Ahn, H.-K., de Berg, M., Bose, P., Cheng, S.-W., Halperin, D., Matousek, J., and Schwarzkopf, O., 2002. "Separating an object from its cast". Computer-Aided Design, 34 , pp. 547--59.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....of genus 0. Related Work There has been a variety of work in the area of algorithmic study of manufacturing processes; see the survey by Bose and Toussaint [7] In particular, there has been algorithmic study of the problems of injection [8, 10, 16] NC machining of pockets [14] gravity casting [2, 6], and stereolithography [5] Rosenbloom and Rappaport [16] give an O(n) time algorithm to decide if a simple polygon having n vertices can have its boundary partitioned in two monotone chains (which is necessary and sufficient for castability in two dimensions) In three dimensions, Bose et al. ....

....give an algorithm requiring O(n 3=2 ffl ) time and space or O(n 2 log n) time and O(n) space to determine if a given polyhedral model is castable, and, if so, to compute a plane that cuts the cast. The assumption that the cast must be cut in two by a plane is removed in the work of Ahn et al. [2], who consider the problem of determining if there is a direction d, and a way to cut the cast in two along some closed curve, so that the two pieces of the cast can be removed without collisions in directions Sigmad. The first algorithmic analysis of the stereolithography process was done by ....

H.-K. Ahn, M. de Berg, P. Bose, S.-W. Cheng, D. Halperin, J. Matousek, and O. Schwarzkopf. Separating an object from its cast. In Proc. 13th Annu. ACM Sympos. Comput. Geom., pages 221--230, 1997.

.... in many instances, including polyhedral assembly with infinitesimal rigid motion [193] see also [206, 207] Other problems in robotics that have exploited arrangements include fixturing [298] MEMS (micro electronic mechanical systems) 75] path planning with uncertainty [124] and manufacturing [29]. 14.6 Molecular modeling In the introduction, we described the Van der Waals model, in which a molecule M is represented as a collection Gamma of spheres in R 3 . See [120, 140, 266] for other geometric models of molecules. Let Sigma = S Gamma) Sigma is called the surface of M . ....

H.-K. Ahn, M. de Berg, P. Bose, S.-W. Cheng, D. Halperin, J. Matousek, and O. Schwarzkopf, Separating an object from its cast, Proc. 13th Annu. ACM Sympos. Comput. Geom., 1997, pp. 221--230. Arrangements May 26, References 62

....to take into account other factors such as heat flow and how air can evade from the cavity. This problem has been studied by Bose, Bremner, and van Kreveld [3] who considered the sand casting model relevant in iron casting, where the two cast parts have to be separated by a plane. Ahn et al. [2] gave, to our knowledge, the first complete algorithm to determine the castability of polyhedral parts for cast removal as we described above, under the assumption that the two cast parts have to be removed in opposite directions. This restriction is true for current casting machinery, and we will ....

.... A motion planning model with directional uncertainty was perhaps first proposed by Lozano Perez, Mason and Taylor [9] An extensive treatment of motion planning with directional uncertainty is given in the book by Latombe [8] We generalize the characterization of castable polyhedra by Ahn et al. [2] to incorporate uncertainty in the directions in which the cast parts are removed. A formal definition of our model is given in Section 2. It turns out that one of the main difficulties is to guarantee that the two cast parts are polyhedral while this is trivial in the exact case, it requires ....

[Article contains additional citation context not shown here]

H.-K. Ahn, M. de Berg, P. Bose, S.-W. Cheng, D. Halperin, J. Matousek, and O. Schwarzkopf. Separating an object from its cast. In Proc. 13th Annu. ACM Sympos. Comput. Geom., pages 221--230, 1997.

.... In space, it has been suggested that the same approach be used to define pockets in a search for casting directions [2] but in fact the difference between a polyhedron and its convex hull need not have a natural decomposition, and may have more complicated topology than the original polyhedron [1]. We propose a reflex free hull, defined as an intersection of reflex free sets. Section 2 defines the reflex free sets and plane cavities, which may be seen as analogues to bays in polygons. Section 3 defines the reflex free hull, Rfh, and Section 4 establishes some basic results about the Rfh ....

....at reflex edges. Figure 2 illustrates one example in which filling cavities must be taken to the limit to attain the reflex free hull. a b g d Figure 2: Each filling step creates reflex and saddle points Start with the cube [ 5,5] 3 and subtract the following sets: x,y,z) x # [ 1,1],z y , x,y,z) x # [1, 3] z y x 1 , x,y,z) x # [3, 5] z y 2 1 , and (x,y,z) x # [ 3, 5] z y 2 1 , to obtain an object illustrated in Figure 2. There are four labeled lines that are relevant in this example. We parameterize them by z. Two are pivots, #(z) ....

[Article contains additional citation context not shown here]

H.-K. Ahn, M. de Berg, P. Bose, S.-W. Cheng, D. Halperin, J. Matou sek, and O. Schwarzkopf. Separating an object from its cast. In Proc. 13th Annu. ACM Sympos. Comput. Geom., pages 221--230, 1997.

.... In space, it has been suggested that the same approach be used to define pockets in a search for casting directions [3] but in fact the difference between a polyhedron and its convex hull need not have a natural decomposition, and may have more complicated topology than the original polyhedron [1]. We propose a reflex free hull, defined as an intersection of reflex free sets. Section 2 defines the reflexfree sets and plane cavities, which may be seen as analogues to bays in polygons. Section 3 defines the reflex free hull, Rfh, and Section 4 establishes some basic results about the Rfh of ....

....at reflex edges. Figure 4 illustrates one example in which filling cavities must be taken to the limit to attain the reflex free hull. 8 Start with the cube [ 5,5] 3 and subtract the following sets: x,y,z) a b g d Figure 4: Each filling step creates reflex and saddle points x # [ 1,1],z y , x,y,z) x # [1, 3] z y x 1 , x,y,z) x # [3, 5] z y 2 1 , and (x,y,z) x # [ 3, 5] z y 2 1 , to obtain an object illustrated in Figure 4. There are four labeled lines that are relevant in this example. We parameterize them by z. Two lines ....

[Article contains additional citation context not shown here]

H.-K. Ahn, M. de Berg, P. Bose, S.-W. Cheng, D. Halperin, J. Matou sek, and O. Schwarzkopf. Separating an object from its cast. In Proc. 13th Annu. ACM Sympos. Comput. Geom., pages 221--230, 1997.

....Bose et al. 4] considered a special model of casting, the sand casting model, where the partition of the cast into two parts must be done by a plane. The first complete algorithm to determine the castability of polyhedral parts for opposite directional cast removal was proposed by Ahn et al. [2]. All the results for opposite cast parts removal in [2, 8, 9] rely on the property that an object is castable if its boundary surface is completely visible from the two opposite removal directions. This is not true when the removal directions are non opposite: there are polyhedra whose whole ....

....the sand casting model, where the partition of the cast into two parts must be done by a plane. The first complete algorithm to determine the castability of polyhedral parts for opposite directional cast removal was proposed by Ahn et al. 2] All the results for opposite cast parts removal in [2, 8, 9] rely on the property that an object is castable if its boundary surface is completely visible from the two opposite removal directions. This is not true when the removal directions are non opposite: there are polyhedra whose whole boundary is visible from the removal directions but which are not ....

[Article contains additional citation context not shown here]

H.K. Ahn, M. de Berg, P. Bose, S.W. Cheng, D. Halperin, J. Matousek, and O. Schwarzkopf. Separating an object from its cast. In Proc. 13th Annu. ACM Sympos. Comput. Geom., pages 221--230, 1997.

....they are not guaranteed to find a feasible cast. Bose et al. 5] considered a special model of casting, the sand casting model, where the partition of the cast into two parts must be done by a plane. Note that even convex polyhedra are not always castable in this model [5] Finally, Ahn et al. [2] gave, to our knowledge, the first complete algorithm to determine the castability of polyhedral parts for opposite directional cast removal. Given a simple polyhedron with n vertices, they presented an O(n log n) time algorithm to compute castability in a given direction. They also presented an ....

....objects. We do not assume any special separability of the two cast parts, and allow parts of arbitrary genus. The running time of our algorithm for determining the castability of an object with a given pair of directions is O(n 3 log n) All the results for opposite cast parts removal in [2, 12, 13] rely on the property that an object is castable if its boundary surface is completely visible from the two opposite removal directions. This is not true when the removal directions are non opposite: there are polyhedra whose whole boundary is visible from the removal directions but which are ....

[Article contains additional citation context not shown here]

H.K. Ahn, M. de Berg, P. Bose, S.W. Cheng, D. Halperin, J. Matousek, and O. Schwarzkopf. Separating an object from its cast. In Proc. 13th Annu. ACM Sympos. Comput. Geom., 1997.

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Ahn, H.-K., de Berg, M., Bose, P., Cheng, S.-W., Halperin, D., Matousek, J., and Schwarzkopf, O., 2002. "Separating an object from its cast". Computer-Aided Design, 34 , pp. 547--59.

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