Articulating Space: Geometric Algebra for Parametric Design -- Symmetry, Kinematics, and Curvature

To advance the use of geometric algebra in practice, we develop computational methods for parameterizing spatial structures with the conformal model. Three discrete parameterizations – symmetric, kinematic, and curvilinear – are employed to generate space groups, linkage mechanisms, and rationalized surfaces. In the process we illustrate techniques that directly benefit from the underlying mathematics, and demonstrate how they might be applied to various scenarios. Each technique engages the versor – as opposed to matrix – representation of transformations, which allows for structure-preserving operations on geometric primitives. This covariant methodology facilitates constructive design through geometric reasoning: incidence and movement are expressed in terms of spatial variables such as lines, circles and spheres. In addition to providing a toolset for generating forms and transformations in computer graphics, the resulting expressions could be used in the design and fabrication of machine parts, tensegrity systems, robot manipulators, deployable structures, and freeform architectures. Building upon existing algorithms, these methods participate in the advancement of geometric thinking, developing an intuitive spatial articulation that can be creatively applied across disciplines, ranging from time-based media to mechanical and structural engineering, or reformulated in higher dimensions

Generative Mesh Modeling

Generative Modeling is an alternative approach for the description of three-dimensional shape. The basic idea is to represent a model not as usual by an agglomeration of geometric primitives (triangles, point clouds, NURBS patches), but by functions. The paradigm change from objects to operations allows for a procedural representation of procedural shapes, such as most man-made objects. Instead of storing only the result of a 3D construction, the construction process itself is stored in a model file. The generative approach opens truly new perspectives in many ways, among others also for 3D knowledge management. It permits for instance to resort to a repository of already solved modeling problems, in order to re-use this knowledge also in different, slightly varied situations. The construction knowledge can be collected in digital libraries containing domain-specific parametric modeling tools. A concrete realization of this approach is a new general description language for 3D models, the "Generative Modeling Language" GML. As a Turing-complete "shape programming language" it is a basis of existing, primitv based 3D model formats. Together with its Runtime engine the GML permits - to store highly complex 3D models in a compact form, - to evaluate the description within fractions of a second, - to adaptively tesselate and to interactively display the model, - and even to change the models high-level parameters at runtime.Die generative Modellierung ist ein alternativer Ansatz zur Beschreibung von dreidimensionaler Form. Zugrunde liegt die Idee, ein Modell nicht wie üblich durch eine Ansammlung geometrischer Primitive (Dreiecke, Punkte, NURBS-Patches) zu beschreiben, sondern durch Funktionen. Der Paradigmenwechsel von Objekten zu Geometrie-erzeugenden Operationen ermöglicht es, prozedurale Modelle auch prozedural zu repräsentieren. Statt das Resultat eines 3D-Konstruktionsprozesses zu speichern, kann so der Konstruktionsprozess selber repräsentiert werden. Der generative Ansatz eröffnet unter anderem gänzlich neue Perspektiven für das Wissensmanagement im 3D-Bereich. Er ermöglicht etwa, auf einen Fundus bereits gelöster Konstruktions-Aufgaben zurückzugreifen, um sie in ähnlichen, aber leicht variierten Situationen wiederverwenden zu können. Das Konstruktions-Wissen kann dazu in Form von Bibliotheken parametrisierter, Domänen-spezifischer Modellier-Werkzeuge gesammelt werden. Konkret wird dazu eine neue allgemeine Modell-Beschreibungs-Sprache vorgeschlagen, die "Generative Modeling Language" GML. Als Turing-mächtige "Programmiersprache für Form" stellt sie eine echte Verallgemeinerung existierender Primitiv-basierter 3D-Modellformate dar. Zusammen mit ihrer Runtime-Engine erlaubt die GML, - hochkomplexe 3D-Objekte extrem kompakt zu beschreiben, - die Beschreibung innerhalb von Sekundenbruchteilen auszuwerten, - das Modell adaptiv darzustellen und interaktiv zu betrachten, - und die Modell-Parameter interaktiv zu verändern

Notes in Pure Mathematics & Mathematical Structures in Physics

These Notes deal with various areas of mathematics, and seek reciprocal combinations, explore mutual relations, ranging from abstract objects to problems in physics.Comment: Small improvements and addition

Gabriel Vacariu (c2023 to 2014) The UNBELIEVABLE similarities between the ideas of some people (2006-2016) and my ideas (2002-2008) in physics (quantum mechanics, cosmology), cognitive neuroscience, philosophy of mind, and philosophy

Unbelievable similar ideas to my ideas published long before..

(b2023 to 2014) The UNBELIEVABLE similarities between the ideas of some people (2006-2016) and my ideas (2002-2008) in physics (quantum mechanics, cosmology), cognitive neuroscience, philosophy of mind, and philosophy (this manuscript would require a REVOLUTION in international academy environment!)

(b2023 to 2014) The UNBELIEVABLE similarities between the ideas of some people (2006-2016) and my ideas (2002-2008) in physics (quantum mechanics, cosmology), cognitive neuroscience, philosophy of mind, and philosophy (this manuscript would require a REVOLUTION in international academy environment!

(2023 to 2014) The UNBELIEVABLE similarities between the ideas of some people (2006-2016) and my ideas (2002-2008) in physics (quantum mechanics, cosmology), cognitive neuroscience, philosophy of mind, and philosophy (this manuscript would require a REVOLUTION in international academy environment!)

The main ideas of the EDWs perspective are in Gabriel Vacariu’s PhD thesis posted online by UNSW (Australia) in 2007!!! I have realized the GREATEST discovery in the history of human knowledge: the EDWs! With discovering the EDWs, I have changed everything in Philosophy, Physics and Cognitive Neuroscience! This has been the main reason, so many people have published UNBELIEVABLE similar ideas to my ideas, many years I published my first works! UNBELIEVABLE, many (hundreds) “great” or small thinkers did the same thing in 2006-2007 and later: they published the same ideas, UNBELIEVABLE similar to my ideas from 2002-2005! They believe they would be considered co-authors of the same new framework of thinking. They did not know that many “professors” would do the same thing: they plagiarized my ideas and they hurry up to published their work as soon as possible (in 2006-2007, depending when they discovered my article 2005). So, in the same 2 years, many people “discovered” the same new framework of thinking, the EDWs perspective, each of them did not think that there would be so many other people doing the same thing, that is, many people “discovered” the same new framework (the greatest challenge in the history of human thinking!) in the same period! Such coincidences (the discovery of the EDWs in the same two years!!!) are quite IMPOSSIBLE!! This is the reason nobody quoted my name, but nobody quoted any name who PLAGIARIZED my ideas… In 2006-2007, I was wondering why nobody quote my name, but in fact, they plagiarized my ideas. Nobody discovered this framework of thinking 2500 years, and in 2-3 years, many people discovered it!!!! IMPOSSIBLE!!!! There were some "professors" who published articles/chapters very close to Bohr's complementarity, Dirac, de Broglie's dualism before 2005 (for instance Carlo Rovelli 1996 or Ladyman), but their works were constructed within the "unicorn world" (Universe/world), therefore, these works had nothing in common with the EDWs perspective!!!! In reality, all of them plagiarized my ideas! It was like many people composed Beethoven Fifth’s Symphony, claiming that they never listen Beethoven! Who would be so stupid to believe them

(b2023 to 2014) The UNBELIEVABLE similarities between the ideas of some people (2006-2016) and my ideas (2002-2008) in physics (quantum mechanics, cosmology), cognitive neuroscience, philosophy of mind, and philosophy (this manuscript would require a REVOLUTION in international academy environment!)

The main ideas of the EDWs perspective are in Gabriel Vacariu’s PhD thesis posted online by UNSW (Australia) in 2007!!! I have realized the GREATEST discovery in the history of human knowledge: the EDWs! With discovering the EDWs, I have changed everything in Philosophy, Physics and Cognitive Neuroscience! This has been the main reason, so many people have published UNBELIEVABLE similar ideas to my ideas, many years I published my first works! UNBELIEVABLE, many (hundreds) “great” or small thinkers did the same thing in 2006-2007 and later: they published the same ideas, UNBELIEVABLE similar to my ideas from 2002-2005! They believe they would be considered co-authors of the same new framework of thinking. They did not know that many “professors” would do the same thing: they plagiarized my ideas and they hurry up to published their work as soon as possible (in 2006-2007, depending when they discovered my article 2005). So, in the same 2 years, many people “discovered” the same new framework of thinking, the EDWs perspective, each of them did not think that there would be so many other people doing the same thing, that is, many people “discovered” the same new framework (the greatest challenge in the history of human thinking!) in the same period! Such coincidences (the discovery of the EDWs in the same two years!!!) are quite IMPOSSIBLE!! This is the reason nobody quoted my name, but nobody quoted any name who PLAGIARIZED my ideas… In 2006-2007, I was wondering why nobody quote my name, but in fact, they plagiarized my ideas. Nobody discovered this framework of thinking 2500 years, and in 2-3 years, many people discovered it!!!! IMPOSSIBLE!!!! There were some "professors" who published articles/chapters very close to Bohr's complementarity, Dirac, de Broglie's dualism before 2005 (for instance Carlo Rovelli 1996 or Ladyman), but their works were constructed within the "unicorn world" (Universe/world), therefore, these works had nothing in common with the EDWs perspective!!!! In reality, all of them plagiarized my ideas! It was like many people composed Beethoven Fifth’s Symphony, claiming that they never listen Beethoven! Who would be so stupid to believe them

LIPIcs, Volume 258, SoCG 2023, Complete Volume

LIPIcs, Volume 258, SoCG 2023, Complete Volum

Advances and Applications of Dezert-Smarandache Theory (DSmT) for Information Fusion (Collected Works), Vol. 4

The fourth volume on Advances and Applications of Dezert-Smarandache Theory (DSmT) for information fusion collects theoretical and applied contributions of researchers working in different fields of applications and in mathematics. The contributions (see List of Articles published in this book, at the end of the volume) have been published or presented after disseminating the third volume (2009, http://fs.unm.edu/DSmT-book3.pdf) in international conferences, seminars, workshops and journals. First Part of this book presents the theoretical advancement of DSmT, dealing with Belief functions, conditioning and deconditioning, Analytic Hierarchy Process, Decision Making, Multi-Criteria, evidence theory, combination rule, evidence distance, conflicting belief, sources of evidences with different importance and reliabilities, importance of sources, pignistic probability transformation, Qualitative reasoning under uncertainty, Imprecise belief structures, 2-Tuple linguistic label, Electre Tri Method, hierarchical proportional redistribution, basic belief assignment, subjective probability measure, Smarandache codification, neutrosophic logic, Evidence theory, outranking methods, Dempster-Shafer Theory, Bayes fusion rule, frequentist probability, mean square error, controlling factor, optimal assignment solution, data association, Transferable Belief Model, and others. More applications of DSmT have emerged in the past years since the apparition of the third book of DSmT 2009. Subsequently, the second part of this volume is about applications of DSmT in correlation with Electronic Support Measures, belief function, sensor networks, Ground Moving Target and Multiple target tracking, Vehicle-Born Improvised Explosive Device, Belief Interacting Multiple Model filter, seismic and acoustic sensor, Support Vector Machines, Alarm classification, ability of human visual system, Uncertainty Representation and Reasoning Evaluation Framework, Threat Assessment, Handwritten Signature Verification, Automatic Aircraft Recognition, Dynamic Data-Driven Application System, adjustment of secure communication trust analysis, and so on. Finally, the third part presents a List of References related with DSmT published or presented along the years since its inception in 2004, chronologically ordered