Abstract
Visibility determination is one of the oldest problems in computer graphics. The visibility, in terms of back-to-front polygon visibility ordering, is determined by updating a priority list as the viewpoint moves. A new list-priority algorithm, utilizing a property of Voronoi diagrams, is proposed in this paper. The operation is in two phases. First, in a pre-processing phase the scene is divided into Voronoi cells. A sub-list associated with each cell contains references to those polygons that intersect with it. The polygons are assigned a fixed set of view-independent priority orders within the cluster. Last, an interactive phase sorts the clusters according to the depth value of each Voronoi site. The most time-consuming work is performed during the pre-processing phase that only has to be executed once for the scene. Since all the polygons in a cell are pre-computed to obtain the fixed priority order within the cluster, a relatively simple task is left in the interactive phase, which is only to sort the clusters repeatedly when the viewpoint is changed. This method contains performance benefits that make it better shaped than previous BSP based methods.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Agarwal, P.K., Murali, T.M., Vitter, J.S.: Practical techniques for constructing binary space partitions for orthogonal rectangles. In: Proceedings of Symposium on Computational Geometry, pp. 382–384 (1997)
Aurenhammer, F.: Voronoi diagrams: a survey of a fundamental geometric data structure. ACM Comput. Surv. 23(3), 346–405 (1991)
Catmull, E.: A hidden-surface algorithm with antialiasing. In: Proceedings of ACM SIGGRAPH’78, pp. 6–11 (1978)
Chen, H., Wang, W.: The feudal priority algorithm on hidden-surface removal. In: Proceedings of ACM SIGGRAPH’96, pp. 55–64 (1996)
Dur, A., Leimgruber, S.: A practical list-priority algorithm for 3D polygons. J. Graph. Tools 8, 25–36 (2003)
Fuchs, H., Abram, G.D., Grant, E.D.: Near real-time shaded display of rigid objects. Comput. Graph. 17(3), 65–72 (1983)
Fuchs, H., Kedem, Z.M., Naylor, B.F.: On visible surface generation by a priori tree structures. In: Proceedings of ACM SIGGRAPH’80, pp. 124–133 (1980)
James, A., Day, A.M.: The priority face determination tree for hidden surface removal. Comput. Graph. Forum 17, 55–71 (1998)
Morer, P., Garcia-Alonso, A.M., Flaquer, J.: Optimization of a priority list algorithm for 3D rendering of buildings. Comput. Graph. Forum 14, 217–227 (1995)
Nayor, B.F.: A priori based techniques for determining visibility priory for 3D scenes. Dissertation, University of Texas at Dallas (1981)
Newell, M.E., Newell, R.G., Sancha, T.L.: A solution to the hidden surface problem. In: Proceedings of the ACM National Conference, pp. 443–450 (1972)
Schumacker, R.A., Brand, B., Gilliland, M.G., Sharp, W.H.: Study for applying computer-generated images to visual simulation. Technical Report AFHRL-TR-69-14, Air Force Human Resources Lab, Brooks Air Force Base, TX (1969)
Sutherland, I.E., Sproull, R.F., Schumacker, R.A.: Sorting and the hidden-surface problem. In: Proceedings of the National Computer Conference, pp. 685–693 (1973)
Yao, F.F.: On the priority approach to hidden-surface algorithms. In: Proceedings of the 21st Annual IEEE Symposium on the Foundations of Computer Science, pp. 301–307 (1980)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Fukushige, S., Suzuki, H. Polygon visibility ordering via Voronoi diagrams. Visual Comput 23, 503–511 (2007). https://doi.org/10.1007/s00371-007-0121-z
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00371-007-0121-z