Relevant bibliographies by topics / Polygyni

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Polygyni'

Author: Grafiati
Published: 4 June 2021
Last updated: 6 February 2022

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Journal articles on the topic "Polygyni"

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Ross, Kenneth G., Michael J. B. Krieger, and D. DeWayne Shoemaker. "Alternative Genetic Foundations for a Key Social Polymorphism in Fire Ants." Genetics 165, no. 4 (December 1, 2003): 1853–67. http://dx.doi.org/10.1093/genetics/165.4.1853.

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Abstract Little is known about the genetic foundations of colony social organization. One rare example in which a single major gene is implicated in the expression of alternative social organizations involves the presumed odorant-binding protein gene Gp-9 in fire ants. Specific amino acid substitutions in this gene invariably are associated with the expression of monogyny (single queen per colony) or polygyny (multiple queens per colony) in fire ant species of the Solenopsis richteri clade. These substitutions are hypothesized to alter the abilities of workers to recognize queens and thereby regulate their numbers in a colony. We examined whether these same substitutions underlie the monogyny/polygyny social polymorphism in the distantly related fire ant S. geminata. We found that Gp-9 coding region sequences are identical in the polygyne and monogyne forms of this species, disproving our hypothesis that one or a few specific amino acid replacements in the protein are necessary to induce transitions in social organization in fire ants. On the other hand, polygyne S. geminata differs genetically from the monogyne form in ways not mirrored in the two forms of S. invicta, a well-studied member of the S. richteri clade, supporting the conclusion that polygyny did not evolve via analogous routes in the two lineages. Specifically, polygyne S. geminata has lower genetic diversity and different gene frequencies than the monogyne form, suggesting that the polygyne form originated via a founder event from a local monogyne population. These comparative data suggest an alternative route to polygyny in S. geminata in which loss of allelic variation at genes encoding recognition cues has led to a breakdown in discrimination abilities and the consequent acceptance of multiple queens in colonies.
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Bettinger, Pete, Gay A. Bradshaw, and George W. Weaver. "Effects of geographic information system vector–raster–vector data conversion on landscape indices." Canadian Journal of Forest Research 26, no. 8 (August 1, 1996): 1416–25. http://dx.doi.org/10.1139/x26-158.

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The effects of geographic information system (GIS) data conversion on several polygon-and landscape-level indices were evaluated by using a GIS vegetation coverage from eastern Oregon, U.S.A. A vector–raster–vector conversion process was used to examine changes in GIS data. This process is widely used for data input (digital scanning of vector maps) and somewhat less widely used for data conversion (output of GIS data to specific formats). Most measures were sensitive to the grid cell size used in the conversion process. At the polygon level, using the conversion process with grid cell sizes of 3.05, 6.10, and 10 m produced relatively small changes to the original polygons in terms of ln(polygon area), ln(polygon perimeter), and 1/(fractal dimension). When grid cell size increased to 20 and 30 m, however, polygons were significantly different (p < 0.05) according to these polygon-level indices. At the landscape level, the number of polygons, polygon size coefficient of variation (CV), and edge density increased, while mean polygon size and an interspersion and juxtaposition index (IJI) decreased. The youngest and oldest age-class polygons followed the trends of overall landscape only in terms of number of polygons, mean polygon size, CV, and IJI. One major side effect of the conversion process was that many small polygons were produced in and around narrow areas of the original polygons. An alleviation process (referred to as the dissolving process) was used to dissolve the boundaries between similarly attributed polygons. When we used the dissolving process, the rate of change for landscape-level indices slowed; although the number of polygons and CV still increased with larger grid cell sizes, the increase was less than when the dissolving process was not used. Mean polygon size, edge density, and fractal dimension decreased after use of the dissolving process. Trends for the youngest and oldest age-class polygons were similar to those for the total landscape, except that IJI was greater for these age-classes than for the total landscape.
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Gau, Y. David, and Lindsay A. Tartre. "The Sidesplitting Story of the Midpoint Polygon." Mathematics Teacher 87, no. 4 (April 1994): 249–56. http://dx.doi.org/10.5951/mt.87.4.0249.

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Understanding what area means and learning ways to calculate the area of various figures are important objectives in geometry. Students as adults will use concepts related to finding areas of polygons in many contexts, such as finding the area of their backyard or knowing how much wallpaper is needed to cover a wall in their dining room. One context for exploring area relationships is comparing the area of a polygon to the area of its associated midpoint polygon, formed by joining the midpoints of consecutive sides of the original polygon. This article describes activities that examine the patterns and relationships between the areas of polygons and those of their associated midpoint polygons for triangles, quadrilaterals, pentagons, and other polygons. We shall also look at the pattern for regular polygons.
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BLACHE, RÉGIS. "NEWTON POLYGONS FOR CHARACTER SUMS AND POINCARÉ SERIES." International Journal of Number Theory 07, no. 06 (September 2011): 1519–42. http://dx.doi.org/10.1142/s1793042111004368.

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In this paper, we precise the asymptotic behavior of Newton polygons of L-functions associated to character sums, coming from certain n variable Laurent polynomials. In order to do this, we use the free sum on convex polytopes. This operation allows the determination of the limit of generic Newton polygons for the sum Δ = Δ1⊕Δ2 when we know the limit of generic Newton polygons for each factor. To our knowledge, these are the first results concerning the asymptotic behavior of Newton polygons for multivariable polynomials when the generic Newton polygon differs from the combinatorial (Hodge) polygon associated to the polyhedron.
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Bernabeu, Melania, Salvador Llinares, and Mar Moreno. "Levels of Sophistication in Elementary Students’ Understanding of Polygon Concept and Polygons Classes." Mathematics 9, no. 16 (August 17, 2021): 1966. http://dx.doi.org/10.3390/math9161966.

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This paper reports sophistication levels in third grade children’s understanding of polygon concept and polygon classes. We consider how children endow mathematical meaning to parts of figures and reason to identify relationships between polygons. We describe four levels of sophistication in children’s thinking as they consider a figure as an example of a polygon class through spatial structuring (the mental operation of building an organization for a set of figures). These levels are: (i) partial structuring of polygon concept; (ii) global structuring of polygon concept; (iii) partial structuring of polygon classes; and (iv) global structuring of polygon classes. These levels detail how cognitive apprehensions, dimensional deconstruction, and the use of mathematical language intervene in the mental process of spatial structuring in the understanding of the classes of polygons.
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Wu, San-Yuan, and Sartaj Sahni. "Fast Algorithms to Partition Simple Rectilinear Polygons." VLSI Design 1, no. 3 (January 1, 1994): 193–215. http://dx.doi.org/10.1155/1994/16075.

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Two algorithms to partition hole-free rectilinear polygons are developed. One has complexity ∼ O(kn) and the other O(n log k) where n is the number of vertices in the polygon and k is the smaller of the number of vertical and horizontal inversions of the polygon, k is a measure of the simplicity of a polygon. Since k is small for most practical polygons, our algorithms are fast in practice. Experimental results comparing our algorithms with that of Imai and Asano [1] are also presented.
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AICHHOLZER, OSWIN, THOMAS HACKL, MATIAS KORMAN, ALEXANDER PILZ, and BIRGIT VOGTENHUBER. "GEODESIC-PRESERVING POLYGON SIMPLIFICATION." International Journal of Computational Geometry & Applications 24, no. 04 (December 2014): 307–23. http://dx.doi.org/10.1142/s0218195914600097.

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Polygons are a paramount data structure in computational geometry. While the complexity of many algorithms on simple polygons or polygons with holes depends on the size of the input polygon, the intrinsic complexity of the problems these algorithms solve is often related to the reflex vertices of the polygon. In this paper, we give an easy-to-describe linear-time method to replace an input polygon [Formula: see text] by a polygon [Formula: see text] such that (1) [Formula: see text] contains [Formula: see text], (2) [Formula: see text] has its reflex vertices at the same positions as [Formula: see text], and (3) the number of vertices of [Formula: see text] is linear in the number of reflex vertices. Since the solutions of numerous problems on polygons (including shortest paths, geodesic hulls, separating point sets, and Voronoi diagrams) are equivalent for both [Formula: see text] and [Formula: see text], our algorithm can be used as a preprocessing step for several algorithms and makes their running time dependent on the number of reflex vertices rather than on the size of [Formula: see text]. We describe several of these applications (including linear-time post-processing steps that might be necessary).
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Wang, Chao, and Zhongzi Wang. "The limit shapes of midpoint polygons in ℝ3." Journal of Knot Theory and Its Ramifications 28, no. 10 (September 2019): 1950062. http://dx.doi.org/10.1142/s0218216519500627.

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For a polygon in the [Formula: see text]-dimensional Euclidean space, we give two kinds of normalizations of its [Formula: see text]th midpoint polygon by a homothetic transformation and an affine transformation, respectively. As [Formula: see text] goes to infinity, the normalizations will approach “regular” polygons inscribed in an ellipse and a generalized Lissajous curve, respectively, where the curves may be degenerate. The most interesting case is when [Formula: see text], where polygons with all its [Formula: see text]th midpoint polygons knotted are discovered and discussed. Such polygonal knots can be seen as a discrete version of the Lissajous knots.
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Verheyen, H. F. "A Single Die-Cut Element for Transformable Structures." International Journal of Space Structures 8, no. 1-2 (April 1993): 127–34. http://dx.doi.org/10.1177/0266351193008001-213.

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Any polyhedral structure composed of identical regular polygons can be turned into an expandable structure by replacing the polygons by pairs of polygons which can rotate about a common central hinge, and connecting a vertex of an upper polygon with the vertex of a lower polygon of an adjacent pair. Most of these structures will collapse in the fully expanded position by losing their rigidity near the final stage, and hence, become deployable. A triangular element which enables one to assemble and dismantle such structures is presented here, together with a series of examples of experimental shapes.
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MELKEMI, MAHMOUD, FREDERIC CORDIER, and NICKOLAS S. SAPIDIS. "A PROVABLE ALGORITHM TO DETECT WEAK SYMMETRY IN A POLYGON." International Journal of Image and Graphics 13, no. 01 (January 2013): 1350002. http://dx.doi.org/10.1142/s0219467813500022.

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This paper deals with the problem of detecting "weak symmetry" in a polygon, which is a special bijective and continuous mapping between the vertices of the given polygon. An application of this work is the automatic reconstruction of 3D polygons symmetric with respect to a plane from free-hand sketches of weakly-symmetric 2D polygons. We formalize the weak-symmetry notion and highlight its many properties which lead to an algorithm detecting it. The closest research work to the proposed approach is the detection of skewed symmetry. Skewed symmetry detection deals only with reconstruction of planar mirror-symmetric 3D polygons while our method is able to identify symmetry in projections of planar as well as nonplanar mirror-symmetric 3D polygons.
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Dissertations / Theses on the topic "Polygyni"

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Hambert, Malin. "”En fru är ett problem, två fruar är två problem” : synen på polygyni bland unga ogifta män i Gambia." Thesis, Stockholm University, Department of Social Work, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-7264.

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Studien syftar till att undersöka attityderna kring polygyni bland unga ogifta män i Gambia. Kvalitativa enskilda intervjuer har utförts på män i landets stadsområden, och svaren har sedan analyserats utifrån ett socialkonstruktivistiskt perspektiv. Resultatet påvisar att polygyni har många negativa aspekter och inte alltid är frivilligt, ens för männen. Det indikerar även att traditionen håller på att avta i landets urbana delar. Attityderna förändras och polygyni anses, av många, vara ett problem mer än ett privilegium. Studien är relevant för socialarbetare och andra yrkesgrupper som arbetar med människor, speciellt de som arbetar internationellt i länder där liknande familjestrukturer är vanliga.

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Burn, Joseph L. "Polygyny and the wren." Thesis, University of Oxford, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.360161.

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Mora, Frédéric. "Visibilité polygone à polygone : calcul, représentation, applications." Phd thesis, Université de Poitiers, 2006. http://tel.archives-ouvertes.fr/tel-00090127.

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Cette thèse aborde le problème du calcul et de la représentation de la visibilité mutuelle de polygones. Elle montre tout le potentiel et l'intérêt de cette information pour la résolution de problèmes difficiles en synthèse d'images et en propagation électromagnétique.
Nous proposons un nouvel algorithme pour calculer la visibilité dans l'espace de Plücker, afin de minimiser les coûts en temps et mémoire vis-à-vis des précédentes approches.
En synthèse d'images, nous utilisons l'information ainsi calculée pourproposer une nouvelle solution au calcul analytique des ombres douces en illumination directe. Cette solution concilie la qualité et la rapidité du rendu.
En propagation électromagnétique, nous proposons l'optimisation sans perte d'un modèle basé rayons. Celle-ci permet d'effectuer des simulations dont la précision est optimale tout en s'appliquant à des environnements de tailles significatives.
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Mora, Frédéric. "Visibilité polygone à polygone : calcul, représentation, application." Poitiers, 2006. http://www.theses.fr/2006POIT2292.

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Cette thèse aborde le problème du calcul et de la représentation de la visibilité mutuelle de polygones. Elle montre tout le potentiel et l'intérêt de cette information pour la résolution de problèmes difficiles en synthèse d'images et en propagation électromagnétique. Nous proposons un nouvel algorithme pour calculer la visibilité dans l'espace de Plücker, afin de minimiser les coûts en temps et mémoire vis-à-vis des précédentes approches. En synthèse d'images, nous utilisons l'information ainsi calculée pour proposer une nouvelle solution au calcul analytique des ombres douces en illumination directe. Cette solution concilie la qualité et la rapidité du rendu. En propagation électromagnétique, nous proposons l'optimisation sans perte d'un modèle basé rayons. Celle-ci permet d'effectuer des simulations dont la précision est optimale tout en s'appliquant à des environnements de tailles significatives
This thesis addresses the visibility computation between two polygons and its representation. We bring up the potential of this information to solve difficult problems in image synthesis and in electromagnetic waves propagation. We present a new algorithm for the visibility computation in the Plücker space. In comparison to previous methods, it reduces the time computation and the memory requirements. In image synthesis, we use the computed information to design a new solution for the analytic computation of soft shadows. This solution is both accurate and fast in comparison with stochastic approaches. In electromagnetic waves propagation, we present the first ray based model optimisation without path lost. This optimisation allows to perform accurate simulations on significant environments
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Bretschneider, Peter. "Polygyny : a cross-cultural study /." Stockholm : Almqvist & Wiqsell, 1995. http://catalogue.bnf.fr/ark:/12148/cb36960460z.

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Tami, Abdelkader. "Etude d'un problème pour le bilaplacien dans une famille d'ouverts du plan." Thesis, Aix-Marseille, 2016. http://www.theses.fr/2016AIXM4362/document.

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L’objet de cette thèse est l’étude du problème Δ 2uω = fω avec les conditions aux limites Uω = Δ uω = 0, le second membre étant supposé dépendre continûment de ω dans L2(ω), où ω = {(r, θ); 0 < r < 1, 0 < θ < ω} , 0 < ω ≤ π, est une famille de secteurs tronqués du plan. Si ω < π on sait d’après Blum et Rannacher (1980) que la solution de ce problème uω se décompose au voisinage de l’origine en uω = u1,ω + u2,ω + u3,ω, (1) où u1,ω, u2,ω sont les parties singulières de uω et u3,ω la partie régulière. En effet, au voisinage de l’origine u1,ω (resp. u2,ω, u3,ω) est de régularité H1+πω−ǫ (resp. H2+πω−ǫ, H4) pour tout Q > 0, tandis que la solution uπ appartient, au moins au voisinage de l’origine, à l’espace H4(π), où π est le demi-disque supérieur de centre 0 et de rayon r = 1. On voit clairement une résolution de la singularité près de l’angle π dont la description est l’objectif principal de ce travail. Le résultat obtenu est que la décomposition (1) de uω est uniforme par rapport à ω, lorsque ω → π, pour les meilleures topologies possibles pour chacun des termes, et converge terme à terme vers le développement limité de uπ au voisinage de 0
In this work, we study the family of problems Δ 2uω = fω with boundary conditionuω = Δ uω = 0. There, the second member is assumed to depend smoothly on ω in L2(ω), where ω = {(r, θ); 0 < r < 1, 0 < θ < ω} , 0 < ω ≤ π, is a family of truncated sectors of the plane. If ω < π it is known from Blum et Rannacher (1980) that the solution uω decomposes as uω = u1,ω + u2,ω + u3,ω, (1) where u1,ω, u2,ω are singular and u3,ω is regular. Indeed, near the origin, u1,ω(resp. u2,ω, u3,ω) is of regularity H1+πω−ǫ (resp. H2+πω−ǫ, H4) for every Q > 0, while the solution uπ is, in the neighborhood of the origin again, of regularity H4. One clearly sees a resolution of the singularity near the angle π whose descriptionis the main objective of this work. The obtained result is that there exists a decomposition (1) of uω which is uniform with respect to ω, when ω → π, with the best possible topologies for each term, and which term by term convergestowards the Taylor expansion of uπ near 0
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Soares, Benedict J. "Polynomial generated polygons." Thesis, University of St Andrews, 1999. http://hdl.handle.net/10023/14198.

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A turtle geometric construction on the plane, called a polynomial generated polygon (PGP) and represented by Pf,pm, is generated from the sequence obtained from evaluating f(x) ∈ Z[x] over Z modulo pm where p is a prime and m ∈ N. Computational methods are developed to pre-calculate the symmetries exhibited by Pf,pm for a given f and pm. These include procedures to find whether Pf,pm is bounded or unbounded, the degree of rotational symmetry present, whether lines of reflectional symmetry can be observed, and in the case of Pf,pm unbounded, whether the PGP has a glide reflection. Methods are also sought to find a suitable f and pm to produce a desired 'feasible' shape in a PGP construction, and how the same shape might be generated modulo pm+k if it cannot be produced modulo pm.
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Kubica, Matěj. "Optický polygon." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2021. http://www.nusl.cz/ntk/nusl-442372.

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Diploma thesis focuses on a problematics of an optical networks in terms of an optical cables laying and a work with individual fibers. Thesis contains an basic physical properties which are used in a fiber optics. Methodology of correct working procedures used in fiber optics is discussed at the same time. Thesis also contains detailed documentation of realized optical connections including scheme of realized outdoor connection. 3D design of an rack case is also part of the thesis. Rack case provides an option to simulate plenty of different lengths of optical routes. Rack case is designed in 6U variant.
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Rafique, Emran Carleton University Dissertation Computer Science. "On asymptotic algorithms for approximating arbitrary polygons by simpler convex polygons." Ottawa, 1993.

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Shermer, Thomas C. "Visibility properties of polygons." Thesis, McGill University, 1989. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=74241.

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In this thesis, we establish tight bounds on the maximum size of maximum hidden sets, minimum guard sets, and minimum partitions and covers of polygons, using link-visibility. These results unify and generalize the guard set results (and combinatorial method) of Chvatal and O'Rourke. Our method also provides tight bounds on independent and dominating sets in triangulation graphs, and almost-tight bounds on the size of hidden sets, guard sets, covers, and partitions of polygon exteriors. We also prove that, using link-visibility, the optimization problems of finding maximum hidden sets, minimum guard sets, or minimum covers are NP-hard.
Link-visibility is an extended notion of visibility arising from robotics and motion planning problems. Hidden sets are sets of points in a polygon such that no two points of the set are visible, and guard sets are sets such that each point of the polygon is visible to some point in the guard set. Both maximum hidden set sizes and minimum guard set sizes can be used as polygon shape complexity measures.
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Books on the topic "Polygyni"

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service), SpringerLink (Online, ed. Polygons, polyominoes and polycubes. Dordrecht: Springer, 2009.

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Pengelly, Helen. Polygons. Sydney(Australia): Ashton Scholastic, 1991.

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Polygons. New York: Crabtree Pub., 2011.

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Stienecker, David. Polygons. New York: Benchmark Books, 1997.

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Polygons. New York: PowerKids Press, 2007.

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Potts, Jeffrey Hal. The decomposition of an arbitrary three-dimensional planar polygon into a set of convex polygons. Monterey, California: Naval Postgraduate School, 1987.

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Tits, Jacques. Moufang Polygons. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002.

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Generalized polygons. Basel: Birkhäuser Verlag, 1998.

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Tits, Jacques, and Richard M. Weiss. Moufang Polygons. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-662-04689-0.

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van Maldeghem, Hendrik. Generalized Polygons. Basel: Birkhäuser Basel, 1998. http://dx.doi.org/10.1007/978-3-0348-8827-1.

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Book chapters on the topic "Polygyni"

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Bhatt, Indu. "Polygyny." In Encyclopedia of Animal Cognition and Behavior, 1–2. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-319-47829-6_1964-1.

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Frank, J. Howard, J. Howard Frank, Michael C. Thomas, Allan A. Yousten, F. William Howard, Robin M. Giblin-davis, John B. Heppner, et al. "Polygyny." In Encyclopedia of Entomology, 2991. Dordrecht: Springer Netherlands, 2008. http://dx.doi.org/10.1007/978-1-4020-6359-6_3047.

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Van Maldeghem, Hendrik. "Basic Concepts and Results." In Generalized Polygons, 1–47. Basel: Springer Basel, 1998. http://dx.doi.org/10.1007/978-3-0348-0271-0_1.

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Van Maldeghem, Hendrik. "Classical Polygons." In Generalized Polygons, 49–86. Basel: Springer Basel, 1998. http://dx.doi.org/10.1007/978-3-0348-0271-0_2.

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Van Maldeghem, Hendrik. "Coordinatization and Further Examples." In Generalized Polygons, 87–134. Basel: Springer Basel, 1998. http://dx.doi.org/10.1007/978-3-0348-0271-0_3.

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Van Maldeghem, Hendrik. "Homomorphisms and Automorphism Groups." In Generalized Polygons, 135–71. Basel: Springer Basel, 1998. http://dx.doi.org/10.1007/978-3-0348-0271-0_4.

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Van Maldeghem, Hendrik. "The Moufang Condition." In Generalized Polygons, 173–238. Basel: Springer Basel, 1998. http://dx.doi.org/10.1007/978-3-0348-0271-0_5.

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Van Maldeghem, Hendrik. "Characterizations." In Generalized Polygons, 239–303. Basel: Springer Basel, 1998. http://dx.doi.org/10.1007/978-3-0348-0271-0_6.

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Van Maldeghem, Hendrik. "Ovoids, Spreads and Self-Dual Polygons." In Generalized Polygons, 305–59. Basel: Springer Basel, 1998. http://dx.doi.org/10.1007/978-3-0348-0271-0_7.

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Van Maldeghem, Hendrik. "Projectivities and Projective Embeddings." In Generalized Polygons, 361–405. Basel: Springer Basel, 1998. http://dx.doi.org/10.1007/978-3-0348-0271-0_8.

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Conference papers on the topic "Polygyni"

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Miao, S., and D. Howard. "An Efficient Algorithm to Determine the Intersection of Simple Polygons for Robot Path Planning." In ASME 1996 Design Engineering Technical Conferences and Computers in Engineering Conference. American Society of Mechanical Engineers, 1996. http://dx.doi.org/10.1115/96-detc/mech-1014.

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Abstract This paper presents an efficient algorithm for determining the intersection of two simple polygons. The proposed algorithm is based on the idea of searching for the vertices of the intersection polygon vertex by vertex along the boundary in a clockwise direction. This method finds the intersection polygon vertices and their order in one pass. The algorithm almost eliminates the need for testing whether candidate vertices are inside both polygons and the sorting stage is no longer needed.
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Yim, Soonkyu, and Hae Chang Gea. "Local Polygon Reduction for Voxel-Based Modeling." In ASME 2002 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2002. http://dx.doi.org/10.1115/detc2002/cie-34480.

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In voxel-based modeling systems, shapes of objects are visualized in terms of many tiny polygons. Because these excessive polygons deteriorate the interactive visualization performance, a grid-dependent local polygon reduction method is developed in this paper. Instead of processing the entire polygons altogether in the reduction process, these polygons are divided into many subgroups and reduced separately. This method has the advantages of having faster computational speed and providing local editing functions. The relations of native voxel data and sub-regions for local reduction are discussed. The partial surface editing function is also presented.
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Rico M., José María, Victor Gallegos J., and Joseph Duffy. "Screw Polygons, Finite Screws, and Biquaternions." In ASME 1998 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/detc98/mech-5892.

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Abstract In this contribution, the close relationship between screw polygons, finite screws, and biquaternions is elucidated. Further, it is shown that a reinterpretation of screw polygon problems in terms of biquaternions leads to a simple and straightforward solution of the direct problem of screw polygons. Moreover, the reintrepretation allows a simple solution of a pair of types of the inverse problem of screw polygons. As indicated by Mavroidis and Roth, these latter problems had not been previously reported in the literature.
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Bai, Guochao, Shimin Wei, Duanling Li, Qizheng Liao, and Xianwen Kong. "A Novel Synthesis Method of Polygon-Scaling Mechanisms." In ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/detc2014-34934.

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A polygon-scaling mechanism is a single DOF (degree-of-freedom) mechanism for scaling a polygon. This paper presents a tetragon-elements based synthesis method of polygon-scaling mechanisms. According to movable conditions of radial scaling elements, four basic tetragon elements (rhombus element, parallelogram element, kite element and general tetragon element) are proposed. For a given polygon, these four types of elements can be selected based on the characteristics of target polygons to construct polygon-scaling mechanisms in a straightforward manner. Using this synthesis method, some planar 1-DOF scaling mechanisms are obtained with the characteristics of retracting and deploying. Their 3D models are also presented to proof the validity of the proposed method. Finally, a table of tetragon elements with the characteristics of their associated polygon-scaling mechanisms is summarized using which polygon-scaling mechanisms can be easily constructed.
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Gao, Sande, Qifu Wang, Ji Zhou, and Jun Yu. "Triangulation Algorithm Based on Narrow Polygon Zone for Trimmed Parametric Surface." In ASME 1994 Design Technical Conferences collocated with the ASME 1994 International Computers in Engineering Conference and Exhibition and the ASME 1994 8th Annual Database Symposium. American Society of Mechanical Engineers, 1994. http://dx.doi.org/10.1115/detc1994-0081.

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Abstract This paper presents a new approach to improving the triangulation of surfaces near intersection curves, i. e. “trim” regions. The main idea is based on constructing narrow polygons around trimming curves. The algorithm consists of: (1) Description of trimmed surface, (2) Reconstruction of intersection curve of surfaces, (3) Adaptive subdivision of the surface, (4) Construction of the narrow polygon zone, (5) Triangulation of the narrow polygon zone, (6) Reconstruction of topological relations.
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Sandgren, E., and T. Dworak. "Part Layout Optimization Using a Quadtree Representation." In ASME 1988 Design Technology Conferences. American Society of Mechanical Engineers, 1988. http://dx.doi.org/10.1115/detc1988-0027.

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Abstract A nonlinear programming formulation is developed for minimizing the area required to position a set of pre-defined objects without overlap. The objects consist of polygons with an arbitrary number of edges. Nonconvex polygons are assumed which allows for the modelling of complex parts, including parte with holes. A quadtree representation is formed for each polygon and intersections are determined by traversing quadtrees for the potentially intersecting objects. The design variables are selected to be the x and y location and the rotation for each polygon that is to be positioned. An exterior penalty function method is used to generate the solution to the resulting nonlinear programming problem. A nongradient search technique is used due to the discrete nature of the overlap constraints. Example problems are presented and extensions to other classes of problems are discussed.
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Xing, David. "Layer Sequencing and Flat-Foldability of Uniformly Gridded Polygons." In ASME 2013 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/smasis2013-3047.

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Lunnon (1969) proposed a method to solve the Stamp Folding Problem which asks how many flat-foldable stack patterns there are for a given M by N rectangle grid (map). This project generalizes the original problem to include arbitrarily shaped polygons, including M by N maps. The purpose of this project is to develop a mathematical theorems that would determine whether or not a uniformly gridded polygon with a given stack pattern is flat-foldable. Furthermore, the theorems will determine the two mountain-valley assignments by which a gridded polygon with the given stack pattern can be folded flat. The results of the number of flat-foldable stack patterns for a given M by N map computed by this method is coincided by the results derived by Lunnon’s method. However, our method extends the scope of the original problem to more arbitrarily shaped polygons. This method will aide in the designing of foldable metal or paper structures.
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Burton, Greg. "A Hybrid Approach to Polygon Offsetting Using Winding Numbers and Partial Computation of the Voronoi Diagram." In ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/detc2014-34303.

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In this paper we present a new, efficient algorithm for computing the “raw offset” curves of 2D polygons with holes. Prior approaches focus on (a) complete computation of the Voronoi Diagram, or (b) pair-wise techniques for generating a raw offset followed by removal of “invalid loops” using a sweepline algorithm. Both have drawbacks in practice. Robust implementation of Voronoi Diagram algorithms has proven complex. Sweeplines take O((n + k)log n) time and O(n + k) memory, where n is the number of vertices and k is the number of self-intersections of the raw offset curve. It has been shown that k can be O(n2) when the offset distance is greater than or equal to the local radius of curvature of the polygon, a regular occurrence in the creation of contour-parallel offset curves for NC pocket machining. Our O(n log n) recursive algorithm, derived from Voronoi diagram algorithms, computes the velocities of polygon vertices as a function of overall offset rate. By construction, our algorithm prunes a large proportion of locally invalid loops from the raw offset curve, eliminating all self-intersections in raw offsets of convex polygons and the “near-circular”, k proportional to O(n2) worst-case scenarios in non-convex polygons.
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Figliolini, Giorgio, Pierluigi Rea, and Salvatore Grande. "Kinematic Synthesis of Rotary Machines Generated by Regular Curve-Polygons." In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-71192.

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This paper deals with the kinematic synthesis of volumetric rotary machines, which are generated by the planetary motion of regular curve-polygons. In particular, the synthesis of both outer and inner conjugate profiles has been formulated as envelope of the polycentric profiles of a generating regular curve-polygon with any number of lobes, different radii of the circumcircle and rounded corners. A regular curve-polygon with cusp corners can be obtained as a particular case, like the Reuleaux triangle. Finally, the proposed formulation has been implemented in a Matlab code and several examples are reported.
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Abrahamsen, Mikkel. "Spiral Toolpaths for High-Speed Machining of 2D Pockets With or Without Islands." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-46255.

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We describe new methods for the construction of spiral toolpaths for high-speed machining. In the simplest case, our method takes a polygon as input and a number δ > 0 and returns a spiral starting at a central point in the polygon, going around towards the boundary while morphing to the shape of the polygon. The spiral consists of linear segments and circular arcs, it is G1 continuous, it has no self-intersections, and the distance from each point on the spiral to each of the neighboring revolutions is at most δ. Our method has the advantage over previously described methods that it is easily adjustable to the case where there is an island in the polygon to be avoided by the spiral. In that case, the spiral starts at the island and morphs the island to the outer boundary of the polygon. It is shown how to apply that method to make significantly shorter spirals in polygons with no islands than what is obtained by conventional spiral toolpaths. Finally, we show how to make a spiral in a polygon with multiple islands by connecting the islands into one island.
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Reports on the topic "Polygyni"

1

Rus, Daniela. On Dexterous Rotations of Polygons. Fort Belvoir, VA: Defense Technical Information Center, December 1991. http://dx.doi.org/10.21236/ada250967.

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Schaub, Hanspeter, and Chris C. Wilson. Matching a statistical pressure snake to a four-sided polygon and estimating the polygon corners. Office of Scientific and Technical Information (OSTI), May 2004. http://dx.doi.org/10.2172/974881.

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Bernal, J. Computing Delaunay triangulations for comet-shaped polygons. Gaithersburg, MD: National Institute of Standards and Technology, 1991. http://dx.doi.org/10.6028/nist.ir.4716.

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Wilson, John E. Polygon Subtraction in 2 or 3 Dimensions. Office of Scientific and Technical Information (OSTI), October 2013. http://dx.doi.org/10.2172/1131385.

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Hills, R. G., P. D. Meyer, and M. L. Rockhold. PolyRES: A polygon-based Richards equation solver. Office of Scientific and Technical Information (OSTI), December 1995. http://dx.doi.org/10.2172/179180.

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Fung, Khun Y., Tina M. Nicholl, Robert E. Tarjan, and Christopher J. Van Wyk. Simplified Linear-Time Jordan Sorting and Polygon Clipping. Fort Belvoir, VA: Defense Technical Information Center, July 1989. http://dx.doi.org/10.21236/ada215110.

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Clarke, Jerry A. Distributed Heterogeneous Visualization, Bop (Bag-O-Polygons) and Bop View. Fort Belvoir, VA: Defense Technical Information Center, September 1994. http://dx.doi.org/10.21236/ada284393.

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Gewali, Laxmi, and Simeon Ntafos. Minimum Covers for Grids and Orthogonal Polygons by Periscope Guards. Fort Belvoir, VA: Defense Technical Information Center, June 1990. http://dx.doi.org/10.21236/ada225443.

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Hjort, Nils L. On Frequency Polygons and Average Shifted Histograms in Higher Dimensions. Fort Belvoir, VA: Defense Technical Information Center, February 1986. http://dx.doi.org/10.21236/ada164680.

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DiDonato, Armido R. An Algorithm to Find the Intersection of Two Convex Polygons. Fort Belvoir, VA: Defense Technical Information Center, September 1993. http://dx.doi.org/10.21236/ada274722.

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