Accelerated Occlusion Culling using ShadowFrusta y T. Hudson D. Mano cha J. Cohen M. Lin K. Ho H. Zhang Department of Computer Science University of North Carolina Chap el Hill, NC 27599-3175 fhudson,mano cha,cohenj,lin,ho ,[email protected] and mo del simpli cation to render such large mo dels. In this Abstract: pap er, we address visibility culling. Many applications in computer graphics and virtual environ- Given a large mo del and a viewp oint, the goal of visibility ments need to render datasets with large numb ers of primitives culling and hidden surface removal algorithms is to determine and high depth complexityatinteractive rates. However, stan- the set of primitives visible from that viewp oint. No general pur- dard techniques like view frustum culling and a hardware z-bu er p ose, interactive algorithms are known for exact visibility deter- are unable to display datasets comp osed of hundred of thousands mination on large mo dels comp osed of hundred of thousands of of p olygons at interactive frame rates on current high-end graph- p olygons. Current graphics hardware provides supp ort for visi- ics systems. We add a \conservative" visibility culling stage to the bility computations on a p er-pixel basis with a z-bu er. However, rendering pip eline, attempting to identify and avoid pro cessing of high-end systems are only able to render a few tens of thousands o ccluded p olygons. Given a moving viewp oint, the algorithm dy- of p olygons at reasonable frame rates, due to b ottlenecks in their namically cho oses a set of occluders. Each o ccluder is used to hardware b efore the p er-pixel analyses can b e carried out. As compute a shadow frustum, and all primitives contained within a result, many applications use the following high-level software this frustum are culled. The algorithm hierarchically traverses the techniques to cull away a subset of the p olygons which are not mo del, culling out parts not visible from the current viewp oint visible from the current viewp oint b efore they are needlessly sent using ecient, robust, and in some cases sp ecialized interference to the rendering hardware: detection algorithms. The algorithm's p erformance varies with the lo cation of the viewp oint and the depth complexity of the View-Frustum Culling: View-frustum culling uses a traver- mo del. In the worst case it is linear in the input size with a small sal of spatial data structures to cull out p ortions of the constant. In this pap er, we demonstrate its p erformance on a mo del not lying in the current view frustum. The viewing city mo del comp osed of 500; 000 p olygons and p ossessing varying volume is represented as a frustum of six planes near plane, depth complexity.We are able to cull an average of 55 of the far plane, and four sides. At runtime the display algorithm p olygons that would not b e culled by view-frustum culling and checks whether each no de of the spatial structure overlaps obtain a commensurate improvement in frame rate. The overall this frustum; only no des partially or completely contained approachis e ective and scalable, is applicable to all p olygonal within the frustum are rendered. mo dels, and can b e easily implemented on top of view-frustum culling. Occlusion Culling: Hidden-surface removal algorithms and o cclusion culling techniques are commonly used for mo dels with high depth complexity to further reject the 1 Intro duction p ortion of geometry obscured by other ob jects in the scene. Some of the existing techniques are based on backface culling, Interactive display of extremely large and complex geometric data binary space partition trees, or partitioning the mo dels into sets has long b een an imp ortant problem in computer graphics. cells and p ortals. Although throughput of graphics systems has improved consid- erably over the years, the size and complexity of mo dels has Desiderata: In designing algorithms for o cclusion culling, we grown even faster. In manywalkthrough and virtual environment recognize the imp ortance of generality and robustness.We make applications, mo dels commonly consist of millions of primitives. no assumptions ab out the structure of our input mo dels { they Rendering such mo dels at interactive rates is a ma jor challenge. may b e arbitrary sets of p olygons with no other top ological in- There is a great b o dy of literature in computer graphics and com- formation, also known as \p olygon soup". The problem of 3D putational geometry using techniques based on visibility culling o cclusion culling involves the computation of some geometric re- lationship b etween two or more ob jects. In our case, we reduce Supp orted in part by a Sloan fellowship, ARO Contract P- the problem to p erforming overlap tests b etween convex ob jects in 34982-MA, NSF grant CCR-9319957, NSF grant CCR-9625217, 2D or 3D. Based on our exp erience in developing twointerference ONR Young Investigator Award, DARPA contract DABT63-93- detection systems, I-COLLIDE [CLMP95] and RAPID [GLM96], C-0048, NSF/ARPA Science and Technology Center for Com- as well as that of other authors in implementing algorithms for puter Graphics & Scienti c Visualization NSF Prime contract + interference detection [HKM95, BCG 96] and intersection com- No. 8920219. y putation for solid mo deling [For96, HHK89 ], wehave realized ro- Also with U.S. Army Research Oce bustness is an imp ortant issue in the design and implementation of interference detection algorithms. Our goal is to develop al- gorithms which are relatively simple, ecient, and not prone to geometric degeneracies. In this pap er, we present ob ject-space techniques for occlu- sion cul ling. This involves computation of a set of p olygons that are within the view frustum but are not visible from the current To app ear in the pro ceedings of the Thirteenth ACM Symp osium viewp oint. We add this conservative visibility culling stage to the on Computational Geometry, June 1997, Nice, France. rendering pip eline in order to reduce the numb er of p olygons sent coherence by p erforming visibility queries on the Z-bu er. Cur- to the graphics hardware. rently, most graphics systems do not supp ort this capabilityin As the viewp ointchanges, the algorithm dynamically cho oses hardware, and simulating the hierarchical Z-bu er in software is a set of o ccluders. Each o ccluder is a convex p olytop e or a union relatively exp ensive. of convex p olytop es. For each o ccluder the algorithm computes The work most directly related to our approach is that of a shadow frustum and uses fast interference detection and a hier- Co org and Teller [CT96, CT97]. Given two convex ob jects an archical representation to nd those p ortions of the mo del within o ccluder and o ccludee, their early work required the construction the shadow frustum. The idea of shadowvolumes was rst intro- and maintenance of a linearized p ortion of an asp ect graph. They duced by Crow [Cro77] to generate shadows by creating for each use this structure to track the viewp oint and determine whether ob ject a shadowvolume that the ob ject blo cks from the light one convex p olytop e o ccludes the other from a given viewp oint. source. This involves enumeration of all visual events and data struc- tures for dynamic plane maintenance. In the worst case, the Main contribution: We present geometric algorithms for numb er of planes used to form a cell of the arrangement can b e 2 O m , where m is the number of vertices of the convex p oly- 1. Occluder selection using o -line and on-line techniques top es, though dynamic and hierarchical data structures are used 2. Robust and ecient o cclusion culling based on sp ecialized in [CT96] to sp eed-up the computation of relevant planes. Each interference detection algorithms, given the o ccluders and a arrangement cell classi es all p olytop es as completely, partially, hierarchical decomp osition of scene geometry into b ounding or un- o ccluded. This approach is similar to earlier shadow com- volumes. putation algorithms which, given a light source and an o ccluder, decomp ose space into p enumbra and umbra volumes. In their The resulting algorithms have b een implemented and we re- newer work they reduce the amount of coherence used and sim- p ort their p erformance on a large mo del. plify the structure of the arrangement. This yields a considerable Organization: The rest of the pap er is organized in the following sp eedup, eliminating the overhead cost of maintaining complex manner. We survey related work in Section 2 and giveanoverview data structures. of the algorithm in Section 3. The o ccluder selection algorithm is presented in Section 4 and visibility culling based on o ccluders 3 Algorithm Overview is describ ed in Section 5. We present implementation details and the p erformance in Section 6 and analyse its complexity in Section Occlusion culling can b e divided into two subproblems. First, for 7. a given viewp ointwemust select a small set of go o d o ccluders to use. Second, given go o d o ccluders, wemust use them to cull away o ccluded p ortions of the mo del. These two problems are partially 2 Related Work indep endent, and so we treat them separately in this pap er.