Готові списки джерел за темами / Simplex form of a polyhedron

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Добірка наукової літератури з теми "Simplex form of a polyhedron"

Автор: Grafiati

Опубліковано: 28 травня 2022

Оновлено: 31 липня 2025

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Статті в журналах з теми "Simplex form of a polyhedron"

Yemets, Oleg A., Alexandra O. Yemets, and Ivan M. Polyakov. "Optimization on Arrangements: the Simplex Form of Polyhedron of Arrangements." Journal of Automation and Information Sciences 49, no. 12 (2017): 14–28. http://dx.doi.org/10.1615/jautomatinfscien.v49.i12.20.

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LAFONT, JEAN-FRANÇOIS, BRUCE A. MAGURN, and IVONNE J. ORTIZ. "Lower algebraic K-theory of certain reflection groups." Mathematical Proceedings of the Cambridge Philosophical Society 148, no. 2 (2009): 193–226. http://dx.doi.org/10.1017/s0305004109990363.

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AbstractFor P ⊂ 3 a finite volume geodesic polyhedron, with the property that all interior angles between incident faces are of the form π/mij (mij ≥ 2 an integer), there is a naturally associated Coxeter group ΓP. Furthermore, this Coxeter group is a lattice inside the semi-simple Lie group O+(3, 1) = Isom(3), with fundamental domain the original polyhedron P. In this paper, we provide a procedure for computing the lower algebraic K-theory of the integral group ring of such groups ΓP in terms of the geometry of the polyhedron P. As an ingredient in the computation, we explicitly calculate the

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GITLIN, CAROLE, JOSEPH O’ROURKE, and VINITA SUBRAMANIAN. "ON RECONSTRUCTING POLYHEDRA FROM PARALLEL SLICES." International Journal of Computational Geometry & Applications 06, no. 01 (1996): 103–22. http://dx.doi.org/10.1142/s0218195996000071.

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The problem of reconstructing a three-dimensional object from parallel slices has application in computer vision and medicine. Here we explore a specific existence question: given two polygons in parallel planes, is it always possible to find a polyhedron that has those polygons as faces, and whose vertices are precisely the vertices of the two polygons? We answer this question in the negative by providing an example of two polygons that cannot be connected to form a simple polyhedron. One polygon is a triangle, the other a somewhat complicated shape with spiraling pockets.

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Naskręcki, Bartosz, Mariusz Jaskolski, and Zbigniew Dauter. "The Euler characteristic as a basis for teaching topology concepts to crystallographers." Journal of Applied Crystallography 55, no. 1 (2022): 154–67. http://dx.doi.org/10.1107/s160057672101205x.

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The simple Euler polyhedral formula, expressed as an alternating count of the bounding faces, edges and vertices of any polyhedron, V − E + F = 2, is a fundamental concept in several branches of mathematics. Obviously, it is important in geometry, but it is also well known in topology, where a similar telescoping sum is known as the Euler characteristic χ of any finite space. The value of χ can also be computed for the unit polyhedra (such as the unit cell, the asymmetric unit or Dirichlet domain) which build, in a symmetric fashion, the infinite crystal lattices in all space groups. In this a

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Gilodo, A. Y., V. P. Kovtun, A. N. Arsirii, and A. A. Angel. "EFFECTIVE STRUCTURE OF A WOODEN RESIDENTIAL BUILDING IN THE FORM OF A GEODESIC DOME WITH A UNIVERSAL CONNECTOR." Bulletin of Odessa State Academy of Civil Engineering and Architecture, no. 82 (March 4, 2021): 19–26. http://dx.doi.org/10.31650/2415-377x-2021-82-19-26.

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Abstract. Since the middle of the twentieth century, a new architectural solution has been spherical shells broken down into elements by geodesic lines – circles with radii equal to the radius of the sphere. A geodesic dome is a dome made of a spherical polyhedron with an optimally distributed arrangement of vertices and edges tending to a perfect sphere. Using the technical capabilities of computer design, digital models of the layout and calculation of geodesic domes became available. It is possible not only to calculate multi-mesh network layouts with high accuracy, but also to automate the

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Xiong, Youlun, Han Ding, and Michael Yu Wang. "Quantitative Analysis of Inner Force Distribution and Load Capacity of Grasps and Fixtures." Journal of Manufacturing Science and Engineering 124, no. 2 (2002): 444–55. http://dx.doi.org/10.1115/1.1459089.

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This paper focuses on a quantitative analysis for grasp planning and fixture design based on an analytical description of point contact restraint. In the framework, the analysis deals with the fundamental concepts of restraint cone, freedom cone, force-determinacy and relative form closure. A method is presented to quantify the performance of a fixture (or grasp) with two major characteristics of inner force distribution and load capacity. Two different fixturing (or grasp) models of simplex grasp and elastic grasp are presented. It is shown that the performance of these two types of grasp (or

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Vovk, O. P., I. M. Naumko, and V. I. Pavlyshyn. "GENETIC SIGNIFICANCE OF VARIATIONS IN THE FACES OF THE SIMPLE FORMS OF TOPAZ CRYSTAL FROM CHAMBER PEGMATITES OF THE KOROSTEN PLUTON (UKRAINIAN SHIELD)." Mineralogical Journal 44, no. 3 (2022): 40–47. http://dx.doi.org/10.15407/mineraljournal.44.03.040.

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Topaz crystal morphology and habit distortion has been studied in various mineral-structural zones of chamber pegmatites of the Korosten pluton, which is located in north-western part of the Ukrainian Shield. It was assumed that the symmetry of the crystals obey the Curie principle. This means that only the symmetry elements common to the crystal and the medium in which it is formed will remain on real polyhedrons. The types of symmetry that contain the axes of infinite order are reduced to the following groups: 1) ∞L∞∞PC is a ball; 2) ∞L∞ is a ball filled with an optically active liquid; 3) L

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Newcomb, William W., Benes L. Trus, Naiqian Cheng, et al. "Isolation of Herpes Simplex Virus Procapsids from Cells Infected with a Protease-Deficient Mutant Virus." Journal of Virology 74, no. 4 (2000): 1663–73. http://dx.doi.org/10.1128/jvi.74.4.1663-1673.2000.

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ABSTRACT Herpes simplex virus type 1 (HSV-1) capsid proteins assemble in vitro into spherical procapsids that differ markedly in structure and stability from mature polyhedral capsids but can be converted to the mature form. Circumstantial evidence suggests that assembly in vivo follows a similar pathway of procapsid assembly and maturation, a pathway that resembles those of double-stranded DNA bacteriophages. We have confirmed the above pathway by isolating procapsids from HSV-1-infected cells and characterizing their morphology, thermal sensitivity, and protein composition. Experiments were

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Dasgupta, Anindya, and Duncan W. Wilson. "ATP Depletion Blocks Herpes Simplex Virus DNA Packaging and Capsid Maturation." Journal of Virology 73, no. 3 (1999): 2006–15. http://dx.doi.org/10.1128/jvi.73.3.2006-2015.1999.

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ABSTRACT During herpes simplex virus (HSV) assembly, immature procapsids must expel their internal scaffold proteins, transform their outer shell to form mature polyhedrons, and become packaged with the viral double-stranded (ds) DNA genome. A large number of virally encoded proteins are required for successful completion of these events, but their molecular roles are poorly understood. By analogy with the dsDNA bacteriophage we reasoned that HSV DNA packaging might be an ATP-requiring process and tested this hypothesis by adding an ATP depletion cocktail to cells accumulating unpackaged proca

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XU, HUIZHONG, YAPING WANG, DAJI LI, JIANYUAN XU, ZHUO WANG, and LIANG ZHEN. "STUDY OF THE NON-NBT PHASE IN Sr DOPED NBT THIN FILMS." Surface Review and Letters 20, no. 06 (2013): 1350056. http://dx.doi.org/10.1142/s0218625x1350056x.

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The morphology, composition and mechanism of the non-NBT phase in the Sr -doped NBT [SNBT, ( Na 0.5 Bi 0.5)1-x Sr x TiO 3] thin films by chemical method were investigated using XRD, SEM, crystallization analysis and thermodynamics analysis. The results showed that the non-NBT phase is the porphyroblastic grains in the matrix and looks like a plate-shaped polyhedron. The mechanism of the non-NBT phase formation is that the Sr 2+ and Na + combined with [Formula: see text] to form initial simple titanate, such as SrTiO 3, Na 2 TiO 3, or NBT phase decomposed because of the volatilization of Bi und

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Більше джерел

Дисертації з теми "Simplex form of a polyhedron"

Iemets, O. O., O. O. Yemets`, and I. M. Polyakov. "About the Simplex Form of the Polyhedron of Arrangements." Thesis, Sumy State University, 2017. http://essuir.sumdu.edu.ua/handle/123456789/55771.

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The simplex form of the general polyhedron of arrangements, which is used in linear programming problems in combinatorial cutting methods is obtained and it increases the efficiency of cutting methods.

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Martin, Andrew K. "A simple primal algorithm for intersecting 3-polyhedra in linear time." Thesis, University of British Columbia, 1991. http://hdl.handle.net/2429/30114.

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This thesis presents, in full, a simple linear time algorithm for intersecting two convex 3-polyhedra P and Q. This differs from the first such algorithm — due to Chazelle — in that it operates entirely in primal space, whereas Chazelle's algorithm relies heavily on duality transforms. We use the hierarchical representations of polyhedra due to Dobkin and Kirkpatrick to induce a cell complexes between coarse approximations, Pk and Pk of P satisfying Pk ⊆ P ⊆ Pk, and similar approximations Qk and Qk of Q satisfying Qk ⊆ Q ⊆ Qk . We show that the structure of such complexes allows intersection q

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Albaret, Marie Alexandra. "Rôle potentiel du virus herpes simplex de type I dans la maladie d'Alzheimer." Thesis, Lyon 1, 2009. http://www.theses.fr/2009LYO10117.

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L'étiologie de la forme sporadique de la maladie d'Alzheimer (AD) reste largement inconnue. Toutefois, une adéquation entre des facteurs environnementaux et génétiques est fortement probable. C'est ainsi que de nombreux arguments suggèrent que le virus herpes simplex de type 1 (HSV1) en infectant et en se répliquant dans le système nerveux central, puisse être un co-facteur impliqué dans le déclenchement et le développement de l'AD. Pour éprouver cette hypothèse, nous avons développé un modèle cellulaire constitué de neurones de rat infectés par HSV1 pour analyser les modifications viro-induit

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Tomek, Peter. "Approximation of Terrain Data Utilizing Splines." Master's thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2012. http://www.nusl.cz/ntk/nusl-236488.

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Pro optimalizaci letových trajektorií ve velmi malé nadmorské výšce, terenní vlastnosti musí být zahrnuty velice přesne. Proto rychlá a efektivní evaluace terenních dat je velice důležitá vzhledem nato, že čas potrebný pro optimalizaci musí být co nejkratší. Navyše, na optimalizaci letové trajektorie se využívájí metody založené na výpočtu gradientu. Proto musí být aproximační funkce terenních dat spojitá do určitého stupne derivace. Velice nádejná metoda na aproximaci terenních dat je aplikace víceroměrných simplex polynomů. Cílem této práce je implementovat funkci, která vyhodnotí dané teren

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Chá, Sílvia Alexandra Carrapato. "Problemas convexos e não-convexos do cálculo das variações." Doctoral thesis, Universidade de Évora, 2014. http://hdl.handle.net/10174/17929.

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Nas aplicações do Cálculo das Variações, Controlo Óptimo & Inclusões Diferenciais, muitos problemas importantes da vida real são vectoriais não-convexos e sujeitos a restrições pontuais. O teorema clássico da convexidade de Liapunov é uma ferramenta crucial para resolver problemas vectoriais não-convexos envolvendo integrais simples. No entanto, a possibilidade da extensão deste teorema para lidar com restrições pontuais manteve-se um problema em aberto durante duas décadas, no caso mais realista usando controlos vectoriais variáveis. Nesta tese apresentamos condições necessárias e condições s

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Pasternack, Sandra Maria [Verfasser]. "Identifizierung und Charakterisierung eines Gens für eine autosomal-rezessive Form der Hypotrichosis simplex : molekulargenetische, zellbiologische und pharmakologische Untersuchungen zum P2RY5-Gen und P2Y5-Protein / vorgelegt von Sandra Maria Pasternack." 2011. http://d-nb.info/101200662X/34.

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Baasch, Marianne. "A review of the homeopathic research studies performed at the Technikon Witwatersrand and a meta-analysis of the homeopathic simplex studies performed on human subjects in the form of random controlled trials." Thesis, 2009. http://hdl.handle.net/10210/2857.

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Книги з теми "Simplex form of a polyhedron"

Epstein, Charles L., and Rafe Mazzeo. Wright-Fisher Geometry. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691157122.003.0002.

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This chapter introduces the geometric preliminaries needed to analyze generalized Kimura diffusions, with particular emphasis on Wright–Fisher geometry. It begins with a discussion of the natural domains of definition for generalized Kimura diffusions: polyhedra in Euclidean space or, more generally, abstract manifolds with corners. Amongst the convex polyhedra, the chapter distinguishes the subclass of regular convex polyhedra P. P is a regular convex polyhedron if it is convex and if near any corner, P is the intersection of no more than N half-spaces with corresponding normal vectors that a

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Частини книг з теми "Simplex form of a polyhedron"

Li, Fajie, and Reinhard Klette. "Approximate Shortest Paths in Simple Polyhedra." In Discrete Geometry for Computer Imagery. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-19867-0_43.

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Liu, Mengman, Chuhua Ding, and Hui Wang. "An Exploration on the Form Design of Movable Structures Based on Uniform Convex Polyhedral Expansion." In Computational Design and Robotic Fabrication. Springer Nature Singapore, 2024. http://dx.doi.org/10.1007/978-981-99-8405-3_7.

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Abstract5 kinds of regular polyhedra and 13 kinds of semi-regular polyhedra are taken as the main research objects in this paper to explore the form design method of polyhedral expansion through the rotation of polygon. Firstly, the expandable range of uniform convex polyhedra is defined and divided into two types of expansion. Then three solutions are proposed, namely, discarding polygonal faces, constructing rigid-foldable origami mechanisms and constructing scissor-like elements, so that the prior unexpandable uniform convex polyhedron can be expanded. These methods extend the range of expa

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Maier, H., M. Siebert, and E. Gramer. "Unterschiede in der form der Papillenexkavation bei Glaucoma chronicum simplex und Glaukom ohne Hochdruck —." In Pharmakotherapie am Auge. Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/978-3-642-77532-1_4.

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Nagano, Akiko, Alexandra Bagasheva, and Vincent Renner. "Chapter 1. Towards a competition-based word-formation theory." In Linguistik Aktuell/Linguistics Today. John Benjamins Publishing Company, 2024. http://dx.doi.org/10.1075/la.284.01nag.

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This chapter provides an overview of the study of competition in word-formation theories, drawing on the findings of the ten chapters collected in this volume and other recent contributions. It explores recurrent issues regarding (i) the triggers and outcomes of competition, (ii) the variety of competing forms, and (iii) the synonymy condition for competition. With respect to the first set of research questions, a binary typology of form-based and meaning-based resolutions is identified, with each pole providing multiple ways to resolve competition. Next, for the form-related research question

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Goharshady, Amir K., S. Hitarth, and Sergei Novozhilov. "Efficient Synthesis of Tight Polynomial Upper-Bounds for Systems of Conditional Polynomial Recurrences." In Lecture Notes in Computer Science. Springer Nature Switzerland, 2025. https://doi.org/10.1007/978-3-031-91121-7_1.

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Abstract Recurrence relations are used in a wide variety of static program analysis tasks such as loop summarization, invariant generation, and, most classically, modeling the (asymptotic) worst-case runtime behavior of recursive divide-and-conquer algorithms. In this work, we focus on the latter use-case. Classical methods for this problem, such as the well-known Master Theorem (MT) or the Akra-Bazzi method (AB) can only handle single recurrences of a certain limited form. Specifically, MT requires that each instance be divided into a fixed number of smaller sub-instances of the same size. AB

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Marius, Arghirescu. "A Preonic Model of Quarks and Particles, Based on a Cold Genesis Theory." In Redefining Standard Model Particle Physics [Working Title]. IntechOpen, 2023. http://dx.doi.org/10.5772/intechopen.109123.

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The theoretic model explains the generating of heavy quarks and of heavy particles using the known quark s(strange) and two semi-light quarks: λ±(435 MeV) and v±(∼574 MeV) resulting from a cold genesis theory1 of astro-particles’ forming, (CGT), the masses of the quarks c• (charm) and b• (bottom) of the Standard Model but also the values used by de Souza: c = 1.7 GeV and b = 5 GeV, being re-obtained as tri-quark clusters in the form: [(qq¯)q]], by a simple de-excitation reaction, with the emission of a preonic boson obtained in CGT: z0 = 34me, respective: z2 = 4z0 and zμ = 6z0- for the quarks

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Maros, István, and Gautam Mitra. "Simplex algorithms." In Advances in Linear and Integer Programming. Oxford University PressOxford, 1996. http://dx.doi.org/10.1093/oso/9780198538561.003.0001.

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Abstract Linear inequality systems were studied by Fourier, Motzkin and Farkas (see [14]) but only in the late 1940s did the work of Dantzig in the USA and Kantorovich in the former USSR make linear programming a leading research topic with wide ranging applications to problems of planning and scheduling as found in business, industry and government [14]. Dantzig developed the celebrated simplex method (in the tableau form) for finding the maximum or minimum of a linear function subject to linear restrictions. The resulting optimization problem because of its many planning applications was cal

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"Clusters of Chemical Compounds as Polytopes of the Highest Dimension." In Normal Partitions and Hierarchical Fillings of N-Dimensional Spaces. IGI Global, 2021. http://dx.doi.org/10.4018/978-1-7998-6768-5.ch002.

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General analytical expressions are obtained for calculating the dimension of multi-shell clusters with a common center of shells in those cases when there is a metal atom in the center of the shells and when it is not. The shells can be in the shape of any body of Plato. It has been established that the gamma-copper cluster has the form of a cross-polytope of high dimension. The forms of clusters with ligands of the core of which is a chain of metal atoms or a metal polyhedron are geometrically investigated. It is shown that if the skeleton is a chain of metal atoms, then the cluster is polyto

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Wood, W. L. "The finite element method." In Introduction to Numerical Methods for Water Resources. Oxford University PressOxford, 1993. http://dx.doi.org/10.1093/oso/9780198596905.003.0006.

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Abstract The finite element method (FEM) is not recommended in this book for the solution of surface flow problems because finite difference methods are easier for these. The FEM is introduced here as applied to the solution of subsurface flow, i.e. for the spatial discretization of elliptic and parabolic problems (Chapter 1). At first it is assumed that the region concerned is two dimensional. The basic idea is that this region in which the solution is required is divided into triangles or quadrilaterals and in each of these a simple polynomial approximation to the exact solution is taken. Th

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Jonckheere, Edmond A. "Piecewise-Linear Nyquist Map." In Algebraic and Differential Topology of Robust Stability. Oxford University PressNew York, NY, 1997. http://dx.doi.org/10.1093/oso/9780195093018.003.0007.

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Abstract Computing the crossover amounts to solving the Nyquist equation f(p) = 0 + jO. Assuming this equation is defined over the polyhedron D × Ω, the natural approach to implement an ad hoc solution in the realm of finite computation is to map the vertex set {ai} of the domain D × Ω to the complex plane, ai↦ bi= f (ai), and then work with the piecewise-linear extension of the vertex transformation ai↦bi. A typical feature of the resulting map is that the image of a simplex is a convex polygon, so that this piecewise-linear extension is not, in general, simplicial. However, an attractive fea

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Тези доповідей конференцій з теми "Simplex form of a polyhedron"

Devadoss, Satyan, and Shannon Starkey. "Flexing on Topology, or, Contrapposto Architecture." In 109th ACSA Annual Meeting Proceedings. ACSA Press, 2021. http://dx.doi.org/10.35483/acsa.am.109.48.

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In 1977, mathematician Robert Connelly discovered a unique eighteen-sided closed, hinged polyhedron that, remarkably, wiggled, overturning centuries of mathematical discourse linking polyhedra with rigidity. This new category of polyhedra is the source of an ongoing interdisciplinary collaboration between architecture and discrete geometry. The flexible polyhedron serves as a generative design tool to develop a new approach to structure and a new relationship of the body in space, as well as an analytical lens through which to understand and challenge the history of architecture’s close associ

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Maza, Stéphane, Jean-Claude Léon, and Frédéric Noël. "Mesh Construction Dedicated to a Multi-Representation for Structure Analysis Based on an Initial Polyhedral Geometry." In ASME 1997 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/detc97/cie-4446.

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Abstract The aim of this paper is to present the first part of a new approach devoted to the generation of a data structure and operators for the hierarchical representation of 3D polyhedra. Here are described the treatments which allow to create some of the elements of this hierarchical model. At first, partitions of the initial polyhedron are mapped into planar connex hulls. Then, these domains are used like a piecewise parametric 2D space for subsequent polyhedra generations. In order to create such a mapping, the initial 3D polyhedron is partitioned to produce simply convex subsets which c

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Ramesh, Madhumati M., Derek Yip-Hoi, and Debasish Dutta. "A Decomposition Methodology for Machining Feature Extraction." In ASME 2000 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2000. http://dx.doi.org/10.1115/detc2000/cie-14645.

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Abstract Many applications such as computer aided process planning require an interpretation of the complex geometry of a mechanical part in terms of simpler local shapes such as machining features. Decomposition of non-polyhedral parts is difficult as compared to that of polyhedrons, but mechanical parts are seldom polyhedral. A decomposition method that makes use of primitives for planar and cylindrical faces of parts is presented in this paper. A semi-automatic method for mapping the resulting shapes to library-features is also presented. The proposed method for decomposition and mapping is

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Xi, Zhonghua, and Jyh-Ming Lien. "Polyhedra Fabrication Through Mesh Convexification: A Study of Foldability of Nearly Convex Shapes." In ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/detc2017-67212.

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A polyhedron can be unfolded to a net, i.e., an unfolding without overlapping, by carefully cutting along the surface. If the cuts are restricted only on the edges of the polyhedron, where should the cuts be? This is called an edge-unfolding problem, which has been extensively studied in the literature for centuries. Although several promising properties have been discovered, several recent preliminary works show that no valid net exists even for certain simple non-convex polyhedra. Therefore, we propose to convexify the input polyhedron before unfolding. More specifically, we remove local con

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Bober, Waldemar, and Przemyslaw Stobiecki. "Experimental geodesic dome with a sandwich panels structure." In Human Interaction and Emerging Technologies (IHIET-AI 2022) Artificial Intelligence and Future Applications. AHFE International, 2022. http://dx.doi.org/10.54941/ahfe100895.

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The popularization of geodesic domes as a living space was one of R. B. Fuller's challenges for modern mankind. The search for a technology that can optimally satisfy this desire in a society living in a temperate climate has become the goal of the structural studies described in this study. The technological solution for the layer of sandwich panels depends on the adopted discrete division of the polyhedron surface. Due to the relatively simple shape of this element, the dodecahedron was adopted as the basis form. The designated triangular elements constitute the initial shape of the basic el

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Cheong, Jae-Sook, and A. Frank van der Stappen. "Computing All Independent Form-Closure Grasp Regions of a Rectilinear Polyhedron." In 2007 IEEE International Conference on Automation Science and Engineering. IEEE, 2007. http://dx.doi.org/10.1109/coase.2007.4341778.

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Tang, Chengcheng, Xiang Sun, Alexandra Gomes, Johannes Wallner, and Helmut Pottmann. "Form-finding with polyhedral meshes made simple." In SIGGRAPH '15: Special Interest Group on Computer Graphics and Interactive Techniques Conference. ACM, 2015. http://dx.doi.org/10.1145/2787626.2787631.

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Jae-Sook Cheong and A. Frank van der Stappen. "Computing all form-closure grasps of a rectilinear polyhedron with seven frictionless point fingers." In 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems. IEEE, 2007. http://dx.doi.org/10.1109/iros.2007.4399113.

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Kim, Suhee, and Hye Jin Lee. "A simple gel electrophoresis method for separating polyhedral gold nanoparticles." In International Conference on Nano-Bio Sensing, Imaging, and Spectroscopy 2015, edited by Donghyun Kim, Min-Gon Kim, and Seung-Han Park. SPIE, 2015. http://dx.doi.org/10.1117/12.2189772.

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Guillet, Stéphane, and Jean-Claude Léon. "Trimmed Free-Form Surfaces Submitted to Parametric Modelling." In ASME 1997 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/detc97/dac-3732.

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Abstract A new parametric modelling approach focusing on trimmed free-form surfaces is introduced. The surface deformation process required is controlled through geometric constraints such as deforming the surface until it becomes tangent to a pre-defined plane. Surfaces are bounded by trimming lines and use a multi-patch representation (i.e.: a B-Spline based model). The G1 continuity across the various surface patches is preserved during the deformation process. Therefore, the C0 and G1 continuities across trimmed surfaces boundaries can be correctly approximated by parametric constraints. T

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