I-COLLIDE: An Interactive and Exact Collision Detection System for Large-Scale Environments Jonathan D. Cohen Ming C. Lin Dinesh Mano cha MadhavK.Ponamgi Department of Computer Science University of North Carolina Chap el Hill, NC 27599-3175 fcohenj,lin,mano cha,p [email protected] ABSTRACT: or grasp ed. Such actions require accurate collision detec- We present an exact and interactive collision detection tion. However, there maybehundreds, even thousands system, I-COLLIDE, for large-scale environments. Such of ob jects in the virtual world, so a brute-force approach environments are characterized by the numb er of ob jects that tests all p ossible pairs for collision s is not acceptable. undergoing rigid motion and the complexity of the mo d- Eciency is critical in a virtual environment, otherwise els. The algorithm do es not assume the ob jects' motions its interactive nature is lost [24]. A fast and interactive can b e expressed as a closed form function of time. The collision detection algorithm is a fundamental comp onent collision detection system is general and can b e easily in- of a complex virtual environment. terfaced with a variety of application s. The algorithm The ob jective of collision detection is to rep ort all geo- uses a two-level approach based on pruning multiple- metric contacts b etween ob jects. If we know the p ositions ob ject pairs using b ounding b oxes and p erforming exact and orientations of the ob jects in advance, we can solve collision detection b etween selected pairs of p olyhedral collision detection as a function of time. However, this mo dels. We demonstrate the p erformance of the system is not the case in virtual environments or other interac- in walkthrough and simulation environments consisting tive applications. In fact, in a walkthrough environment, of a large numberofmoving ob jects. In particular, the we usually do not haveany information regarding the system takes less than 1=20 of a second to determine all maximum velo city or acceleration, b ecause the user may the collisio ns and contacts in an environment consisting move with abrupt changes in direction and sp eed. Due to of more than a 1000 moving p olytop es, each consisting of these unconstrained variables, collision detection is cur- more than 50 faces on an HP-9000/750. rently considered to b e one of the ma jor b ottlenecks in building interactive simulated environments [20]. 1 INTRODUCTION Main Contribution: We present a collision de- Collision detection is a fundamental problem in computer tection algorithm and system for interactive and exact animation, physically -based mo deling, computer simu- collision detection in complex environments. In contrast lated environments and rob otics. In these applications , to the previous work, we show that accurate, interac- an ob ject's motion is constrained by collisio ns with other tive p erformance can b e attained in most environments if ob jects and by other dynamic constraints. The prob- we use coherence to sp eed up pairwise interference tests lem has b een well studied in the literature. However, no and to reduce the actual numb er of these tests we p er- 2 go o d general collision detection algorithms and systems form. We are able to successfully trim the O n p os- are known for interactive large-scale environments. sible interactions of n simultaneousl y moving ob jects to A large-scale virtual environment, likeawalkthrough, O n + m where m is the numb er of ob jects very close creates a computer-generated world, lled with real and to each other. In particular, two ob jects are very close, virtual ob jects. Suchanenvironment should give the user if their axis-aligne d b ounding b oxes overlap. Our ap- a feeling of presence, which includes making the images of proach is exible enough to handle dense environments b oth the user and the surrounding ob jects feel solid. For without making assumptions ab out ob ject velo city or ac- example, the ob jects should not pass through each other, celeration. The system has b een successfully applied to and things should move as exp ected when pushed, pulled architectural walkthroughs and simulated environments and works well in practice. CurrentlyatNCA&TState University, Greensb oro. Ap- proved by ARPA for public release; distribution unlimited The rest of the pap er is organized as follows. In Sec- tion 2, we review some of the previous work in collision detection. Section 3 de nes the concept of coherence and describ es an exact pairwise collision detection algorithm which applies it. We describ e our algorithm for collision detection b etween multiple ob jects in Section 4 and dis- cuss its implementation in Sections 5 and 6. Section 7 presents our exp erimental results on walkthrough envi- ronments and simulations. 1 2 PREVIOUS WORK steps are smal l enough that the ob jects to do not travel large distances b etween frames. The problem of collision detection has b een extensively studied in rob otics, computational geometry, and com- 3.2 Pairwise Collision Detection for Convex Polytop es puter graphics. The goal in rob otics has b een the planning of collision-free paths b etween obstacles [15]. We brie y review the Lin-Canny collision detection algo- This di ers from virtual environments and physically- rithm which tracks closest p oints b etween pairs of convex based simulations , where the motion is sub ject to dy- p olytop es [16, 17 ]. This algorithm is used at the lowest namic constraints or external forces and cannot typi- level of collision detection to determine the exact contact cally b e expressed as a closed form function of time status b etween convex p olytop es. The metho d maintains [1, 3, 11, 18 , 20 , 21 ]. a pair of closest features for each convex p olytop e pair At the same time, the emphasis in the computational and calculates the Euclidean distance b etween the fea- geometry has b een on theoretically ecientintersection tures to detect collisio ns. This approach can b e used in detection algorithms [22]. Most of them are restricted to a static environment, but is esp ecially well-suited for dy- a static instance of the problem and are non-trivial to namic environments in which ob jects move in a sequence 1 implement. For convex 3-p olytop es linear time algo- of small, discrete steps. rithms based on linear programming and tracking closest The metho d takes advantage of coherence: the closest p oints [10] have b een prop osed. More recently, temp oral features change infrequently as the p olytop es move along and geometric coherence have b een used to devise algo- nely discretized paths. The algorithm runs in expected rithms based on checking lo cal features of pairs of convex constant time if the p olytop es are not moving swiftly. 3-p olytop es [3, 17]. Alonso et al.[1] use b ounding b oxes Even when a closest feature pair is changing rapidly, the 2 and spatial partitioning to test all O n pairs of arbi- algorithm takes only slightly longer the running time trary p olyhedral ob jects. is prop ortional to the numb er of feature pairs traversed, Di erent metho ds have b een prop osed to overcome the which is a function of the relative motion the p olytop es 2 b ottleneckofOn pairwise tests in an environmentof undergo. The metho d for nding closest feature pairs is nb o dies. The simplest of these are based on spatial sub- based on Voronoi regions. The algorithm starts with a division. The space is divided into cells of equal vol- candidate pair of features, one from each p olytop e, and ume, and at each instance the ob jects are assigned to one checks whether the closest p oints lie on these features. or more cells. Collision s are checked b etween all ob ject Since the p olytop es and their faces are convex, this is a pairs b elonging to a particular cell. This approachworks lo cal test involving only the neighb oring features of the well for sparse environments in which the ob jects are uni- current candidate features. If either feature fails the test, formly distributed through the space. Another approach the algorithm steps to a neighb oring feature of one or op erates directly on four-dimensional volumes swept out b oth candidates, and tries again. With some simple pre- by ob ject motion over time [4, 14 ]. pro cessing, the algorithm can guarantee that every fea- ture has a constantnumb er of neighb oring features. None of these algorithms adequately address the issue of collision detection in a virtual environment which re- 3.3 Penetration Detection for Convex Polytop es quires p erformance at interactive rates for thousands of pairwise tests. Hubbard has prop osed a solution to ad- The core of the collision detection algorithm is built us- dress this problem by trading accuracy for sp eed [14]. ing the prop erties of Voronoi regions of convex p olytop es. In an early extension of their work, Lin and Canny [16 ] The Voronoi regions form a partition of space outside the prop osed a scheduling scheme to handle multiple moving p olytop e. When p olytop es interp enetrate, some features ob jects. Dworkin and Zeltzer extended this work for a may not fall into anyVoronoi regions. This can at times sparse mo del [7]. lead to cycling of feature pairs. To circumvent this prob- lem, we partition the interior space of the convex p oly- 3 BACKGROUND top es.