Browsing by Author "Ilinkin, Ivaylo"

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    A Decomposition-Based Approach to Layered Manufacturing
    (2000-10-10) Ilinkin, Ivaylo; Janardan, Ravi; Majhi, Jayanth; Schwerdt, Jörg; Smid, Michiel; Sriram, Ram
    This paper introduces a new approach for improving the performance and versatility of Layered Manufacturing (LM), which is an emerging technology that makes it possible to build physical prototypes of 3D parts directly from their CAD models using a relatively small and inexpensive "3D printer" attached to a personal computer. LM provides the designer with an additional level of physical verification that makes it possible to detect and correct design flaws that may have, otherwise, gone unnoticed in the virtual model.Current LM processes work by viewing the CAD model as a single, monolithic unit. By contrast, the approach proposed here decomposes the model into a small number of pieces, by intersecting it with a suitably chosen plane, builds each piece separately using LM, and then glues the pieces together to obtain the physical prototype. This approach allows large models to be built quickly in parallel and also lends itself naturally to applications where the model needs to be built as several pieces, such as in the manufacture of mold halves for injection molding. Furthermore, this approach is very efficient in its use of so-called support structures that are generated by the LM process.This paper presents the first provably correct and efficient geometric algorithms to decompose polyhedral models so that the support requirements (support volume and area of contact) are minimized. Algorithms based on the plane-sweep paradigm are first given for convex polyhedra. These algorithms run in O(n log n) time for n -vertex convex polyhedra and work by generating expressions for the support volume and contact-area as a function of the height of the sweep plane, and optimizing them during the sweep. Experimental results are given for randomly-generated convex polyhedra with up to 200,000 vertices. These algorithms are then generalized to non-convex polyhedra, which are considerably more difficult due to the complex structure of the supports. It is shown that, surprisingly, non-convex polyhedra can be handled by first identifying certain critical facets using a technique called cylindrical decomposition, and then applying the algorithm for convex polyhedra to these critical facets. The resulting algorithms run in O(n2log n) time.
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    Approximating Contact-Area of Supports in Layered Manufacturing
    (2004-01-05) Ilinkin, Ivaylo; Janardan, Ravi; Smid, Michiel; Johnson, Eric; Castillo, Paul; Schwerdt, Jörg
    Layered Manufacturing is a technology that allows physicalprototypes of three-dimensional models to be built directlyfrom their digital representation, as a stack of two-dimensional layers. A key design problem here is the choice of a suitable direction in which the digital model should be oriented and built so as to minimize the area of contact between the prototype and temporary support structures that are generated during the build. Devising an efficient algorithm for computing such a direction has remained a difficult problem for quite some time. In this paper, a suite of efficient and practical heuristics is presented for approximating the minimum contact-area. Also given is a technique for evaluating the quality of the approximation of any heuristic, which doesnot require knowledge of the (unknown and hard-to-compute) optimal solution; instead, it provides an indirect upper bound on the quality of the approximation via two relatively easy-to-compute quantities. The algorithms are based on various techniques from computational geometry, such as ray-shooting, convex hulls, boolean operations on polygons, and spherical arrangements, and have been implemented and tested. Experimental results on a wide range of real-world models show that the heuristics perform quite well in practice.