J. S. Chang and C. K. Yap. A polynomial solution for the potato-peeling problem. Discrete Comput. Geom., 1:155--182, 1986.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....polygons. For each polygon in the tree, the algorithm generates (an approximation to) the largest area convex subset. These convex subsets form the set icc(P i ) The largest convex subset problem is called the potato cutting problem , and the fastest theoretical algorithm runs in time O(n 7 ) [5]. Since this algorithm is very complicated and may be impractical to implement, we use the following approximate algorithm for the potato cutting problem. The largest area convex subset can be generated as follows: for each concave chain of the input polygon, construct a cut which is an internal ....

J.S. Chang, C.K. Yap, A polynomial solution for the potato-peeling problem, Discrete Comput. Geom. 1 (1986) 155--182.

....task. For instance, the potatopeeling problem (a.k.a. the convex skull problem) consists in computing the largest convex contained in a given n vertex object. It has been studied both in 2D and 3D with several convex shapes. Arbitrary convex shapes lead to prohibitive solutions even in 2D cases [5]. Better solutions are known for restricted convex objects. The axis parallel rectangle of largest area inside a general polygon can be found in O(n log 2 n) time [10] the same bound holds for orthogonal polygons [16] unless further constraints such as orthogonally convexity are met. In three ....

J. S. Chang and C. K. Yap. A polynomial solution for the potato-peeling problem. Discrete & Computational Geometry, 1:155--181, 1986.

....4 item stacks of pants panels for layouts in apparel manufacturing. In computational geometry, algorithmic work appears on various types of enclosure problems for single items. Finding a minimal enclosure for a single polygon can also be viewed as a polygon approximation problem, as noted in [CY86]. Chang and Yap define inclusion and enclosure problems [CY86] They define an enclosure problem as follows: Enc(P, Q, Given P 2 P, find the smallest Q 2 Q that encloses P , where P and Q are families of polygons, and is a real function on polygons such that: 8Q; Q 0 2 Q; Q 0 Q ) Q ....

....In computational geometry, algorithmic work appears on various types of enclosure problems for single items. Finding a minimal enclosure for a single polygon can also be viewed as a polygon approximation problem, as noted in [CY86] Chang and Yap define inclusion and enclosure problems [CY86]. They define an enclosure problem as follows: Enc(P, Q, Given P 2 P, find the smallest Q 2 Q that encloses P , where P and Q are families of polygons, and is a real function on polygons such that: 8Q; Q 0 2 Q; Q 0 Q ) Q 0 ) Q) Chang and Yap [CY86] review work on a variety of ....

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J.S. Chang and C.K. Yap. A Polynomial Solution for the Potato-peeling Problem. Discrete and Computational Geometry, 1:155--182, 1986.

....Supported by NSF grants CCR 89 02500 and CCR 92 00884 and by DARPA AFOSR F4962 92 J 0466. 1 Introduction The problem of finding the Largest area axis parallel Rectangle (LR) inside a general polygon 1 of n vertices is a geometric optimization problem in the class of polygon inclusion problems [8]. Define Inc(P; Q; Given P 2 P, find the largest Q 2 Q inside P , where P and Q are families of polygons, and is a real function on polygons such that: 8Q; Q 0 2 Q; Q 0 Q ) Q 0 ) Q) Our problem is an inclusion problem where Q is the set of axis parallel rectangles, P is the ....

J. S. Chang and C. K. Yap. A Polynomial Solution for the Potato-peeling Problem. Discrete and Computational Geometry, 1:155--182, 1986.

....2 n) for general polygons with holes. Keywords: Rectangles, geometric optimization 1 Introduction The problem of finding the maximum area axis parallel rectangle (MAAPR) inside a general polygon 1 of n vertices is a geometric optimization problem in the class of polygon inclusion problems [10]: Inc(P; Q; Given P 2 P, find the largest Q 2 Q inside P , where P and Q are families of polygons, and is a real function on polygons such that: 8P 2 P; Q 2 Q;P Q ) P ) Q) Our problem is an inclusion problem where Q is the set of axis parallel rectangles, P is the set of polygons, ....

J.S.Chang and C.K. Yap. A Polynomial Solution for the Potato-peeling Problem. Discrete Computational Geometry, 1:155--182, 1986.

....University, supported by NSF grant CCR 92 00884 and by DARPA AFOSR F4962 92 J 0466. 1 Introduction The problem of finding the Largest area axis parallel Rectangle (LR) inside a general polygon 1 of n vertices is a geometric optimization problem in the class of polygon inclusion problems [7]. Define Inc(P; Q; Given P 2 P, find the largest Q 2 Q inside P , where P and Q are families of polygons, and is a real function on polygons such that: 8Q; Q 0 2 Q; Q 0 Q ) Q 0 ) Q) Our problem is an inclusion problem where Q is the set of axis parallel rectangles, P is the ....

J. S. Chang and C. K. Yap. A Polynomial Solution for the Potato-peeling Problem. Discrete and Computational Geometry, 1:155--182, 1986.

....be tight by proving an Omega Gamma n log n) lower bound. We also consider the unrestricted monotone hull problem, which we solve in O(nq(n) time, where q(n) is the time needed to find the roots of two polynomial equations in two unknowns with degrees 2 and O(n) Related Work. Chang and Yap [3, 4] have studied optimization problems for inclusion and enclosure problems, and have obtained polynomial time algorithms for finding a maximum area convex subset of a polygon, a minimum area enclosing convex k gon, and a minimum enclosing k gon of a fixed shape. Other convex optimal enclosure ....

J. S. Chang and C. K. Yap. A polynomial solution for the potato-peeling problem. Discrete Comput. Geom., 1:155--182, 1986.

....polygons. For each polygon in the tree, the algorithm generates (an approximation to) the largest area convex subset. These convex subsets form the set icc(P i ) The largest convex subset problem is called the potato cutting problem, and the fastest theoretical algorithm runs in time O(n 7 ) [4]. Since this algorithm is very complicated and may be impractical to implement, we use the following approximate algorithm for the potato cutting problem. The largest area convex subset can be generated as follows: for each concave chain of the input polygon, construct a cut which is an internal ....

J. S. Chang and C. K. Yap. A polynomial solution for the potato-peeling problem. Discrete Comput. Geom., 1:155--182, 1986.

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J. S. Chang and C. K. Yap. A polynomial solution for the potato-peeling problem. Discrete Comput. Geom., 1:155--182, 1986.

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