Search results for "Geometric"
showing 10 items of 652 documents
Geometric Algebra Rotors for Sub-Symbolic Coding of Natural Language Sentences
2007
A sub-symbolic encoding methodology for natural language sentences is presented. The procedure is based on the creation of an LSA-inspired semantic space and associates rotation operators derived from Geometric Algebra to word bigrams of the sentence. The operators are subsequently applied to an orthonormal standard basis of the created semantic space according to the order in which words appear in the sentence. The final rotated basis is then coded as a vector and its orthogonal part constitutes the sub-symbolic coding of the sentence. Preliminary experimental results for a classification task, compared with the traditional LSA methodology, show the effectiveness of the approach.
Sentence Induced Transformations in Conceptual Spaces
2008
The proposed work illustrates how "primitive concepts" can be automatically induced from a text corpus. The primitive concepts are identified by the orthonormal axis of a "conceptual" space induced by a methodology inspired to the latent semantic analysis approach. The methodology represents a natural language sentence by means of a set of rotations of an orthonormal basis in the "conceptual"space. The rotations, triggered by the sequence of words composing the sentence and realized by means of geometric algebra rotors, allow to highlight "conceptual" relations that can arise among the primitive concepts.
An Embedded, FPGA-based Computer Graphics Coprocessor with Native Geometric Algebra Support
2009
The representation of geometric objects and their transformation are the two key aspects in computer graphics applications. Traditionally, computer-intensive matrix calculations are involved in modeling and rendering three-dimensional (3D) scenery. Geometric algebra (aka Clifford algebra) is attracting attention as a natural way to model geometric facts and as a powerful analytical tool for symbolic calculations. In this paper, the architecture of Clifford coprocessor (CliffoSor) is introduced. CliffoSor is an embedded parallel coprocessing core that offers direct hardware support to Clifford algebra operators. A prototype implementation on a programmable gate array (FPGA) board is detailed…
A Dual-Core Coprocessor with Native 4D Clifford Algebra Support
2012
Geometric or Clifford Algebra (CA) is a powerful mathematical tool that is attracting a growing attention in many research fields such as computer graphics, computer vision, robotics and medical imaging for its natural and intuitive way to represent geometric objects and their transformations. This paper introduces the architecture of CliffordCoreDuo, an embedded dual-core coprocessor that offers direct hardware support to four-dimensional (4D) Clifford algebra operations. A prototype implementation on an FPGA board is detailed. Experimental results show a 1.6× average speedup of CliffordCoreDuo in comparison with the baseline mono-core architecture. A potential cycle speedup of about 40× o…
Fixed-size Quadruples for a New, Hardware-Oriented Representation of the 4D Clifford Algebra
2010
Clifford algebra (geometric algebra) offers a natural and intuitive way to model geometry in fields as robotics, machine vision and computer graphics. This paper proposes a new representation based on fixed-size elements (quadruples) of 4D Clifford algebra and demonstrates that this choice leads to an algorithmic simplification which in turn leads to a simpler and more compact hardware implementation of the algebraic operations. In order to prove the advantages of the new, quadruple-based representation over the classical representation based on homogeneous elements, a coprocessing core supporting the new fixed-size Clifford operands, namely Quad-CliffoSor (Quadruple-based Clifford coproces…
Accelerating Clifford Algebra Operations using GPUs and an OpenCL Code Generator
2015
Clifford Algebra (CA) is a powerful mathematical language that allows for a simple and intuitive representation of geometric objects and their transformations. It has important applications in many research fields, such as computer graphics, robotics, and machine vision. Direct hardware support of Clifford data types and operators is needed to accelerate applications based on Clifford Algebra. This paper proposes a mixed software-hardware system that exploits the computational power of Graphics Processing Units (GPUs) to accelerate Clifford operations. A code generator, namely OpenCLifford, is presented that automatically generates Java and C libraries for the direct support of Clifford ele…
An FPGA Implementation of a Quadruple-Based Multiplier for 4D Clifford Algebra
2008
Geometric or Clifford algebra is an interesting paradigm for geometric modeling in fields as computer graphics, machine vision and robotics. In these areas the research effort is actually aimed at finding an efficient implementation of geometric algebra. The best way to exploit the symbolic computing power of geometric algebra is to support its data types and operators directly in hardware. However the natural representation of the algebra elements as variable-length objects causes some problems in the case of a hardware implementation. This paper proposes a 4D Clifford algebra in which the variable-length elements are mapped into fixed-length elements (quadruples). This choice leads to a s…
Embedded Coprocessors for Native Execution of Geometric Algebra Operations
2016
Clifford algebra or geometric algebra (GA) is a simple and intuitive way to model geometric objects and their transformations. Operating in high-dimensional vector spaces with significant computational costs, the practical use of GA requires dedicated software and/or hardware architectures to directly support Clifford data types and operators. In this paper, a family of embedded coprocessors for the native execution of GA operations is presented. The paper shows the evolution of the coprocessor family focusing on the latest two architectures that offer direct hardware support to up to five-dimensional Clifford operations. The proposed coprocessors exploit hardware-oriented representations o…
Piergiorgio Zangara. Artista Madi
2016
L’arte Madi, umana e universale, propugna l’uso di libere forme in senso dinamico-spaziale e recupera le istanze avanguardistiche del XX secolo, dall’Astrazione al Suprematismo e al Costruttivismo, raccogliendo la lezione di grandi maestri, da Kandinsky e Mondrian a Malevič e Tatlin, da Rodchenko e Moholy Nagy a Gabo e Pevsner, e abbracciando anche lo Spazialismo e il Minimalismo. Sfruttando tutta la gamma cromatica a sua disposizione e ricorrendo alla libertà d’invenzione e al ludus propri degli artisti, Piergiorgio Zangara è portatore di un linguaggio privo di illusori condizionamenti mimetici che trova nel Suprematismo, nel Costruttivismo e in De Stijl i propri referenti privilegiati. In…
Yumiko Kimura. Invenzione e geometria
2016
Il saggio prende in esame la ricerca artistica di Yumiko Kimura (Tokyo, 1961), artista specializzata in sculture in vetro che coniugano arte geometrica e ricerca della luce. Il contributo è stato realizzato in occasione della mostra "Universi geometrici", che ha presentato una selezione di opere dell'artista giapponese all’interno della Valle dei Templi di Agrigento e poi alla FAM gallery con il patrocinio del Museum of Geometric and MADI Art di Dallas e l'inserimento nelle celebrazioni ufficiali del 150° anniversario delle relazioni tra Giappone e Italia. The essay examines the artistic research of Yumiko Kimura (Tokyo, 1961), an artist specializing in glass sculptures that combine geometr…