Virtual 3D city models act as valuable central information hubs supporting many aspects of cities, from management to planning and simulation. However, we noted that 3D city models are still underexploited and believe that this is partly due to inefficient visual communication channels across 3D model producers and the end-user. With the development of a formalized 3D geovisualization approach, this paper aims to support and make the visual identification and recognition of specific objects in the 3D models more efficient and useful. The foundation of the proposed solution is a knowledge network of the visualization of 3D geospatial data that gathers and links mapping and rendering techniques. To formalize this knowledge base and make it usable as a decision-making system for the selection of styles, second-order logic is used. It provides a first set of efficient graphic design guidelines, avoiding the creation of graphical conflicts and thus improving visual communication. An interactive tool is implemented and lays the foundation for a suitable solution for assisting the visualization process of 3D geospatial models within CAD and GIS-oriented software. Ultimately, we propose an extension to OGC Symbology Encoding in order to provide suitable graphic design guidelines to web mapping services.
We prove an algebraic canonicity theorem for normal LE-logics of arbitrary signature, in a generalized setting in which the non-lattice connectives are interpreted as operations mapping tuples of elements of the given lattice to closed or open elements of its canonical extension. Interestingly, the syntactic shape of LE-inequalities which guarantees their canonicity in this generalized setting turns out to coincide with the syntactic shape of analytic inductive inequalities , which guarantees LE-inequalities to be equivalently captured by analytic structural rules of a proper display calculus. We show that this canonicity result connects and strengthens a number of recent canonicity results in two different areas: subordination algebras, and transfer results via Gödel-McKinsey-Tarski translations.
Let X be a compact Hausdorff space. It is well known that X can be characterized by its ring of real continuous functions, by its set of regular open subsets or more simply by its set of open subsets. These characterizations lead to dualities between the category KHaus, of compact Hausdorff space and respectively the categories C -alg (or equivalently ubal), of commutative C -algebras, DeV of de Vries algebras and KRFrm of compact regular frames. Later, G.Bezhanishvili and J.Harding extended in [1] a part square to dualities between the categories StKSp of stably compact spaces, RPrFrm of regular proximity frames and StKFrm of stably compact frames.We thus get the square of dualities extended this way. StKSp RPrFrmKHaus DeV C -alg KRFrm StKFrmOur aim is to complete the outside triangle, looking for a category generalizing the Calgebras.Using the equivalences between StKSp and the category KPSp of compact po-spaces (see [4]), an essential fact, due to G.Hansoul in [5] leads us to consider a category of ordered semiring. Indeed, we can see that the Nachbin-Stone-Cech compactification of a completely regular ordered po-space X can be realized through its semi-ring of increasing, continuous and real, positive functions, denoted I(X, R + ). Following the definitions of G.Bezhanishvili, P.Morandi and B.Olberding in [2], we define the bounded Archimedean -semi-algebras this way. Definition 1.1. An -semi-ring is an algebra (A, +, ., 0, 1, ≤) with the following axioms :(a) (A, +, 0) and (A, ., 1) are commutative monoids.2. An -semi-ring A is bounded if for all a ∈ A, there is n ∈ N such that a ≤ n.1.3. An -semi-ring A is Archimedean if for all a, b, c, d ∈ A, whenever n.a + b ≤ n.c + d, then a ≤ c.
We prove an algebraic canonicity theorem for normal LE-logics of arbitrary signature, in a generalized setting in which the non-lattice connectives are interpreted as operations mapping tuples of elements of the given lattice to closed or open elements of its canonical extension. Interestingly, the syntactic shape of LE-inequalities which guarantees their canonicity in this generalized setting turns out to coincide with the syntactic shape of analytic inductive inequalities, which guarantees LEinequalities to be equivalently captured by analytic structural rules of a proper display calculus. We show that this canonicity result connects and strengthens a number of recent canonicity results in two different areas: subordination algebras, and transfer results via Gödel-McKinsey-Tarski translations.
ABSTRACT:This paper deals with the establishment of a comprehensive methodological framework that defines 3D visualisation rules and its application in a decision support tool. Whilst the use of 3D models grows in many application fields, their visualisation remains challenging from the point of view of mapping and rendering aspects to be applied to suitability support the decision making process. Indeed, there exists a great number of 3D visualisation techniques but as far as we know, a decision support tool that facilitates the production of an efficient 3D visualisation is still missing. This is why a comprehensive methodological framework is proposed in order to build decision tables for specific data, tasks and contexts. Based on the second-order logic formalism, we define a set of functions and propositions among and between two collections of entities: on one hand static retinal variables (hue, size, shape…) and 3D environment parameters (directional lighting, shadow, haze…) and on the other hand their effect(s) regarding specific visual tasks. It enables to define 3D visualisation rules according to four categories: consequence, compatibility, potential incompatibility and incompatibility. In this paper, the application of the methodological framework is demonstrated for an urban visualisation at high density considering a specific set of entities. On the basis of our analysis and the results of many studies conducted in the 3D semiotics, which refers to the study of symbols and how they relay information, the truth values of propositions are determined. 3D visualisation rules are then extracted for the considered context and set of entities and are presented into a decision table with a colour coding. Finally, the decision table is implemented into a plugin developed with three.js, a cross-browser JavaScript library. The plugin consists of a sidebar and warning windows that help the designer in the use of a set of static retinal variables and 3D environment parameters.
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