=-. Another approach is to leverage existing graphics hardware, such as the texture-mapping based technique of Cabral et al. [1]. Although different, these two techniques have something fundamentally in... |

65 | Sorting and Hardware Assisted Rendering for Volume Visualization
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Citation Context ...me rendering as opposed to approaches based on texture mapping hardware. In this sense, PT is conceivably a superior approach, even though it is currently being used to render only unstructured grids =-=[20]. -=-In order to apply PT, one needs to compute a visibility-ordering of the cells. Williams’ Meshed Polyhedra Visibility Ordering (MPVO) algorithm [25] developed in the early 1990s provides a very fast ... |

53 | A High Accuracy Volume Renderer for Unstructured Data
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Citation Context ...gorithm compares to these techniques in Table 2. We also include two previous techniques for exact polyhedral cell sorting, the algorithm of Stein et al. [20], the multi-tiled sort of Williams et al. =-=[26] in -=-our comparison for completeness. We ran these experiments for three (irregular) datasets. The boundary of the meshes are shown in Figs. 7 (Phoenix, NASAselapsed time (sec) � 4 3 2� 1 Octane: witho... |

50 | Efficient conservative visibility culling using the prioritized-layered projection algorithm
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Citation Context ...is possible to use the histogramming facility available in the ARB imaging extension of OpenGL 1.2 to make the graphics hardware perform those computations (we refer the reader to Klosowski and Silva =-=[11]-=-, and Westermann et al [24] for details). Unfortunately, those pixel paths are not optimized, and are often slower than our current implementation. If future hardware optimizes that functionality, it ... |

47 |
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Citation Context ...derably faster than the VSbuffer. Quite possibly, this is due to the fact that for typical datasets, we require a much smaller number of buffer reads.sAnother related technique is presented by Mammen =-=[14]-=-, where he uses a multi-pass rendering technique with a “moving” depth buffer to render transparent objects. Building complicated data structures to solve the visibility-ordering problem is a fairly d... |

45 | Fast polyhedral cell sorting for interactive rendering of unstructured grids,” Computer Graphics Forum (Eurographics ’99) 18
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Citation Context ...lity-ordering of the boundary cells by first performing a sufficient set of ray shooting queries, then running a topological sort on the visibility relations found to infer the ordering. Comba et al. =-=[6] further improved these res-=-ults with BSP-XMPVO to ©������������ (where � is the size of a small subset of the boundary cells), and leading to an order of magnitude improvement in sorting times over XM... |

39 | An exact interactive time visibility ordering algorithm for polyhedral cell complexes
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- 1998
(Show Context)
Citation Context ...ng the intrinsic connectivity of the unstructured grids and works well for well-behaved meshes (acyclic and convex). MPVO has recently been extended for general acyclic meshes by Silva et al.’s XMPV=-=O [18], which lead to an ©����-=-���������� algorithm (where � is the total number of cells, and � is the number of cells in the boundary of the mesh). The work of Silva et al. relies on being able to compute a ... |

35 |
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Citation Context ... Kedem, and Naylor [9] developed the Binary Space Partitioning tree (BSP-tree), which is a data structure that represents a hierarchical convex decomposition of a given space (in our case, ��� )=-= (see [8, 9, 16]). Each node � of a BSPtree � corresponds to a c-=-onvex polyhedral region, ������������� ; the root node corresponds to all of ��� . Each non-leaf node � also corresponds to a plane, ������� , which par... |

33 | Visibility Sorting and Compositing without Splitting for Image Layer Decompositions - Snyder, Lengyel - 1998 |

28 |
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Citation Context ...ently being used to render only unstructured grids [20]. In order to apply PT, one needs to compute a visibility-ordering of the cells. Williams’ Meshed Polyhedra Visibility Ordering (MPVO) algorith=-=m [25]-=- developed in the early 1990s provides a very fast visibility-ordering algorithm suitable for use in real-time rendering of unstructured grids. MPVO, which runs in linear time, works by exploiting the... |

23 |
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Citation Context ... Work on visibility ordering in computer graphics was pioneered by Schumacker et al. [21]. An earlier (complete) solution to computing a visibility-order was given by Newell, Newell, and Sancha (NNS) =-=[13]-=- which is the basis for several recent techniques [20]. The NNS algorithm starts with a rough ordering in z (depth) of the primitives, then for each primitive, it fine tunes the ordering by checking w... |

23 |
Cellfast: Interactive Unstructured Volume Rendering
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Citation Context ...approach is that it is not specific to a regular volumetric grid. Another nice property is that it is quite efficient in terms of the number of triangles it needs to render per primitive. Wittenbrink =-=[27]-=- found experimentally that, on average, one needs 3.4 triangles per tetrahedron. On a fast graphics board, such as the recent Nvidia GeForce, one can potentially render several million tetrahedra per ... |

22 | The VSBUFFER: Visibility Ordering Unstructured Volume Primitives By Polygon Drawing
- Westermann, Ertl
- 1999
(Show Context)
Citation Context ...explore temporal coherency, and in fact is optimized for dynamic geometry. They also propose a technique for correct rendering in the presence of cycles. The VSbuffer technique of Westermann and Ertl =-=[22]-=- is related to our work. In their algorithm, they exploit the graphics hardware for performing depth-sorting of volumetric primitives by rendering the cells on a plane perpendicular to the scanline; t... |

19 | On the optimization of projective volume rendering
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Citation Context ...Since the ray shooting queries are relatively expensive both in time and memory, this can be inefficient. Another class of sorting techniques are based on power-sorting, see the work of Cignoni et al =-=[2, 4, 3]-=-. These techniques are quite fast, since they reduce the 3D sorting problem to a one dimensional sort, which can be done quite efficiently with quicksort. Unfortunately, these techniques make limiting... |

14 | Tetrahedra based volume visualization
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(Show Context)
Citation Context ...Since the ray shooting queries are relatively expensive both in time and memory, this can be inefficient. Another class of sorting techniques are based on power-sorting, see the work of Cignoni et al =-=[2, 4, 3]-=-. These techniques are quite fast, since they reduce the 3D sorting problem to a one dimensional sort, which can be done quite efficiently with quicksort. Unfortunately, these techniques make limiting... |

8 | Decoupling polygon rendering from geometry using rasterization hardware
- Westermann, Sommer, et al.
- 1999
(Show Context)
Citation Context ...ogramming facility available in the ARB imaging extension of OpenGL 1.2 to make the graphics hardware perform those computations (we refer the reader to Klosowski and Silva [11], and Westermann et al =-=[24]-=- for details). Unfortunately, those pixel paths are not optimized, and are often slower than our current implementation. If future hardware optimizes that functionality, it would be possible to furthe... |

4 | Floriani, “Power diagram depth sorting
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- 1998
(Show Context)
Citation Context ...Since the ray shooting queries are relatively expensive both in time and memory, this can be inefficient. Another class of sorting techniques are based on power-sorting, see the work of Cignoni et al =-=[2, 4, 3]-=-. These techniques are quite fast, since they reduce the 3D sorting problem to a one dimensional sort, which can be done quite efficiently with quicksort. Unfortunately, these techniques make limiting... |

4 |
Kinetic Vertical Decomposition Trees
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Citation Context ...or visibility-ordering. Building a BSP-tree is a computationally intensive process. Thus, handling dynamic geometry is a challenge. Using techniques from the field of “kinetic” data structures, Co=-=mba [5]-=- developed an efficient extension of BSPtrees for handling moving primitives. At this time, his technique requires apriori (actually analytical) knowledge of the motion of the geometry to efficiently ... |

4 |
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Citation Context ... , and the intersection point of � with � is before the intersection point with ��� along the ray. Theoretical results on exact visibility ordering are described by de Berg, Overmars, and Sc=-=hwarzkopf [7], who give an algorithm requiring worst-cas-=-e time ©�������� ����� � (for any fixed ����� ) for determining an order or reporting that none exists (because of a cycle in the “behind” relation). Althoug... |

1 |
Parallelizing and Implementing an Exact Topological Sort For The HIAC Volume Renderer
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Citation Context ... cells in a correct layer is probably enough to avoid generating any sorting error. We believe this is one of the reasons that the MPVONC heuristic proposed by Williams [26] is so effective. See Cook =-=[5]-=- for an alternative sorting technique also based on a discretization of XMPVO. 5 Conclusion and Future Work We have presented a hardware-assisted algorithm for visibility ordering. From a given viewpo... |