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PFG – Journal of Photogrammetry, Remote Sensing and Geoinformation Science
, Volume 88 (1) – Feb 3, 2020

/lp/springer-journals/a-concept-of-quality-management-of-3d-city-models-supporting-rVrAbhzHEU

- Publisher
- Springer Journals
- Copyright
- Copyright © The Author(s) 2020
- ISSN
- 2512-2789
- eISSN
- 2512-2819
- DOI
- 10.1007/s41064-020-00094-0
- Publisher site
- See Article on Publisher Site

In this paper, a novel approach to specify application-specific requirements for 3D City Models is proposed. A modular set of geometric and semantic requirements that are based on the OGC CityGML Quality Interoperability Experiment (Coors and Wagner in Fernerkundung und Geoinformation eV 24:288–295, 2015) has been specified. Depending on the purpose of the model, not all requirements are mandatory. For example, if the model is used for visualization only, solid geometry is not required. However, if the same model should be used for analytic purpose such as heating demand simulation, solid geometry is mandatory. A formal definition of a validation plan is proposed in this paper to specify the application-specific set of requirements. This gives the city model manufacturers the possibility to provide proof that their model is usable in certain applications and can certify a certain level of quality. The concept is evaluated with the definition of a validation plan for heating demand simulation. It has been successfully implemented using the Software CityDoctor and SimStadt. Keywords 3D City Model · CityGML · Quality management · Heating demand simulation Zusammenfassung Ein Konzept für das Qualitätsmanagement von 3D-Stadtmodellen zur Unterstützung von anwendungsspezifischen Anforderun- gen. In diesem Beitrag wird eine neue Methode zur Spezifikation anwendungsabhängiger Anforderungen an 3D-Stadtmodelle vorgestellt. Ein modularer Satz von geometrischen und semantischen Anforderungen, die auf dem “OGC CityGML Quality Interoperability Experiment” basieren (Coors und Wagner in Fernerkundung und Geoinformation eV 24:288–295, 2015) wurde definiert. Je nach Zweck des Modells sind nicht alle Anforderungen zwingend erforderlich. Wenn das Modell beispiels- weise nur zur Visualisierung verwendet wird, spielt die Volumengeometrie keine Rolle. Wenn jedoch dasselbe Modell für analytische Zwecke wie der Simulation des Heizungsbedarfs verwendet werden soll, ist die genaue 3D-Geometrie erforder- lich. Der Artikel schlägt einen Validierungsplan vor, der abhängig von der Anwendung jeweils einen Satz von Anforder- ungen festlegt. Dies gibt den Herstellern von Stadtmodellen die Möglichkeit, den Nachweis zu erbringen, dass ihr Modell für bestimmte Anwendungen geeignet ist und dabei ein bestimmtes Qualitätsniveau garantiert. Unser Konzept wurde am Beispiel einer Heizungsbedarfsanalyse überprüft und erfolgreich in der Software CityDoctor und SimStadt implementiert. Schlüsselwörter 3D-Stadtmodell · CityGML · Qualitätsmanagement · Heizungsbedarfssimulation 1 Introduction The digital transformation process of cities has become vis- ible through the concept of a “Smart City”. More and more * Matthias Betz matthias.betz@hft-stuttgart.de information and communication technology are employed to solve urban development challenges such as natural resource Volker Coors volker.coors@hft-stuttgart.de management, air quality, mobility, sustainable food, water, and energy supply (Balakrishna 2012; Calvillo et al. 2016; Eric Duminil eric.duminil@hft-stuttgart.de Nam and Pardo 2011). Cities have a share of up to 80% of the world’s greenhouse gas emissions (Murray 2015). HFT Stuttgart, Stuttgart, Germany Vol.:(0123456789) 1 3 4 PFG (2020) 88:3–14 Fig. 1 Data quality matters: changing just the orientation of one polygon in the building geometry reduces the calculated volume from 56.25 (correct) to 18.75 m using FME volume calculator Besides industry and transportation, heating and cooling cooling demand of a building depends on the volume, this of buildings is one of the main sources of CO emission. will lead to wrong simulation results. Reducing this heating and cooling demand will have a sig- In this paper, a general methodology to define applica- nificant impact on climate protection worldwide. tion-specific requirements to a 3D City Model is proposed. To achieve this aim and to develop integrated energy con- This methodology is independent of a specific software solu- cepts in urban districts, it is necessary to have an insight tion, but of course, an implementation is needed to validate into the energetic performance of the areas of interest. Fore- existing models. In this paper, the software CityDoctor is casting the future energy demand for heating and cooling used for this purpose. for buildings at district level and beyond is essential for the The paper is organized as follows: Sect. 2 will give a brief development of climate protection strategies for munici- summary of the state of the art in quality management of 3D palities world wide. This requires methods to simulate the City Models. In Sect. 3, an overview of a monthly energy impact of future developments such as refurbishment of balance to calculate the heating and cooling demand of a buildings and reliable data of the existing building stock. building is given. A general methodology to validate 3D The availability of 3D building models has increased tre- City Models is introduced in Sect. 4, with a focus on geom- mendously. Most of the models are available in CityGML etry validation in Sect. 5. This methodology is applied in (Kolbe 2009; Gröger and Plümer 2012). Some urban simula- Sect. 6 to validate if a 3D City Model is suitable for heating tion tools such as SimStadt (Nouvel et al. 2015) and City- and cooling demand simulation. Section 7 shows an imple- Sim (Robinson et al. 2009) support CityGML as an input mentation of this validation process in a use case in the city heating and cooling demand simulation. The simulation district “Stadtgärtnerei” in Mainz, Germany. The paper con- results strongly depend on the quality of the input data. As cludes with discussion of the proposed methodology and the an example, small errors in the building geometry can have achieved results in Sect. 8. a big impact on the calculated volume of a building (Biljecki et al. 2018). To illustrate this, a simple experiment has been set up. 2 State of the Art A building with a rectangular footprint (3 m × 5 m) and a saddle roof with 3 m eaves height and 4.5 m ridge height In 2015, Biljecki et al. summarized applications that make is modelled in CityGML with LoD 2 solid geometry. Each use of 3D City Models from interactive visualization, urban polygon of the building geometry is defined by a sequence planning, shadow and viewshed analysis to urban analytic of points in counterclockwise order. A FME workbench is and simulation (Biljecki et al. 2015). These applications have created to read the model and calculate the volume using very different requirements to the input data. For interactive the Transformer VolumeCalculator (Fig. 1). The result- visualization, it is sufficient to represent a building geometry ing volume is 56.25 m , which is correct. An error is then by a set of non-overlapping polygons, with no further con- introduced into the model. The orientation of one polygon straints. In contrast, urban analytics and simulation usually is changed by defining it with a sequence of points in clock - includes the calculation of building volumes. In this case, a wise order. The geometry is still the same, no coordinates solid geometry of the building is mandatory. These differ - have been modified. But calculating the volume of this ent requirements have to be taken into account in quality model leads to a volume of 18.75 m . As the heating and management of 3D City Models. As CityGML is an XML 1 3 PFG (2020) 88:3–14 5 process is not in practise yet. On the other hand, many exist- ing models are suited for visualization, but not necessarily for urban analytics and simulation applications, as this usu- ally requires a valid solid geometry. 3 Monthly Energy Balance 3.1 Balance Equations By applying the first law of thermodynamics to a given building (see Fig. 2), we have: Fig. 2 Modelling building energy performance (http://opene nergy Solar gain + internal gains + heating monit or.org). CC-BY-SA − ventilation losses − conduction losses = change in the internal energy of the building. format, any CityGML document can be validated against the XSD schema. However, this does not include any validation Assuming a constant temperature inside the building (thanks of the geometry or can take into account application-specic fi to an idealized heating system), we get: requirements. Heating = ventilation losses + conduction losses Ledoux (2013) has proposed a methodology to validate (1) solid geometry. Wagner et al. (2013a, b) take into account − solar gain − internal gains not only geometry, but also include some semantics such as BoundarySurface into the validation process. Both approaches have laid the foundations for the OGC CityGML Quality Interoperability Experiment (QIE) to define a uni- 3.2 Building Simulation in SimStadt fied method for the validation of 3D City Models (Coors and Wagner 2015). The result of this activity was the specifica- SimStadt is an urban energy simulation tool (Nouvel et al. tion of a set of validation rules that can be used to validate 2015). Several workflows are available, including a Monthly CityGML models and conformance requirements as defined Energy Balance simulation based on DIN V 18599 (Din in the CityGML standard. However, application-specific 2007). requirements are not taken into account. In 2016, Biljecki at The geometry is imported and then analyzed to determine al. did a survey on the quality of existing CityGML models building type, volume, external area and shared walls area. in Biljecki et al. (2016). However, the purpose of the model Additional attributes are required for the simulation, e.g. was not taken into account in this study. This is fundamental, building function and year of construction. A coordinate ref- as for example, a building geometry that consists of Multi- erence system also needs to be defined in order for weather Surface geometry using triangles only is valid according to and irradiance calculations to be possible. the CityGML standard. The standard requires a MultiSurface OR a solid geometry in all levels of detail. 3.3 Influence of Geometry on the Energy Balance The Working Committee of the Surveying Authorities of the Laender of the Federal Republic of Germany (AdV) The building geometry has an influence on each of the terms has defined a CityGML profile for a nation-wide CityGML included in the Eq. (1). As an example: building model in 2016 (Landesamt 2019). This profile defines some restrictions such as a building has to have a • Polygon orientation must be correct to calculate solar solid geometry, and requires some mandatory attributes such gain. as building function. Based on the results of CityGML Qual- • Building volume is used to estimate the internal area, ity Interoperability Experiment, the AdV has published a which impacts internal gains and specific heat demand. validation plan for their profile in 2017 to enable quality • The total area of exterior surfaces is used to estimate management on a nation-wide CityGML 3D building model ventilation and conduction losses. in LoD 1 and LoD 2. To summarize, lot of work has been done to validate Trying to calculate the volume of buildings as described in solid geometry. However, a systematic approach to take into the introduction with a faulty geometry can lead to wrong account application-specific requirements in the validation 1 3 6 PFG (2020) 88:3–14 Fig. 3 Iterative process to vali- date and repair a 3D City Model against an application-specific validation plan. Both the vali- dated (and repaired) model and the validation plan are used as input in SimStadt to calculate monthly heating energy demand results. To avoid those errors, SimStadt flags building with 5 CityGML Validation negative volume or with volumes that are larger than their bounding box. They can be either ignored or replaced by As CityGML is based on XML, each CityGML file is an their bounding boxes. XML document. Definition 1 A CityGML document is schema conform, if it is validated against the CityGML XML Schema Definition 4 Methodology and no errors are found. To validate if a CityModel or more precisely a XSD-valid However, an XSD valid CityGML file is not always suited CityGML document fulfills the requirements of a specific for simulation purposes, as CityGML itself allows many dif- application, the following approach is proposed in this paper. ferent options to model a building (Coors and Wagner 2015). First of all, a formal system to specify such requirements Several additional requirements have to be fulfilled for this has been developed. In addition, an algorithm is needed to purpose. check whether a CityGML document fulfills a requirement or not. A validation software implements these algorithms. Definition 2 A requirement r is a verifiable criterion that To ensure interoperability, the specification of the validation says something about the content of a CityGML document plan as well as the requirements have to be agreed upon. or the data described therein. Based on the CityGML QIE, a modular set of requirements is proposed. As an example, a building has to have a valid solid geom- For a specific application, a subset of these requirements etry and the attributes yearOfConstruction and usage are is chosen to define a validation plan. This approach will be mandatory in heating demand simulation. Even if these evaluated by a validation plan for heating demand simula- attributes and the building geometry are missing, the tion. The results of the model validation include a reference CityGML document is XSD valid, as all these elements are to the validation plan to report what has been validated, and optional in the standard. the validation results of any CityObject. The entire process from the CityGML document to the simulation results is Definition 3 Let D be the set of valid CityGML documents shown in Fig. 3. Please note that the improvement of the 3D and d ∈ D . A check c ∶ D → Boolean is a function to vali- City Model usually requires some semi-automatic iterations. date a given CityGML document against the requirement r: The entire process has been evaluated with a use case in the City of Mainz. To calculate the heating energy demand, the true, if r is fulﬁlled in d c (d)= software SimStadt has been used. Data were provided by r false, else the City of Mainz. The focus of this study is the validation process, not the simulation itself. If c returns false, a specific error code including addi- tional parameters can be stored. 1 3 PFG (2020) 88:3–14 7 Definition 4 A validation plan is a set of require- the CityGML document has to be XSD valid • element yearOfConstruction is mandatory for each build- ments R ={r , r , ..., r } together with a set of checks 0 1 n C ={c , c , ..., c } that shall be used to validate these ing r r r 0 1 n • element function is mandatory for each building requirements. each building and building part has to have a valid lod2Solid geometry It is possible that some requirements are necessary in every validation plan for every application. To be as gen- each valid building and building part has to have valid Roof-, Wall-, Ground-, OuterFloor-, eral as possible, no set of requirement is defined which may be applied to all city models. If there is such a set, those OuterCeilingSurfaces with an unambiguous azimuth and tilt requirements are simply included in every validation plan. Remark 2 According to the CityGML standard, boundary Definition 5 A validation software is an implementation of algorithms to perform the checks of the validation plan. surfaces such as Wall-, Roof-, and GroundSurface shall not be used in LoD 1. In SimStadt, they are required, but can be The requirements and the related checks have to be automatically derived from a valid solid geometry. defined and agreed by data suppliers, data producers and data consumers to be able to develop data sets that can be Some of these requirements can be expressed in a for- mal language such as XQuery or Schematron (Wagner et al. used for multiple purposes. The aim of the OGC CityGML QIE (Coors and Wagner 2015) is to come up with such defi- 2014). In Coors and Wagner (2015), Schematron is pro- posed to validate CityGML conformance requirements. This nitions. In the following section, a validation plan for a 3D building model to be used to calculate the heating demand approach is used to formalize the above-mentioned require- ments as well. Each requirement will be identified by a given of a set of buildings using a monthly energy balance in the simulation software SimStadt, will be proposed. The valida- id and a related error code if the requirement is not fulfilled. The requirement that the element yearOfConstruction tion plan is based on the CityGML QIE and can be used for input data to a similar simulation software such as CitySim. is given per building in the CityGML document can be expressed in Schematron as follows: 5.1 Validation Plan for Heating Demand Simulation <rule context=”Building”> Using CityGML Building Models <assert t est=”count( yearOfConstruction) >=1”> The requirements of a CityGML data building model for SE MISSING ELEMENT heating demand simulation using a monthly energy balance yearOfConstructionin buildin g < method can be summarized as follows, depending on the value−of select =”@id”/> level of detail of the building model: </assert> In case of LoD 1: </rule> the CityGML document has to be XSD valid • element yearOfConstruction is mandatory for each Similar rules can be defined for other mandatory elements building such as function and lod1Solid. For simplicity, the name of • element function is mandatory for each building the mandatory element is a parameter of this requirement. It each building and building part has to have a valid is named SE-bldg:BU-0001 following the naming conven- lod1Solid geometry tions of Coors and Wagner (2015). The same requirement for building parts is called SE-bldg:BP-0001. However, geometry validation cannot be expressed as a Remark 1 If a building part has no element Schematron statement as several geometric constrains have yearOfConstruction or function, the value from the parent to be full fi led to proof that a collection of polygons is a valid building shall be used in SimStadt. solid. A solid is defined in ISO 19107 (ISO 2003) as: “A Solid is the basis for 3-dimensional geometry. In case of LoD 2: The extent of a solid is defined by the boundary sur- faces. The boundaries of Solids shall be represented as SolidBoundary. [...] The OrientablesSurfaces that bound a yearOfConstruction is a child element of building, and not an attribute in CityGML. solid shall be oriented outward.” Function is a child element of building, and not an attribute in CityGML. 1 3 8 PFG (2020) 88:3–14 Table 1 Requirements for linear rings Requirement id Description Error code GE-gml:LR-0001 R ≥ 4 GE_R_TOO_FEW_POINTS GE-gml:LR-0002 Two consecutive points shall not be the same GE_R_CONSECUTIVE_POINTS_SAME GE-gml:LR-0003 First-last points have to be the same GE_R_NOT_CLOSED GE-gml:LR-0004 No self-intersection GE_R_SELF_INTERSECTION GE-gml:LR-0005 Linear ring shall enclose a no empty area GE_R_COLLAPSED_TO_LINE In CityGML, the SolidBoundary consists of polygons but may give some hints to improve the building geometry only. A polygon is defined by one exterior linear ring and 0 later. or more interior linear rings. Interior linear rings are used Planarity of a linear ring is not required, but is defined to model polygons with holes. Rules to validate solid in on polygon level. CityGML have been published in Coors et al. (2019) and Usually, the coordinates of a point p ∈ R are given as Ledoux (2013). floating point numbers. A parameter 𝜏> 0 and a norm have to be introduced to define equality of two points. The default 5.2 Ring Checks norm is the l norm. Definition 6 An ordered set or sequence is an ordered list Definition 8 Two points P and Q are the same if of elements. Unlike a set, order matters, and the exact same ‖(P,Q)‖ <𝜏 . 𝜏> 0 is called the just notable difference elements can appear multiple times at different positions (JND) of two points. in the sequence. A finite sequence a with n + 1 elements is denoted as a =(a , a , ..., a ) . The empty sequence a = () Remark 3 The JND of two points is not the same as the 0 1 n has no elements. precision of the point location. For example, the precision of a measured point location can be 10 cm, but two different Definition 7 A finite sequence of points points might have a distance of 1 cm. These points are still R =(P , P , ..., P ) is a valid linear ring if two different points, even though there are some uncertainty 0 1 n in the location of the points. I R has at least four points: n ≥ 3 The impact of such a definition is illustrated by the fol- II All points of the sequence besides first and last point lowing example of a real-world CityGML building model. are different: P ≠ P , i = 0..n − 1, k = 0..n − 1, i ≠ k The building model with gml:id=DENW22AL10000c8S i k III The first and last point P and the last point P are the of the CityGML document LoD1_362_5700_1_NW.gml 0 n same: P = P contains a very small polygon in the LoD 1 geometry. 0 n IV Two edges (P , P + 1) and(P , P + 1), i = 0, ...n − 1, Two times two consecutive points of that polygon have i i k k k = 0, ..n − 1, i ≠ k do only intersect in one start-/ just a 1mm difference in the x -coordinate, y- and z-values endpoint. No other intersection is allowed. are exactly the same. If the model is validated against the linear ring requirements with a minimal point distance If all points of the sequence are co-planar, the linear ring is = 0.0005 , the geometry is valid. With a minimal point planar. distance of = 0.0011 , the linear ring is not valid any more. Table 1 defines five requirements GE-gml:LR-0001 to Two GE_R_CONSECUTIVE_POINTS_SAME errors GE-gml:LR-0005 that are necessary to validate a linear will be thrown during validation. And it will lead to ring. If a requirement is not fulfilled, a specific error code GE_R_SELF_INTERSECTION and GE_R_COLLAPSED_ is reported. Requirement GE-gml:LR-0001 corresponds TO_LINE errors as the polygon degenerates to a line in this to (I). GE-gml:LR-0002 only ensures that two consecu- case (Fig. 4). tive points are different. If two non-consecutive points As the ADV specifies the use of three digits after the beside the first and the last point are the same, it vio- decimal separator in its CityGML profile for LoD 1 and lates requirement GE-gml:LR-0004 (self intersection). LoD 2 building geometry (Landesamt 2019), = 0.0005 is GE-gml:LR-0002 and GE-gml:LR-0004 together are the same as II and IV. GE-gml:LR-0005 is redundant, as it is Open data: https ://www.openg eodat a.nrw.de/produ kte/geoba sis/3d- always a violation of GE-gml:LR-0004 (self intersection), gm/3d-gm_lod1/3d-gm_lod1_EPSG2 5832_CityG ML, last access 20.9.2019. 1 3 PFG (2020) 88:3–14 9 Fig. 4 Very small polygon with 1 mm width in an LoD 2 geometry of a building part. Validation using = 0.0005 results in a valid solid. With a minimal point distance of = 0.0011 , the linear ring is not valid any more Table 2 Polygon requirements Requirement id Description Error code GE-gml:PO-0001 2 + rings intersect GE_P_INTERSECTING_RINGS GE-gml:PO-0002 Planar polygon distance and/or GE_P_NON_PLANAR_POLYGON_ planar polygon normal deviation DISTANCE_PLANE GE_P_NON_PLANAR_POLYGON_ NORMALS_DEVIATION GE-gml:PO-0003 Interior is not connected GE_P_INTERIOR_DISCONNECTED GE-gml:PO-0004 1 or more interior rings are located GE_P_HOLE_OUTSIDE outside the exterior ring GE-gml:PO-0005 Interior ring is located inside other GE_P_INNER_RINGS_NESTED GE-gml:PO-0006 Exterior and interior rings GE_P_ORIENTATION_RINGS_SAME have same orientation a good threshold value in this case and the model is valid. V The order of points of the exterior linear ring defines The parameter JND of two points is very essential for the the orientation of the polygon. The interior linear validation process and should be added to the metadata of rings have to have the opposite orientation. the CityGML document. The interior linear rings define holes in the polygon. 5.3 Polygon Checks Table 2 gives an overview of the related requirements for polygons. Requirement GE-gml:PO-0002 ensures that Definition 9 A set of planar linear rings (I) is fulfilled. Planarity of a polygon (within a given S ={R , R , ..., R }, S ≠ � is a valid polygon if tolerance) can be defined using distance of all point to a 0 1 n regression plane or by the deviation of the normal vec- tor. For the deviation algorithm, the polygon needs to be I the exterior linear ring R and all interior linear rings tesselated. Each of the resulting triangles has a normal R , ..., R are co-planar. vector n resulting in a set of normal vectors for the poly- 1 n II The interior linear rings must be completely included gon N ={n , n , ..., n }, S ≠ � . The polygon is planar if the 0 1 m in the area defined by the exterior linear ring. Inte- scalar product of two normal vectors is less than a given rior linear rings must not overlap or be included in threshold ∀N ∈ N, ∀N ∈ N ∶ ⟨N , N ⟩ <𝜏 . i k i k another interior linear ring. GE-gml:PO-0001, GE-gml:PO-0004 and GE- III Interior linear rings and the exterior linear ring touch gml:PO-0005 correspond to (II) and (III), GE- each other in a finite number of points. gml:PO-0003 to (IV) and GE-gml:PO-0006 to (V). IV The inner of the polygon, as defined as the inner of the exterior ring excluding the inner of the interior rings, is connected. 1 3 10 PFG (2020) 88:3–14 Table 3 Requirements for solid geometry Requirement id Description Error code GE-gml:SO-0001 W ≥ 4 polygons GE_S_TOO_FEW_POLYGONS GE-gml:SO-0002 No edge has only GE_S_NOT_CLOSED one incident polygon (II).1 GE-gml:SO-0003 No non-manifold vertex (V) GE_S_NON_MANIFOLD_VERTEX GE-gml:SO-0004 No edge has more than GE_S_NON_MANIFOLD_EDGE 2 incident polygons (II).2 GE-gml:SO-0005 Only one connected component (IV) GE_S_MULTIPLE_CONNECTED_COMPONENTS GE-gml:SO-0006 No self intersection (I) GE_S_SELF_INTERSECTION GE-gml:SO-0007 (II).3 no edge (a,b) is used by GE_S_POLYGON_WRONG_ORIENTATION another polygon in the same order But only in order (b,a) GE-gml:SO-0008 All polygons have to be given in GE_S_ALL_POLYGONS_WRONG_ORIENTATION counterclockwise order (III) an edge e ∈ E if the two polygons represented by the 5.4 Solid Checks nodes have a common edge that touches P. Definition 10 The set W ={S , S , ..., S }, n ≥ 4 of polygons 0 1 n The statement of (I) formulates the intersection of the two is a solid geometry if: polygons S and S . The intersection results in an edge, a b which is an existing edge in both of the polygons. Polygons should always only “touch” along existing edges. The inter- I The intersection of two polygons S ∈ W defined as a a a a section must not be a new edge. set of planar linear rings S ={R , R , ..., R }, S ≠ � a a 0 1 n The statement of (VI) formulates the requirement that the and S ∈ W defined as a set of planar linear rings b b b graph is connected. S ={R , R , ..., R }, S ≠ � is either empty or con- b b 0 1 m From (I) and (II) follows that the surface defined by W has tains only a set of points Q ≠ and a set of edges no holes. Together with conditions (IV) and (V), it follows E ≠ that are part of both sets of linear rings: that the inner of the solid is connected. Q ≠ �, ∀q ∈ Q ∶ q ∈ R ∧ i=0...n If all these requirements of a solid’s geometry have been q ∈ R , and E ≠ �, s ∩ s = j=0...m fulfilled, the solid is valid (Table 3). a b ⎨ j ∀e =(q , q )∈ E ∶ q ∈ Q, q ∈ Q, i j i j a b ∃i, j ∶ e is an edge in both R and R Definition 11 The set M ={S , S , ..., S }, M ≠ � of poly- i j 0 1 n gons is a MultiSurface geometry. II e =(p , p ) is an edge in i j R ∈ S , j = 0...n ⟹ (e =(p , p ) is an edge in 1 j j i R ∈ S , k = 0...n, k ≠ j ∧ e =(p , p ) is not an edge 2 k i j5.5 Scalability in any other polygon R ∈ S , k = 0...n, k ≠ j. III All polygons R ∈ S , j = 0...n are oriented such that j All geometric requirements have been implemented as the normal vector of each polygon points to the out- checks in the CityDoctor software and tests have been con- side of the solid. ducted to ensure that massive amount of data can be pro- VI The dual graph G =(V ,E ) of W is connected. G W W W W cessed in a reasonable time frame. consists of a set of nodes V and a set of edges E . W W For this test, a PC with an i5-2400 @ 3.1 GHz was used. Every node v ∈ V represents one polygon of S ∈ W . W The file was a DLM-Model of Niedernhall with a filesize An edge e =(q , q ) shared by two polygons S ∈ W i j a of 3.3 GB. The batch process was completed in 4 m and 50 s and S ∈ W is represented by an edge e b in E . b a W while utilizing 1 core and less than 2 GB RAM, producing a V For every point P of a linear ring R of a polygon pdf and an xml report output file. S ∈ W applies: The graph G =(V , E ) , that is built P P P by polygons and edges that touch P is connected. Each node v ∈ V represents a polygon in which a linear ring contains P. Two nodes are connected by 1 3 PFG (2020) 88:3–14 11 Table 4 Requirements of a CityGML LoD 1 building model for monthly energy balance in SimStadt Requirement id Description Error code SC-all-0001 CityGML document is XSD valid SC-all-NOT_XSD_VALID SE-bldg:BU-0001 (yearOfConstruction) Mandatory element SE_MISSING_ELEMENT SE-bldg:BU-0001 (function) Mandatory element SE_MISSING_ELEMENT SE-bldg:BU-0001 (lod1Solid) Mandatory element SE_MISSING_ELEMENT SE-bldg:BP-0001 (lod1Solid) Mandatory element SE_MISSING_ELEMENT GE-gml:SO-0009 All solid geometries have to be valid One or many of the above defined error codes Table 5 Requirements for boundary surfaces Requirement id Description Error code SE-bldg:BS-0001 All polygons S ∈ M of the lod2MultiSurface geometry M of the Boundary- SE_BS_NON_PLANAR_MULTISURFACE Surface shall be coplanar within a given tolerance Table 6 Validation plan of a CityGML LoD 2 building model for monthly energy balance in SimStadt Requirement id Description SC-all-0001 CityGML document is XSD valid SE-bldg:BU-0001 (yearOfConstruction) Mandatory element yearOfConstruction SE-bldg:BU-0001 (function) Mandatory element function SE-bldg:AB-0001 (lod2Solid) Mandatory element lod2Solid GE-gml:SO-0009 All solid geometries have to be valid SE-bldg:AB-0001 (BoundedBy) Boundary surfaces mandatory conformance requirement solid ref Solid geometry reference boundary surface SE-bldg:AB-0001 (BoundedBy/RoofSurface) At least one RoofSurfaces mandatory SE-bldg:AB-0001 (BoundedBy/WallSurface) At least one WallSurfaces mandatory SE-bldg:AB-0002 (BoundedBy/GroundSurface) Exactly one GroundSurfaces mandatory GE-gml:MS-0001 All MultiSurface geometries have to be valid SE-bldg:BS-0001 All surfaces have an unambiguous azimuth and tilt SE-bldg:RS-0001 All RoofSurfaces have normal vector up (positve z) SE-bldg:WS-0001 All WallSurfaces have horizontal normal vector (z = 0) SE-bldg:GS-0001 All GroundSurfaces have normal vector down (negative z) SE-bldg:OFS-0001 All OuterFloorSurfaces have vector up (positive z), if any SE-bldg:OCS-0001 All OuterCeilingSurfaces have vector down (negative z), if any requirements and checks are listed and described. A depend- 5.6 Order of Requirements ency graph can be found in Coors and Betz (2019). Requirements depend on each other. In general, polygon 5.7 Storing the Validation Results as Metadata requirements depend on the ring requirements and solid requirement depend on the polygon and ring requirements. The results of the performed checks and the validation plan Every polygon has to be a valid polygon before the solid itself need to be stored as metadata. Other applications can requirements can be checked, otherwise it is possible to get use the metadata to ensure the validity of their calculations. false positive or false negative errors, which only lead to Once there are known errors, the result may also be wrong but confusion. if no error has been reported, one can assume the correctness For a detailed view of the dependencies, refer to the of the calculation. wiki of CityDoctor Validation Plan for SimStadt where all 1 3 12 PFG (2020) 88:3–14 Fig. 5 Initial error distribution of Stadtgärtnerei Mainz The metadata need to contain the validation plan to know The validation plans for SimStadt have already been which requirements were checked, the parameters used for the implemented in CityDoctor to verify CityGML files for the checks (e.g. point equality distance), the validation results, the usage in SimStadt. date and the file or model that was validated. For this purpose, a reference between metadata and model is possible. 7 Example Stadtgärtnerei Mainz 6 Validation Plan for Monthly Energy As a use case, the heating demand of the city district Balance Stadtgärtnerei in the City of Mainz, Germany is simulated using SimStadt based on a 3D Model of the existing building Not every requirement is useful for every use case. Each stock. As input data, a CityGML file containing the use case must specify a set of requirements and parameters LoD 2 geometry of the buildings was provided by the to ensure that it works correctly. City of Mainz. The first step before the simulation can To simplify the definition of a validation plan, an addi- be performed is to validate the model according to tion requirement GE-gml:SO-0009 (valid solid geometry) the specified validation plan. CityDoctor v3.2.0 was is introduced to group all the necessary requirements. used. As a result, the application found several hundred The validation plan for building models with LoD GE_R_CONSECUTIVE_POINTS_SAME errors. An 2 geometry is more complex as each building and overview of the initial error distribution can be seen in Fig. 5. building part has to have valid Roof-, Wall-, and These kinds of errors are not necessarily detrimental to the GroundSurfaces with an unambiguous azimuth and tilt. A simulation process, but they do inhibit some algorithms in boundary surface has a lod2MultiSurface geometry with the calculation. If two points have the same or nearly the no further constraints. same coordinates, they create an edge that has a zero-length Similar to the solid geometry, a grouping requirement or a nearly zero-length. Such an edge can result in some GE-gml:MS-0001 is introduced to validate multisurface extreme values for some calculations. The checks are geometry. A MultiSurface geometry M is valid if all poly- organized hierarchically. Thus, a following check depends gons S ∈ M are valid. To ensure that BoundarySurfaces such on the result of the previous. However, in some cases it is as Roof-, Wall-, and GroundSurface have an unambiguous azimuth and tilt, all polygons S ∈ M of the lod2MultiSur- face geometry M of the BoundarySurface shall be coplanar within a given tolerance. For the monthly energy balance in SimStadt the require- ments for LoD 1 are listed in Tables 4 and 5. For LoD 2, more requirements are needed because of the necessary boundary surfaces which need to be referenced by the solid. Table 6 has those additional requirements listed. Addition- ally for both LoD 1 and LoD 2, a coordinate system needs to be defined in the CityGML file. This is necessary to retrieve weather data for the city, which is needed for the simulation. Fig. 6 Visualization of test area Stadtgärtnerei Mainz. Model was provided by the City of Mainz (©Stadt Mainz) 1 3 PFG (2020) 88:3–14 13 necessary to perform a check without having completed Our investigation has rather revealed a hierarchy of cat- the previous checks. In this case, the error code egories where the lower categories are specializations of the GE_R_CONSECUTIVE_POINTS_SAME “hides” any higher ones. Consequently, a city model manufacturer has previous errors, which are to be detected at a later stage. the choice of selecting a higher category with its usability Consequently, those checks are not executed and it is, therefore, for all applications or a lower category, which serves specic fi unknown if they would have found further errors (Fig. 6). requirements. Fixing the model was an iterative process starting with GE_R_CONSECUTIVE_POINTS_SAME errors. After 8.1 Future Work removing those, further errors were found. Most of them were GE_S_NON_MANIFOLD_EDGE, GE_S_NOT_CLOSED It is planned to extend CityDoctor to implement a repair and GE_S_MULTIPLE_CONNECTED_COMPONENTS feature where faulty buildings are allowed to be in a (semi-) errors. More rare were GE_S_POLYGON_WRONG_ automatic process. This is not a simple task, as there are ORIENTATION errors were found more rarely. many ways to fix seemingly simple errors with different The manifold edge errors were the result of polygons results and repercussions. located inside the geometry. While the geometry looks A working group is implementing validation plans for correctly from the outside, these superfluous polygons have further applications to ensure that the methodology provided an impact in the calculations, specifically the volume calcu- in this paper is applicable to multiple applications. lation. The volume calculation takes every available polygon Acknowledgements Open Access funding provided by Projekt DEAL. into account, which consequently results in wrong results. The authors would like to thank the participants of the research pro- Another error that has a major impact on the volume cal- jects SimStadt and CityDoctor as well as the members of 3D City culation is the wrong orientation of a polygon. Model quality management working group of their for valuable input After the repair of the CityGML model, SimStadt was and discussion. The project SimStadt 2.0 is supported by the German Ministry of Economics (Contract 3ET1459A). The Project CityDoc- able to calculate the heat demand of the city quarter. tor 2.0 is funded within the program Forschung an Fachhochschulen by the German Federal Ministry of Education and Research (Contract 13FH179PB6). The 3D City Model quality management working group 8 Conclusion is voluntary work under the umbrella of the Joint Commission on 3D City Models (https ://3d-stadt model le.org/) of the German Society of Cartography and the German Society of Photogrammetry, Remote The workflow of validating the GML models before the Sensing, and Geoinformation. simulation works very well as there is now a possibility to judge the validity of the simulation results. The validation Compliance with Ethical Standards plan will be used in the simulation software SimStadt in the workflow to automatically create an indicator on the uncer - Conflict of interest The authors declare that they have no conflict of tainty of the resulting values. interest. For better feasibility in validating the models, it is imper- Open Access This article is licensed under a Creative Commons Attri- ative that the creator of the CityGML files inserts the accu- bution 4.0 International License, which permits use, sharing, adapta- racy of the vertices into the file as a mandatory parameter. tion, distribution and reproduction in any medium or format, as long Otherwise, choosing a useful JND may result in “guess- as you give appropriate credit to the original author(s) and the source, work” or the chosen JND may not be useful. As an exam- provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are ple, if a file has a vertex accuracy of three decimal places included in the article’s Creative Commons licence, unless indicated and two JNDs are chosen for two different validation plans, otherwise in a credit line to the material. If material is not included in respectively, 0.0001 m and 0.00001 m. They would both the article’s Creative Commons licence and your intended use is not have the same result as the input data do not have the neces- permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a sary accuracy to support those JNDs. copy of this licence, visit http://creativ ecommons .or g/licenses/b y/4.0/. The validation plans can also lead to a categorization of the 3D-Models. Not every CityGML file is applicable for any application. To check whether the file can be used or not, References the validation plans and the validation software are applied. Manufacturers can on the basis of our approach specify that Balakrishna C (2012) Enabling technologies for smart city services their model can be used for some applications while for oth- and applications. 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PFG – Journal of Photogrammetry, Remote Sensing and Geoinformation Science – Springer Journals

**Published: ** Feb 3, 2020

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