Snoeyink, J. and Stolfi, J., Objects that Cannot be Taken Apart with Two Hands, Proc. 9th ACM Symp. on Computational Geometry, 247-256, 1993.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....The unboundedness test is useful for the motion planning problem of computing assembly sequences: given a set of objects in the plane or in space, decide whether these objects can be assembled (or, disassembled) without collision. This problem has been studied in a variety of contributions [1, 2, 6, 8]. The problem of finding a sequence of translational motions for partitioning a given assembly has expo Figure 2: An assembly requiring m hands to disassemble nential lower bounds [2] This is illustrated in Fig. 1: to free the dark gray object, it is necessary to move the k u shaped parts ....

J. Snoeyink, J. Stolfi. Objects that Cannot be Taken Apart with Two Hands. Discrete and Computational Geometry, 12: 367-384, 1994.

.... assemblies of polyhedra, where the separating motions are either infinite translations or infinitesimal rigid motions (the latter identifying a superset of the removable subassemblies for general separating motions) Infinitesimal rigid motions are also treated in [3] Snoeyink and Stolfi [12] present an assembly of convex polyhedra that cannot be partitioned. Other related geometric separation problems are studied in [4, 9, 10, 13] In [6, 7, 16] it was shown that the partitioning problem for polygons in the plane is NP complete. Let us remark here that the corresponding decision ....

J. Snoeyink and J. Stolfi, "Objects that cannot be taken apart with two hands", Proc. of the 9th ACM Symp. on Computational Geometry, pp. 247256, 1993.

.... Wilson [13] presents algorithms to partition assemblies of polyhedra, where the separating motions are either infinite translations or infinitesimal rigid motions (the latter identifying a superset of the removable subassemblies for general separating motions) Interestingly, Snoeyink and Stolfi [11] present an assembly of convex polyhedra that cannot be partitioned. Other related geometric separation problems are studied in [3, 8, 9, 12] In this paper we show that the partitioning problem for polygons in the plane is NP complete. Our proof extends to some interesting variants of the ....

J. Snoeyink and J. Stolfi, "Objects that cannot be taken apart with two hands", Proc. of the 9th ACM Symp. on Computational Geometry, pp. 247-256, 1993.

....A box in a cage: the parts are not separated but the set of separating directions is not convex. An interesting general difference between polygonal and polyhedral assemblies is that, unlike assemblies of convex polygons, assemblies of convex polyhedra cannot always be assembled with a single hand [66]. Therefore for polyhedral assemblies it is not sufficient that all pairs of parts be separated in order to allow for single handed separability. In contrast, as shown above, m handed separability is always possible for pairwise separated parts in any dimension. Showing that m handed separability ....

J. Snoeyink and J. Stolfi. Objects that cannot be taken apart with two hands. In Proc. of the 9th ACM Symp. on Computational Geometry, 1993.

....rotation [16] Fore more information on assembly planning see, e.g. 6] 15] In 1988, in his paper On Planning Assemblies [11] Natarajan conjectured that two hands suffice to assemble any composite comprised of convex polyhedra in 3 space . In a surprising result, Snoeyink and Stolfi [13] have recently been able to disprove this conjecture: they gave an example consisting of thirty convex polyhedral parts that cannot be taken apart with two hands. The proof of the validity of the construction relies on a computer program that (up to symmetries in their construction) exhaustively ....

....described above has been implemented and in this section we present preliminary experimental results. The linear programming part is solved using the MINOS package [10] The contact constraints are computed by the algorithm described in [5] The first example, given by Snoeyink and Stolfi [13], consists of six identical tetrahedra in contact and shown in Figure 2. They proved that no proper subset is separable by infinitesimal translation. We revisit this example, confirm their result with our program, and show that if we also allow infinitesimal rotation, then this object can be ....

J. Snoeyink and J. Stolfi, Objects that cannot be taken apart with two hands, Proc. 9th ACM Symposium on Computational Geometry, 1993, pp. 247--256.

.... guessing candidate sequences and geometric reasoning modules checking their feasibility [20, 40] More efficient techniques were later proposed to replace time consuming generate and test [4, 41] Research on separability problems in Computational Geometry is also related to assembly sequencing [8, 32, 35, 37]. Assembly sequencing has been shown to be intractable [21, 22, 23, 29, 44] leading researchers to consider restricted, but still interesting subsets of assembly sequences, e.g. monotone sequences, where each operation generates a final subassembly, and two handed sequences, where every ....

Snoeyink, J. and Stolfi, J., Objects that Cannot be Taken Apart with Two Hands, Proc. 9th ACM Symp. on Computational Geometry, 247-256, 1993.

....Dawson [4] shows that two or more star shaped objects can always be separated by translating the objects in 2 Figure 1: An assembly in which no single part can be removed C 1 C C C 2 3 4 x z Figure 2: An assembly of cubes 3 different directions simultaneously. However, it is shown in [14] that for some assemblies of convex polyhedra, no subassembly may be removed, using general rigid motions, without disturbing the rest of the parts. Homem de Mello and Sanderson [6] give a method to calculate the polyhedral convex cone containing the infinitesimal translations allowed by a set of ....

J. Snoeyink and J. Stolfi. Objects that cannot be taken apart with two hands. In Proc. of the 9th ACM Symp. on Computational Geometry, to appear, 1993. 16

.... assemblies of polyhedra, where the separating motions are either infinite translations or infinitesimal rigid motions (the latter identifying a superset of the removable subassemblies for general separating motions) Infinitesimal rigid motions are also treated in [3] Snoeyink and Stolfi [12] present an assembly of convex polyhedra that cannot be partitioned. Other related geometric separation problems are studied in [4, 9, 10, 13] In [6, 7, 16] it was shown that the partitioning problem for polygons in the plane is NP complete. Let us remark here that the corresponding decision ....

J. Snoeyink and J. Stolfi, "Objects that cannot be taken apart with two hands", Proc. of the 9th ACM Symp. on Computational Geometry, pp. 247-256, 1993.

....described above can be used to visualize a new idea, with the visualization appearing simultaneously with the research paper that presents the new concept. In practice, however, most algorithm animations describe ideas which are already well known. Objects that Cannot be Taken Apart With Two Hands [VR2h], is remarkable for appearing at the same time as the discovery it explains. An Animation of a Fixed Radius All Nearest Neighbors Algorithm [VR3c] is an excellent video. The algorithm described here solves the following problem: Given a set of points and a distance ffi, find groups of points ....

Jack Snoeyink "Objects That Cannot Be Taken Apart With Two Hands"

....a two handed assembly sequence of translations, but with a three handed sequence of translations. Every assembly of five or fewer convex polyhedra admits a two handed assembly sequence of translations. There exists an assembly of thirty convex polyhedra that cannot be assembled with two hands [Snoeyink and Stolfi, 1994]. 3.2.3 Complexity of assembly sequencing When arbitrary sequences are allowed, assembly sequencing is PSPACE hard. The problem remains PSPACE hard even when the bodies are polygons, each with a constant maximal number of vertices [Natarajan, 1988] When only two handed monotone sequences are ....

Snoeyink, J. and Stolfi, J. 1994. Objects That Cannot Be Taken Apart with Two Hands.

....Computational Geometry. Assembly sequencing is an intriguing combination of a combinatorial and geometric problem. Quite naturally, research from computational geometry relates very closely to assembly sequencing. The separability of objects has been well studied in the geometric community [8, 9, 10, 20, 41, 42]. In a single direction, a depth order of a set of parts is an ordering of the parts which allows for collision free translations of the individual parts to infinity. A classic result states that given a collection of convex shapes in two dimensions, for any translational direction there exists ....

.... in the plane for which the removal of a certain disk may require the prior removal of Omega Gamma n) other disks [21] Also, there exists a set of convex parts in three dimensions which cannot be disassembled using two hands, with only translations, or even generalized rotations and translations [41]. A surprising element of our problem is that the general lower bounds can be realized for a simple geometric setting consisting of a collection of unit disks in the plane. More often than not, an optimization problem becomes significantly easier when its input is restricted to a geometric ....

J. Snoeyink and J. Stolfi. Objects that cannot be taken apart with two hands. In Proc. ACM Symp. on Computational Geometry, pages 247--256, 1993.

....developed by Rohnert [5] The object to be moved is a disc, the obstacles are simple disjoint polygons inside a bounding polygon. We are looking for a collision free path for the disc between two given positions. The Algorithm Rohnert s algorithm is based on an algorithm by O Dunlaing and Yap [4] and moves the disc along the Voronoi diagram of the polygons. The set of obstacles is preprocessed such that find path queries in the same polygonal environment can be answered quickly. A find path query fixes the size of the disc, its initial position p in and its final position p fi . In the ....

....R.E. Tarjan. Fast algorithms for finding nearest common ancestors. SIAM Journal on Computing, 13(2) 338 355, 1984. 3] S. Naher and K. Mehlhorn. LEDA A Library of Efficient Data Types and Algorithms. In Int. Coll. on Automata, Languages and Programming, ICALP 90, LNCS 443, pages 1 5, 1990. [4] C. O Dunlaing and C. Yap. A retraction method for planning the motion of a disk. Journal of Algorithms, 6:104 111, 1985. 5] H. Rohnert. Moving a disc between polygons. Algorithmica, 6:182 191, 1991. 6] C. Yap. An O(n log n) algorithm for the Voronoi diagram of a set of simple curve ....

[Article contains additional citation context not shown here]

J. Snoeyink and J. Stolfi. Objects that cannot be taken apart with two hands. In Proc. 9th ACM Symp. Comp. Geom., 1993.

....[5] 9] 17] Fore more information on assembly planning see, e.g. 6] 16] 18] In 1988, in his paper On Planning Assemblies [12] Natarajan conjectured that two hands suffice to assemble any composite comprised of convex polyhedra in 3 space . In a surprising result, Snoeyink and Stolfi [14] have recently been able to disprove this conjecture: They gave an example consisting of thirty convex polyhedral parts that cannot be taken apart with two hands. The proof of the validity of the construction relies on a computer program that (up to symmetries in their construction) exhaustively ....

....have conducted more experiments and these will be reported in a forthcoming full version of the paper. The linear programming problems are solved using the MINOS package [11] The contact constraints are computed by the algorithm described in [5] The first example, given by Snoeyink and Stolfi [14], consists of six identical tetrahedra in contact and shown in Figure 2. They proved that no proper subset is separable by infinitesimal translation. We revisit this example, confirm their result with our program, and show that if we allow general infinitesimal motion (i.e. including rotation) ....

[Article contains additional citation context not shown here]

J. Snoeyink and J. Stolfi, Objects that cannot be taken apart with two hands, Discrete and Computational Geometry, 12 (1994), pp. 367--384.

....2.3 Computational Geometry Assembly sequencing is an intriguing combination of a combinatorial and geometric problem. Quite naturally, research from computational geometry relates very closely to assembly sequencing. The separability of objects has been well studied in the geometric community [13, 14, 15, 23, 48, 49]. In a single direction, a depth order of a set of parts is an ordering of the parts which allows for collisionfree translations of the individual parts to infinity. A classic result states that given a collection of convex shapes in two dimensions, for any translational direction there exists ....

.... , there exists at least d 1 balls, each of which can be translated to infinity in some direction [13] However, there exists a set of convex parts in three dimensions which cannot be disassembled using two hands, with only translations to infinity, or even generalized rotations and translations [48]. A surprising element of our problem is that the general lower bounds given in Section 8, are realized in Section 9, for a simple geometric setting consisting of a collection of unit disks in the plane. More often than not, an optimization problem becomes significantly easier when its input is ....

J. Snoeyink and J. Stolfi. Objects that cannot be taken apart with two hands. In Proc. ACM Symp. on Computational Geometry, pages 247--256, 1993.

....of detail [74] Courtesy of Randy Wilson. Description: A model aircraft engine, modeled with varying levels of detail [74] Courtesy of Randy Wilson. Description: Snoeyink and Stolfi describe a model of a 30 part assembly of convex parts in three dimensions, for which there is no legal separation [70]. We have deleted one of the pieces to provide an interesting model that may be disassembled. Courtesy of Jack Snoeyink. File jP j jF j bell9 9 5 bell17 17 5 bell22 22 5 eng12 12 5 eng23 23 12 eng30 30 13 eng42 42 13 sno29 29 1250 4.5.2 Experiment Setup In our experiments, we consider two ....

J. Snoeyink and J. Stolfi. Objects that cannot be taken apart with two hands. In Proc. ACM Symp. on Computational Geometry, pages 247--256, 1993.

....a two handed assembly sequence of translations, but with a three handed sequence of translations. Every assembly of five or fewer convex polyhedra admits a two handed assembly sequence of translations. There exists an assembly of thirty convex polyhedra that cannot be assembled with two hands [SS94] COMPLEXITY OF ASSEMBLY SEQUENCING When arbitrary sequences are allowed, assembly sequencing is PSPACE hard. The problem remains PSPACE hard even when the bodies are polygons, each with constant number of vertices [Nat88] When only two handed monotone sequences are permitted, deciding if an ....

J. Snoeyink and J. Stolfi. Objects that cannot be taken apart with two hands. Discrete Comput. Geom., 12:367--384, 1994.

.... Wilson [13] presents algorithms to partition assemblies of polyhedra, where the separating motions are either infinite translations or infinitesimal rigid motions (the latter identifying a superset of the removable subassemblies for general separating motions) Interestingly, Snoeyink and Stolfi [11] present an assembly of convex polyhedra that cannot be partitioned. Other related geometric separation problems are studied in [3, 8, 9, 12] In this paper we show that the partitioning problem for polygons in the plane is NP complete. Our proof extends to some interesting variants of the ....

J. Snoeyink and J. Stolfi, "Objects that cannot be taken apart with two hands", Proc. of the 9th ACM Symp. on Computational Geometry, pp. 247-256, 1993.

....Computational Geometry. Assembly sequencing is an intriguing combination of a combinatorial and geometric problem. Quite naturally, research from computational geometry relates very closely to assembly sequencing. The separability of objects has been well studied in the geometric community [8 10,20,41,42]. In a single direction, a depth order of a set of parts is an ordering of the parts which allows for collision free translations of the individual parts to infinity. A classic result states that given a collection of convex shapes in two dimensions, for any translational direction there exists ....

.... unit disks in the plane for which the removal of a certain disk may require the prior removal of# (n) other disks [21] Also, there exists a set of convex parts in three dimensions which cannot be disassembled using two hands, with only translations, or even generalized rotations and translations [41]. A surprising element of our problem is that the general lower bounds can be realized for a simple geometric setting consisting of a collection of unit disks in the plane. More often than not, an optimization problem becomes significantly easier when its input is restricted to a geometric ....

J. Snoeyink and J. Stolfi. Objects that cannot be taken apart with two hands. In Proc. ACM Symp. on Computational Geometry, pages 247--256, 1993.

....Computational Geometry. Assembly sequencing is an intriguing combination of a combinatorial and geometric problem. Quite naturally, research from computational geometry relates very closely to assembly sequencing. The separability of objects has been well studied in the geometric community [8 10,20,41,42]. In a single direction, a depth order of a set of parts is an ordering of the parts which allows for collision free translations of the individual parts to infinity. A classic result states that given a collection of convex shapes in two dimensions, for any translational direction there exists ....

.... disks in the plane for which the removal of a certain disk may require the prior removal of Omega (n) other disks [21] Also, there exists a set of convex parts in three dimensions which cannot be disassembled using two hands, with only translations, or even generalized rotations and translations [41]. A surprising element of our problem is that the general lower bounds can be realized for a simple geometric setting consisting of a collection of unit disks in the plane. More often than not, an optimization problem becomes significantly easier when its input is restricted to a geometric ....

J. Snoeyink and J. Stolfi. Objects that cannot be taken apart with two hands. In Proc. ACM Symp. on Computational Geometry, pages 247--256, 1993.

....control panel of GASP allows us to fast forward over these initial fragments to get to the section of interest. Single stepping through the section under consideration and rewinding are also highly valuable tools. B. Objects that Cannot be Taken Apart with Two Hands This animation is based on [26]. This paper shows a configuration of six tetrahedra that cannot be taken apart by translation with two hands (Fig. 5) Then, it presents a configuration of thirty objects that cannot be taken apart by applying an isometry to any proper subset (Fig. 6) The ASCII data of the configurations was ....

J. Snoeyink and J. Stolfi. Objects that cannot be taken apart with two hands. In The Ninth Annual ACM Sym- 16 posium on Computational Geometry, pages 247--256, May 1993.

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Snoeyink, J. and Stolfi, J., Objects that Cannot be Taken Apart with Two Hands, Proc. 9th ACM Symp. on Computational Geometry, 247-256, 1993.

No context found.

J. Snoeyink and J. Stolfi. Objects that cannot be taken apart with two hands. In Proc. of the 9th ACM Symp. on Computational Geometry, 1993.

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J. Snoeyink and J. Stolfi, "Objects that cannot be taken apart with two hands," in Proc. Ninth Annual Symp. on Computational Geometry, San Diego, California, May 1993, pp. 247--256.

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