A Tool for the 3D Spatio-Temporal Structuring of Historic Building Reconstructions

The difficulty in the description, the analysis and the comprehension of cultural heritage often stands on the fact that buildings undergo numerous changes over time. Three factors condition the knowledge of historical heritage. Firstly, 3D reconstructions of heritage buildings focus normally on existing states and not on the management of historical evolutions. Secondly, if on one side iconographic sources are generally used like visual memory of a building temporal state to be restored graphically, on the other side few works today focus on the use of all metric and visual information contained in sources. At last, iconographic documentation concerning building past states is sometimes contradictory, dubious and incomplete. As a consequence, in 3D reconstructions uncertainties, contradictions and gaps in information should be highlighted. We present a methodological approach basing on the existing iconographic corpus for the analysis and the 3D management of building transformations. This approach joins three main aspects in a complete workflow. Firstly, it concerns the spatial and temporal referencing of 2D iconographic sources for the 3D reconstruction of disappeared building states. Secondly, it allows the analysis of building transformations by means of a temporal state distribution. Lastly, it uses spatial relations established between 2D iconography and 3D representation for the visual browsing of information based on spatiotemporal criteria. In particular, in this paper we detail the interface developed in order to accomplish multiple related tasks concerning the spatio-temporal structuring of the morphology to be reconstructed

A fixed point theorem without convexity

The purpose of this paper is to extend Himmelberg's fixed point theorem replacing the usual convexity in topological vector spaces by an abstract topological notion of convexity which generalizes classical convexity as well as several metric convexity structures found in the literature. We prove the existence, under weak hypotheses, of a fixed point for a compact approachable map and we provide sufficient conditions under which this result applies to maps whose values are convex in the abstract sense mentionned above

An image-based approach for the architectural modeling of past states

During the modelling process, 3D models are not easily conceived to support changes over time. On the contrary, for the description of cultural heritage, it is often necessary to display not only the actual state of buildings but also their previous states so to understand their modifications. The construction and structuring of spatio-temporal models of cultural heritage demand a double conceptual effort: on one side, 3D models must be reconstructed and structured in space according to architectural concepts; on the other one, such elements should follow the criteria of temporal decomposition. For this reason, links between structured elements should be established to keep track of changes over time. Moreover, only the current state can be reconstructed in a rigorous way using a combination of different 3D measurement techniques (such as laser scanning and photogrammetry); on the contrary, knowledge about past states is conditioned by missing elements, whose morphology and dating can reveal uncertain. For this reason, this paper describes a methodological approach to make use of the existing iconographic corpus for the analysis and the 3D management of building transformations. The aim is to establish a relation between the iconography used for the hypothetical reconstruction and the 3D representation that depends on it. As a result, 3D representations can be used like visualization systems capable of reflecting the amount of knowledge produced studying historic building

An Iconography-Based Modeling Approach for the Spatio-Temporal Analysis of Architectural Heritage

The study of historic buildings is usually based on the collection and analysis of iconographic sources such as photographs, drawings, engravings, paintings or sketches. This paper describes a methodological approach to make use of the existing iconographic corpus for the analysis and the 3D management of building transformations. Iconography is used for different goals. Firstly, it's a source of geometric information (image-based-modeling of anterior states); secondly, it's used for the re-creation of visual appearance (image-based texture extraction); thirdly it's a proof of the temporal distribution of shape transformations (spatio-temporal modeling); finally it becomes a visual support for the study of building transformations (visual comparison between different temporal states). The aim is to establish a relation between the iconography used for the hypothetical reconstruction and the 3D representation that depends on it. This approach relates to the idea of using 3D representations like visualization systems capable of reflecting the amount of knowledge developed by the study of a historic buildin

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Banda Ace

A Tool for the 3D Spatio-Temporal Structuring of Historic Building Reconstructions

The difficulty in the description, the analysis and the comprehension of cultural heritage often stands on the fact that buildings undergo numerous changes over time. Three factors condition the knowledge of historical heritage. Firstly, 3D reconstructions of heritage buildings focus normally on existing states and not on the management of historical evolutions. Secondly, if on one side iconographic sources are generally used like visual memory of a building temporal state to be restored graphically, on the other side few works today focus on the use of all metric and visual information contained in sources. At last, iconographic documentation concerning building past states is sometimes contradictory, dubious and incomplete. As a consequence, in 3D reconstructions uncertainties, contradictions and gaps in information should be highlighted. We present a methodological approach basing on the existing iconographic corpus for the analysis and the 3D management of building transformations. This approach joins three main aspects in a complete workflow. Firstly, it concerns the spatial and temporal referencing of 2D iconographic sources for the 3D reconstruction of disappeared building states. Secondly, it allows the analysis of building transformations by means of a temporal state distribution. Lastly, it uses spatial relations established between 2D iconography and 3D representation for the visual browsing of information based on spatiotemporal criteria. In particular, in this paper we detail the interface developed in order to accomplish multiple related tasks concerning the spatio-temporal structuring of the morphology to be reconstructed

Equilibrium existence in infinite horizon economies

In sequential economies with finite or infinite-lived real assets in positive net supply, we introduce constraints on the amount of borrowing in terms of the market value of physical endowments. We show that, when utility functions are either unbounded and separable in states of nature or separable in commodities, these borrowing constraints not only preclude Ponzi schemes but also induce endogenous Radner bounds on short-sales. Therefore, we obtain existence of equilibrium. Moreover, equilibrium also exists when both assets are numéraire and utility functions are quasilinear in the commodity used as numéraire.info:eu-repo/semantics/publishedVersio