Level of” Matrix (LoX)
1. Level of Detail (LoD)
Ever since the dawn of architecture, there is a tradition of architectural models. These models differ from actual computer-based models by a certain degree of abstraction that can be tied to a certain scale. Digital 3D models have no scale. They are always thought to be a 1:1 representation of objects. Nevertheless there is a concept of different degrees of abstraction in digital 3D models too which is called level of detail (LoD). This concept originates from the need to reduce render time: „Discrete level of detail, the traditional approach creates LoD for each of the object separately in a pre-process. At run-time, it picks each object’s LoD according to the particular selection criterions.“ [ A Review on Level of Detail, p. 71.]
Version 2.0 of CityGML a geographic markup language describing 3D city models includes rules for the representation of buildings in five different levels of detail which are strongly connected to the semantics of that language: „In CityGML, all object classes are associated to the LoDs with respect to the proposed minimum acquisition criteria for each LoD (…) An object can be represented simultaneously in different LoDs by providing distinct geometries for the corresponding LoDs.“ [KOLBE 2009] According to Tan and Daut this is a concept of discrete LoDs enriched by semantic rules for the use of these LoDs: „For example, a building may be assigned a solid geometry in LoD2. If the building is further decomposed into thematic surfaces like WallSurface, RoofSurface etc. their associated geometries should refer to those surface geometry objects which are part of the outer shell of the building’s solid geometry.“ [OGC City Geography Markup Language ] This is a promising idea for semantic 3D reconstruction models which is further developed for CHML. We call this semantic LoD (Hauck 2014).
The semantic LoD stands for a strong connection between building parts (model components) and their CHML type. Architectural terms in general imply a certain scale or LoD: if someone talks about a palace this includes everything inside the building like storeys, rooms, ceilings, doors, paintings etc. This means that the term building implies a lower LoD as the term room which implies a lower LoD than the term wainscot. These terms can also be linked to traditional architectural scales: a 1:100 section plan does not show details like baseboards, but a 1:20 wallelevation plan does. We suggest nine different LoDs for CHML without strict rules for which CHML type has to modelled in which LoD. We recommend to decide this on the basis of the project’s requirements following one strict rule: broader types should have a lower LoD than narrower types and the modelling of one object/type in more than one LoD should be avoided.
In other words: the semantic LoD can be connected to traditional plan and model scales. Thus the information granularity of sources can be expressed in a similar way called „level of information“ (LoI). Concerning plans with scales, it appears quite obvious, but also images and even text mentions can relate to scales using the semantic LoD: if an image shows objects that would be shown by plans at a certain scale, the image is consistent with the same scale and LoD/LoI (Tab.1). This leads to a convenient way of expressing the hypothetical aspect („level of hypothesis“ LoH) of a 3D reconstruction model: LoD – LoI = LoH. Tab 1 shows the resulting “Level of” matrix called „LoX“ (HAUCK 2014)
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