Rapid Collision Detection by Dynamically Aligned DOP-Trees

Transcription

1 Rapd Collson Detecton by Dynamcally Algned DOP-Trees Gabrel Zachmann Fraunhofer Insttute for Computer Graphcs Rundeturmstraße 6, 648 Darmstadt, Germany emal: Abstract Based on a general herarchcal data structure, we present a fast algorthm for exact collson detecton of arbtrary polygonal rgd objects. Objects consstng of hundreds of thousands of polygons can be checked for collson at nteractve rates. The pre-computed herarchy s a tree of dscrete orented polytopes (DOPs). An effcent way of re-algnng DOPs durng traversal of such trees allows to use smple nterval tests for determnng overlap between DOPs. The data structure s very effcent n terms of memory and constructon tme. Extensve experments wth synthetc and real-world CAD data have been carred out to analyze the performance and memory usage of the data structure. A comparson wth OBB-trees ndcates that DOP-trees as effcent n terms of collson query tme, and more effcent n memory usage and constructon tme. Keywords: Interference detecton, vrtual prototypng, herarchcal boundng volumes, physcally-based modelng, shape approxmaton. Introducton Real-tme collson detecton of polygonal objects undergong rgd moton s of crtcal mportance n many nteractve vrtual envronments. In partcular, smulaton algorthms, utlzed n vrtual realty systems to enhance object behavor and propertes, need several collson queres per frame. It s a fundamental problem of dynamc smulaton of rgd bodes and smulaton of natural nteracton wth objects. For example, n vrtual prototypng, parts should be rgd and slde along each other. A very demandng smulaton s force-feedback whch needs at least collson queres per second. It s very mportant for a VR system to be able to do all smulatons at nteractve frame rates. Otherwse, the feelng of mmerson, the belevablty of the vrtual envronment, and even the usablty of the VR system wll be mpared severely. For real-tme smulatons, the collson detecton must be fast enough under all crcumstances to allow several teratons per frame wth objects consstng of 5, to 5, polygons at least. The algorthm must not make any assumpton about the nput, such as convexty, topology, or manfolded-ness, because polygonal geometry, converted from CAD data, s usually not well-formed : t may have cracks, dentcal or degenerate polygons, etc. (hence they have been named polygon soups ). Also, t cannot make any assumptons or estmatons about the poston of movng objects n the future, especally when they are beng moved by the user. Most collson response algorthms need at least one pont of ntersecton (a wtness) n order to take reasonable steps. Fast collson detecton of movng non-convex polygonal objects seems to be a hard problem because of ts mmanent all-pars weakness []. Several boundng volume (BV) herarches have been developed to overcome ths problem n order to fnd quckly a par of ntersectng polygons, or to reject pars of polygons whch cannot ntersect. The performance of any collson detecton based on herarchcal boundng volumes depends on two conflctng constrants: () the tghtness of the BVs, whch wll nfluence the number of BV tests, and () the smplcty of the BVs, whch determnes the effcency of an overlap test of BVs. Our algorthm s more based towards optmzng (). However, the bas can be shfted to () by makng them arbtrarly tght. Our approach s based on the BVs ntroduced by [5]. They have been named dscrete orentaton polytopes (DOPs) by []. For each object, we buld a herarchy of DOPs (DOP-Tree), each leave of whch encloses a sngle polygon of the object. In order to quckly determne ether two DOPs overlap, one of them has to be re-algned. Ths can be done on-the-fly durng traversal of the two DOP-Trees by a smple affne transformaton of the nonalgned DOPs. We conjecture that for any algorthm there are two objects and two postons for them such that the algorthm performs no better than (n ).

2 The next secton provdes a quck overvew of other herarchcal collson detecton methods. Secton descrbes the general framework whch most herarchcal collson detecton methods are based on. In Secton 4 we explan the applcaton of herarchcal DOPs to collson detecton ncludng the constructon of DOP-trees. Secton 5 presents results of the effect of the number of orentatons on collson detecton tme. Also, our DOP-Trees are compared to OBB-Trees. Fnally, Secton 6 draws some conclusons and descrbes future drectons for research on herarchcal collson detecton. Related work Interference and collson detecton problem have been extensvely studed n the lterature. Computatonal geometry frst focused on the constructon of the ntersecton of two polyhedra [8, 7] and later on the detecton problem [5, ]. The algorthms are very effcent n the asymptotcal worst-case. However, most of them are restrcted to statc envronments and many of them have not been mplemented. Confguraton space has been used to detect collsons for path-plannng n robotcs (see [6], for example). For collson avodance, Shaffer et al. [4] have used an octree to approxmate objects. Good results have been acheved for convex polyhedra [6,, 8]. Almost all approaches for general, non-convex objects utlze some sort of BV herarchy. A few nonherarchcal approaches have been taken as well. Garca- Alonso et al. [7] partton the set of polygons of an object by a unform grd. Sphere trees were developed by [, 4, 9]. Gottschalk et al. [] developed a boundng box herarchy based on orented boxes (OBBs). Its box overlap test s much more expensve than for DOPs. Algned Box-Trees have been presented n []. Barequet et al. [] presented some theoretcal results on a class of BV herarches called BOX- TREE, too. DOP-trees have been used for collson detecton before by []. However, they seem to use more general DOPs and do hll-clmbng to compute the axs-algned DOPs from the tumbled ones, whch s probably less effcent than our method. The herarchcal collson detecton scheme The goal of any herarchcal BV scheme used for collson detecton s to dscard quckly any pars of polygons whch cannot ntersect. Each node n the tree s assocated wth a subset of the prmtves of the object, together wth a BV that encloses ths subset wth a smallest contanng nstance of some specfed class of shapes. Gven two objects and the roots of ther assocated BV trees, a smultaneous traversal of the two trees recursvely checks all pars of ther chldren BVs for overlap. If such a par does not overlap, then the polygons enclosed by them cannot ntersect. The followng pseudo-code outlnes the basc scheme of collson detecton algorthms based on a BV herarchy: Smultaneous traversal of BV trees a = boundng volume of A s tree, b = boundng volume of B s tree a[], b[] chldren of a and b, resp. traverse(a,b): a or b s empty! return b leaf! a leaf! check prmtves enclosed by a and b return a not leaf! forall : a[],b overlap! traverse(a[],b) b not leaf! a leaf! forall : a,b[] overlap! traverse(a,b[]) a not leaf! forall : forall j: a[],b[j] overlap! traverse(a[],b[j]) Fgure vsualzes the set of polygons consdered n the worst-case for exact ntersecton calculatons. The pcture has been obtaned wth our DOP-Tree data structure, but all other herarchcal BV schemes would produce a smlar mage. 4 Dscrete orentaton polytopes Dscrete orentaton polytopes (DOPs) are convex polytopes whose faces can have only normals whch come from a fxed small set of k orentatons (k-dops). Probably the fastest overlap check for axs-algned boxes s the wellknown nterval test. In order to be able to apply such a test to DOPs, we restrct the set of orentatons further such that for each orentaton of the set there s also an ant-parallel one; the two correspondng faces form what s commonly known as a slab. Thus, ths specal knd of k-dops can be vewed as a generalzaton of axs-algned boxes. Beng the ntersecton of k half-spaces H : B x - d ; a k-dop can be represented by the pont d R k, where B are the k fxed orentatons. We wll call d the plane

3 d B B d d 5 D d5 b b B4 b B d b6 b4 d4 b5 B 5 B6 Fgure : A rotated DOP can be enclosed by an algned one by computng new plane offsets d. Each can be computed by an affne combnaton of d Fgure : All polygons whch are consdered for ntersecton n the worst-case are rendered sold. The rejecton of all other polygons s based on the herarchcal BV data structure. offsets for that DOP. At each node of our herarchcal data structure we need to store only k floatng pont numbers (snce the orentatons are the same for all DOPs) plus ponters (assumng bnary trees). We would lke to remark that, except for the just mentoned nterval overlap test of DOPs, all other parts of our algorthms apply to the case of general DOPs as well. 4. Algnng DOPs Gven two DOP-Trees A and B, the basc step of the smultaneous traversal s an overlap test of two nodes. In order to apply the smple and very fast nterval overlap test to DOP- Trees, they must be gven n the same space. However, at least one of the assocated objects has been transformed by a rgd moton. By choosng A s object space (w.l.o.g.), we need to re-algn only B s nodes as we encounter them durng traversal. Algnng a node (a non-algned DOP ) s done by enclosng t n another (algned) DOP. We wll show that ths can be done by a smple affne transformaton of the node s plane offsets. Assume we are gven a (non-algned) DOP D of B s DOP-Tree, whch s represented by d. Assume also, that the object assocated wth B has been transformed by a rotaton M and a translaton o, wth respect to A s reference frame. Then D s the ntersecton of k half-spaces h : b x - d + o ; where b = B M - (see Fgure ). d j l; l ( n -space). The correspondence j l depends only on the affne transformaton of the assocated object and the fxed orentatons B. Now suppose we want to compute the d of the enclosng DOP D of D. There s (at least) one extremal vertex P of the convex hull of D wth respect to B. Ths vertex s the ntersecton of (or more) half-spaces h j ; l. l It s easy to see that d = B b j b j b j C A - d j d j d j C A + B o The correspondence establshed by j s the same for l all (non-algned) DOPs of the whole tree, f the followng condton s met: DOPs must not possess any completely redundant half-spaces,.e., all planes must be supported by at least one vertex of the convex hull of the DOP. (We do allow almost redundant half-spaces,.e., planes whch are supported by only a sngle vertex of the convex hull.) Fortunately, ths condton s trvally met when constructng the DOP-Tree. Thus, enclosng a non-algned DOP by an algned one takes only k multplcatons and k addtons. The correspondence j s establshed by two steps: l Frst, we compute the vertces of the convex hull of a generc DOP (all d = ). Each vertex s supported by three planes (or more), the orentatons of whch we store wth that vertex n an ntermedate correspondence. Ths has to be done only once for a gven set of orentatons. We can choose any DOP to establsh ths (ntermedate) correspondence. However, we must make sure that all planes do support a non-degenerate face.

4 Fgure : The sute of test objects. They are (left to rght): the skn of a car door (, polygons; data courtesy of BMW), the lock of a car door (, polygons; data courtesy of BMW), skn and seats of a car( 6, polygons; data courtesy of VW), a secton of ppes(, polygons). Second, at the begnnng of each DOP-tree traversal, we transform the vertces of the generc DOP by the object s rotaton. Then, we use these to establsh the fnal correspondence j l. 4. Buldng DOP-Trees Any herarchcal algorthm can be only as good as the herarchcal data structures. Good herarchcal data structures for ray-tracng are characterzed by a low stabbng number []. Good BV trees for collson detecton are characterzed by a low number of prmtve ntersecton tests. It s not clear yet, f there s a sngle measure whch should be optmzed durng the constructon of a BV herarchy n order to acheve an optmal tree for collson detecton. Obvously, the followng crtera should gude the constructon algorthm: The total volume of all BVs should be small []. The tree should be balanced n terms of polygon counts. The volume of overlap of two sblngs should be small. Our constructon of DOP-Trees can be contrasted to nserton methods [9, ] and bottom-up methods []. We proceed n a top-down fashon startng wth the complete set of polygons, splttng the set at each node. For our applcaton t s very mportant, that the constructon process be fast, so that t can be done at load tme. Therefore, we make use of several heurstcs and estmatons whch try to emulate the crtera lsted above. The nput to the constructon algorthm s a set F of k-dops (each of them encloses one of the polygons of the object) and a set C of ponts whch are the barycenters of the polygons. The algorthm starts by fndng c ; c j C wth almost maxmal dstance. Then t determnes that orentaton whch s most parallel to c c j. Now we sort C along that orentaton, whch nduces a sortng on F. After these prelmnares (whch are done for each step of the recurson), we can splt F n two parts F and F. We start wth F = f, F = f j, where f ; f j are assocated to c ; c j, resp. Then, we consder all other f F n turn and assgn them to F or F, whchever BV ncreases less. If both BVs of F and F would ncrease by the same amount (n partcular, f they would not ncrease at all), then f s added to the set whch has fewer polygons so far. Ths algorthm seems to produce very good trees. In partcular, they are farly well balanced. Therefore, the average depth s almost the same for all sets of orentatons (whch has been verfed by our experments). The followng table shows a hstogram of the depth of the leaves of the 6-DOP-Tree for two objects. The sphere has approxmately, polygons, whle the car door has approxmately, polygons: depth sphere car door Other heurstcs have been mplemented and tested, but the one descrbed above has produced the best results. 4. Geometrc robustness and accuracy The constructon algorthm s geometrcally robust and can be appled to all unstructured models. No adjacency nformaton s requred. There are no connectvty restrctons and the faces can be degenerate (a lne segment or a pont), whch happens frequently n CAD data. The overlap test s very robust, snce t nvolves only multplcatons, addtons, and comparsons. A small We compute only a near-optmal par by a smple O(n) heurstc.

5 margn guards aganst arthmetc round-off errors. Actually, that guard can be appled to the DOPs whle the DOP- Tree s beng constructed (by nflatng them a lttle), so durng traversal, no addtons/subtracton need to be done. No error accumulaton can occur durng traversal of the tree. 5 Benchmarks and results It s extremely dffcult to evaluate and compare collson detecton algorthms, because n general they are very senstve to specfc scenaros,.e., the relatve sze of the two objects, the relatve poston to each other, the dstance, etc. We propose a smple benchmark program whch (hopefully) elmnates these effects. It has been kept very smple so that other researchers can easly reproduce our results and compare ther algorthms to ours. Our test scenaro nvolves two dentcal objects whch are postoned at a certan dstance from each other. The dstance s computed between the centers of the boundng boxes of the two objects. Then one of them performs a full revoluton around the z-axs (whch s pontng towards the vewer n Fgure ) n a fxed, large number (here ) of small steps. Wth each step a collson query s done, and the average collson detecton tme for that dstance s computed. Ths procedure s done for dfferent dstances, whch yelds graphs as shown n Fgures 4, 5. We have carred out extensve experments usng ths benchmark procedure wth dfferent objects, both synthetc and real-world CAD data. Synthetc objects are spheres, tor, cylnders n varous resolutons from, polygons through, polygons. The CAD data are depcted n Fgure. The complexty ranges from, to, polygons. All objects are scaled to ft n a cube of sze. All test have been done on a SGI R (94 MHz). 5. The optmal number of orentatons Obvously, there are two contradctory effects when the number of orentatons of DOP-Trees s ncreased: on the one hand, they can better approxmate the convex hull of the set of polygons enclosed by them; on the other hand, an overlap test between them s more expensve. Three dfferent sets wth 6, 8, and 4 orentatons have been tested: the faces of 6-DOPs have the same normals as a cube, 8-DOPs have normals of an octahedron, and 4- DOPs have normals of the unon of the former two. The results are depcted n Fgures 4 and 5. From the fgures t becomes clear why comparng collson detecton The source code of the man loop and the synthetc objects can be ftp ed from coldet/benchmark.html. The CAD objects can be obtaned va the author (for scentfc purposes only). tme / mllsec slabs 4 slabs 7 slabs # polygons per torus Fgure 6: As complexty ncreases the average collson detecton tme ncreases only slghtly for DOP- Trees. avg. tme / mllsec k-dop-tree #polygons k = 6 k = 8 k = 4 door lock car ppes Table : Comparson of 6-, 8-, and 4-DOPs. There s no sgnfcant advantage of 4-DOPs over 6-DOPs. algorthms s dffcult: Dependng on the stuaton and the partcular objects chosen for the tests, the collson query tmes can vary by an order of magntude. We feel that a far measure for the overall performance s the mean collson detecton tme averaged over all dstances and all rotatons. The average tme for tor s shown n Fgure 6 whle Table summarzes the results for all CAD objects. There doesn t seem to be a sgnfcant and general performance beneft from usng 4 orentatons compared to 6 orentatons. It s not clear to us why 8 orentatons perform so bad. We also compared the memory requrements and constructon tme among DOP-Trees usng 6, 8, or 4 orentatons. As expected, constructon tme ncreases slghtly as the number of orentatons ncreases (see Table ). Also, the amount of memory requred ncreases slghtly (see Table ). Ths s due to the fact that the depth of trees doesn t change wth dfferent sets of orentatons.

6 .5 slabs 4 slabs 7 slabs 6 5 slabs 4 slabs 7 slabs tme / mllsec.5.5 tme / mllsec dstance dstance Fgure 4: Two tor (584 polygons each), one of them s rotatng. At each dstance, rotatons and collson queres have been performed. The tme shown s the average collson detecton tme. Fgure 5: The locks (898 polygons each) are dfferent n that most of the polygons are n the nteror, b/c t has many parts on the nsde. Ths mght explan the nverson of the shape of the curve. tme / sec # orentatons #polygons door lock car ppes Table : Constructon tme of the BV herarchy for varous CAD and synthetc objects. The tme ncreases by about percent when 4-DOPs are used nstead of 6-DOPs. MB # orentatons #polygons door 9... lock 898 car ppes Table : The amount of memory requred by a DOP- Tree wth varous orentaton sets. 4-DOP-Trees need about percent more memory than 6-DOP- Trees. avg. tme / mllsec #pgons 6-DOP-Tree OBB-Tree speedup door lock car ppes tor spheres tor spheres Table 4: Summary comparng the performance of DOP-Trees and OBB-Trees. 5. Comparson of DOP-Trees and OBB-Trees Snce there s no sgnfcant advantage n 4-DOPs over 6- DOPs, we used 6-DOPs to compare DOP-Trees wth OBB- Trees. For OBB-Trees, the Rapd mplementaton [] has been used. Fgures 7 and 8 show the results of the benchmark for DOP-Trees and OBB-Trees. Table 4 summarzes the results for several other objects. All tmngs nclude the tme to transform the (necessary) vertces and normals. Table 5 shows the amount of memory requred by DOP-Trees and OBB-Trees. For both, memory usage depends lnearly on the number of polygons. At each node DOP-Trees store only 6 floats whereas an OBB-node stores (at least) 8 floats. The table ndcates that DOP-Trees need about 4-8 tmes less memory. (For the memory comparson, we have changed all doubles to floats n the Rapd

7 DOP-Tree OBB-Tree 9 6-DOP-Tree OBB-Tree tme / mllsec tme / mllsec dstance dstance Fgure 7: Comparson of DOP-Trees and OBB-Trees for the car model. Fgure 8: Comparson for the door lock. MB #polygons 6-DOP OBB door 9. lock car ppes tor spheres 95 7 tor spheres Table 5: A comparson of memory requrements ndcates that DOP-Trees need about 4-8 tmes less memory then OBB-Trees. We have developed and mplemented a herarchcal data structure for fast and exact collson detecton of polygonal models wth very large polygon counts. The algorthm s general-purpose and makes no assumpton about the ntme / sec #polygons 6-DOP-Tree OBB-Tree door 9..4 lock car ppes tor spheres tor spheres Table 6: Comparson of the constructon tme of the BV herarchy for varous CAD and synthetc objects. The constructon of DOP-Trees s about -4 tmes faster. code []. Of course, the memory requred by the lst of vertces and polygons s counted, too.) For vrtual realty applcatons to be utlzed at floor shops and at desgn evaluaton sessons t s mportant that startup tme be as short as possble. Snce t s not desrable to store an abundance of auxlary data structures wth a vrtual envronment on dsk, constructon tme of data structures needed for collson detecton should be mnmal. Table 6 summarzes the comparson of the constructon tme of the data structures for DOP- and OBB-Trees. 6 Concluson and future work put model. It utlzes dscrete orented polytopes (DOPs) for boundng volumes. We show that re-algnng rotated DOPs can be done by a smple affne transformaton of ther plane offset representatons. Also, we have presented a new method of constructng DOP-Trees. We have carred out extensve and thorough experments to analyze the mpact of the orentaton count on performance, constructon tme and memory usage. Our experments ndcate that 6-DOPs (.e., boxes) are as good as 4-DOPs. Our algorthm usng DOP-Trees s about as fast as Rapd usng OBB-Trees. Furthermore, DOP-Trees are sgnfcantly more memory effcent and can be constructed much faster than OBB-Trees. There are several ssues of herarchcal collson detecton whch stll need to be nvestgated. One of them s

8 the characterzaton and constructon of optmal BV herarches for collson detecton. Whle our method of constructng DOP-Trees performs qute well, t would be nterestng to develop precse crtera for the constructon of optmal BV trees n the sense of mnmum average collson detecton tme. Also, t would be nterestng to ncrease the orentaton count even further to verfy our hypothess stated above. So far, we have appled our herarchcal data structures only to the problem of collson detecton. However, we feel that t has great potental for other applcatons, such as ray-tracng, nterference detecton of curved surfaces, and pont-locaton and range queres. Fnally, the algorthm s a good canddate for mplementaton n hardware, snce the flow of control s qute smple, and the overlap test nvolves only smple lnear arthmetc. References [] G. Barequet, B. Chazelle, L. J. Gubas, J. S. B. Mtchell, and A. Tal. BOXTREE: A herarchcal representaton for surfaces n D. Computer Graphcs Forum, 5():87 96, Sept [] N. Beckmann, H.-P. Kregel, R. Schneder, and B. Seeger. The R - tree: An effcent and robust access method for ponts and rectangles. In Proc. ACM SIGMOD Conf. on Management of Data, pages, 99. [] K. Chung. Quck collson detecton of polytopes n vrtual envronments. In M. Green, edtor, Proc. of the ACM Symposum on Vrtual Realty Software and Technology, pages 5, 996. [4] G. M. H. Clfford A. Shaffer. A real-tme robot arm collson avodance system. IEEE Transactons on Robotcs and Automaton, 8(), Aprl 99. [5] D. P. Dobkn and D. G. Krkpatrck. A lnear algorthm for determnng the separaton of convex polyhedra. J. Algorthms, 6:8 9, 985. [6] M. Erdmann and T. Lozano-Pérez. On multple movng objects. Algorthmca, :477 5, 987. [7] A. García-Alonso, N. Serrano, and J. Flaquer. Solvng the collson detecton problem. IEEE Computer Graphcs and Applcatons, pages 6 4, May 994. [8] E. G. Glbert, D. W. Johnson, and S. S. Keerth. A fast procedure for computng the dstance between complex objects n threedmensonal space. IEEE Journal of Robotcs and Automaton, 4():9, 988. [9] J. Goldsmth and J. Salmon. Automatc creaton of object herarches for ray tracng. IEEE Computer Graphcs and Applcatons, 7(5):4, May 987. [] S. Gottschalk. Rapd lbrary. geom/obb/- OBBT.html, Vers... [] S. Gottschalk, M. Ln, and D. Manocha. OBB-Tree: A herarchcal structure for rapd nterference detecton. In H. Rushmeer, edtor, SIGGRAPH 96 Conference Proceedngs, Annual Conference Seres, pages 7 8. ACM SIGGRAPH, Addson Wesley, Aug held n New Orleans, Lousana, 4-9 August 996. [] M. Held, J. T. Klosowsk, and J. S. Mtchell. Real-tme collson detecton for moton smulaton wthn complex envronments. In Sggraph 996 Techncal Sketches, Vsual Proceedngs, page 5, New Orleans, Aug [] P. M. Hubbard. Interactve collson detecton. In IEEE Symposum on Research Fronters n VR, San José, Calforna, pages 4, October [4] P. M. Hubbard. Collson detecton for nteractve graphcs applcatons. IEEE Transactons on Vsualzaton and Computer Graphcs, ():8, Sept ISSN [5] T. L. Kay and J. T. Kajya. Ray tracng complex scenes. In D. C. Evans and R. J. Athay, edtors, Computer Graphcs (SIGGRAPH 86 Proceedngs), volume, pages 69 78, Aug [6] M. C. Ln and D. Manocha. Effcent Contact Determnaton Between Geometrc Models. PhD dssertaton, Unversty of Calforna, Unversty of North Carolna Chapel Hll, URL: ftp://ftp.cs.unc.edu/pub/techreports/94-4.ps.z, 99(?). [7] K. Mehlhorn and K. Smon. Intersectng two polyhedra one of whch s convex. In L. Budach, edtor, Proc. Found. Comput. Theory, volume 99 of Lecture Notes Comput. Sc., pages Sprnger- Verlag, 985. [8] D. E. Muller and F. P. Preparata. Fndng the ntersecton of two convex polyhedra. Theoret. Comput. Sc., 7:7 6, 978. [9] I. J. Palmer and R. L. Grmsdale. Collson detecton for anmaton usng sphere-trees. Computer Graphcs Forum, 4():5 6, June 995. [] M. Rechlng. On the detecton of a common ntersecton of k convex polyhedra. In Computatonal Geometry and ts Applcatons, volume of Lecture Notes Comput. Sc., pages Sprnger-Verlag, 988. [] G. Zachmann. The BoxTree: Enablng real-tme and exact collson detecton of arbtrary polyhedra. In Informal Proc. Frst Workshop on Smulaton and Interacton n Vrtual Envronments, SIVE 95, Unversty of Iowa, Iowa Cty, July 995. The OX Assocaton for Computng Machnery.