Three-Dimensional Thematic Map Imaging of the Yacht Port on the Example of the Polish National Sailing Centre Marina in Gda ´Nsk

applied sciences

Article Three-Dimensional Thematic Map Imaging of the Yacht Port on the Example of the Polish National Sailing Centre Marina in Gda ´nsk

Pawel S. Dabrowski 1 , Cezary Specht 1,* , Mariusz Specht 2 and Artur Makar 3

1 Department of Geodesy and Oceanography, Gdynia Maritime University, 81-347 Gdynia, Poland; [email protected] 2 Department of Transport and Logistics, Gdynia Maritime University, 81-225 Gdynia, Poland; [email protected] 3 Department of Navigation and Hydrography, Polish Naval Academy, 81-127 Gdynia, Poland; [email protected] * Correspondence: [email protected]

Abstract: The theory of cartographic projections is a tool which can present the convex surface of the Earth on the plane. Of the many types of maps, thematic maps perform an important function due to the wide possibilities of adapting their content to current needs. The limitation of classic maps is their two-dimensional nature. In the era of rapidly growing methods of mass acquisition of spatial data, the use of flat images is often not enough to reveal the level of complexity of certain objects. In this case, it is necessary to use visualization in three-dimensional space. The motivation to conduct the study was the use of cartographic projections methods, spatial transformations, and the possibilities offered by thematic maps to create thematic three-dimensional map imaging (T3DMI). The authors presented a practical verification of the adopted methodology to create a T3DMI visualization of Citation: Dabrowski, P.S.; Specht, C.; Specht, M.; Makar, A. the marina of the National Sailing Centre of the GdańskUniversity of Physical Education and Sport Three-Dimensional Thematic Map (Poland). The profiled characteristics of the object were used to emphasize the key elements of its Imaging of the Yacht Port on the function. The results confirmed the increase in the interpretative capabilities of the T3DMI method, Example of the Polish National relative to classic two-dimensional maps. Additionally, the study suggested future research directions Sailing Centre Marina in Gdańsk. of the presented solution. Appl. Sci. 2021, 11, 7016. https:// doi.org/10.3390/app11157016 Keywords: three-dimensional imaging; thematic map; T3DMI; data harmonization; laser scanning; bathymetry Academic Editor: Paraskevi Nomikou

Received: 4 July 2021 Accepted: 27 July 2021 1. Introduction Published: 29 July 2021 The purpose of using cartographic projections and creating maps is to present a convex

Publisher’s Note: MDPI stays neutral surface approximating to the shape of the Earth (sphere or rotational ellipsoid) on a flat with regard to jurisdictional claims in two-dimensional surface [1]. The mapping functions enable the transition from angular published maps and institutional affil- coordinates of longitude and latitude to orthogonal coordinates on the plane [2]. Attributes iations. containing selected spatial information such as the course of borders, height in the adopted reference system, or the manner of land use are assigned to the planar coordinates [3]. A key feature of cartographic mapping is the mutual assignment of points on the Earth’s surface and the map’s surface [4]. As a result, a unique assignment of each point on the surface of the original to exactly one point on the surface of the image is obtained [5]. An Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. inherent feature of all mapping is the occurrence of mapping distortions. Hence, when This article is an open access article creating maps, the available projections are analyzed and the mapping is carefully selected, distributed under the terms and which in turn represents the desired region of the Earth in the least disturbed manner [6,7]. conditions of the Creative Commons Maps, due to various content and purpose, are divided according to various criteria. Attribution (CC BY) license (https:// Thanks to mathematical properties, mappings dedicated to the needs of specific areas of creativecommons.org/licenses/by/ human activity are known, e.g., navigation [8,9], or land surveying [10]. In turn, in order to 4.0/). present local and global processes, thematic maps are created [11]. The catalog of thematic

Appl. Sci. 2021, 11, 7016. https://doi.org/10.3390/app11157016 https://www.mdpi.com/journal/applsci Appl. Sci. 2021, 11, 7016 2 of 12

Maps, due to various content and purpose, are divided according to various criteria. Appl. Sci. 2021, 11, 7016 Thanks to mathematical properties, mappings dedicated to the needs of specific areas2 of 12 of human activity are known, e.g., navigation [8,9], or land surveying [10]. In turn, in order to present local and global processes, thematic maps are created [11]. The catalog of thematic map applications is constantly growing alongside the development of technology mapand applicationshuman needs is [12]. constantly An important growing theoretical alongside aspect the development of creating ma ofps technology is spatial visual- and humanization needs semiotics [12]. [13]. An important Semantic, theoretical syntactic, aspectand pragmatic of creating components maps is spatial determine visualization how to semioticsbuild and [13 connect]. Semantic, cartographic syntactic, elements and pragmatic on the map components and their determine relationship how with to buildthe re- andcipient. connect Technological cartographic development elements on over the the map past and few their decades relationship has largely with eliminated the recipient. the Technologicaluse of classic paper development maps. Currently, over the pastthe standard few decades use of has maps largely is electronic eliminated imaging, the use often of classicavailable paper on-line maps. [14]. Currently, The first signals the standard of a diametrical use of maps change is in electronic cartography imaging, were noticed often available on-line [14]. The first signals of a diametrical change in cartography were noticed as early as the 1990s [15]. as early as the 1990s [15]. Rapid technological development observed in recent years is also reflected in meas- Rapid technological development observed in recent years is also reflected in measure- urement technologies used to obtain source data for creating maps. Particularly notewor- ment technologies used to obtain source data for creating maps. Particularly noteworthy thy are the measurement methods that implement mass data acquisition in a short time, are the measurement methods that implement mass data acquisition in a short time, such such as laser scanning [16], bathymetric surveys [17], satellite GNSS measurements [18] as laser scanning [16], bathymetric surveys [17], satellite GNSS measurements [18] or or photogrammetric flight missions by unmanned aerial vehicles [19]. The large amount photogrammetric flight missions by unmanned aerial vehicles [19]. The large amount of data collected during these measurement methods calls for generalization, e.g., in the of data collected during these measurement methods calls for generalization, e.g., in the form of three-dimensional models [20]. Nevertheless, even after applying cartographic form of three-dimensional models [20]. Nevertheless, even after applying cartographic generalization procedures, the presentation of all objects at once is a complex problem. generalization procedures, the presentation of all objects at once is a complex problem. This especially applies to areas with a high degree of urbanization, where significant in- This especially applies to areas with a high degree of urbanization, where significant in- frastructurefrastructure facilities facilities are are located located at at points points with with the the same same horizontal horizontal coordinates, coordinates, but but at at differentdifferent heights. heights. Generally,Generally, maps maps differ differ in in both both the the content content and and component component parts. parts. Simple Simple maps maps consist consist ofof several several elements, elements, while while more more complex complex maps maps (e.g., (e.g., topographical) topographical) contain contain more elements.more ele- Everyments. map Every is a setmap of strictlyis a set defined of strictly graphical defined elements. graphical Some elements. of the signs Some are of subordinated the signs are tosubordinated cartographic to rules cartographic and depict rules some and real depict world some objects. real Other world elements objects. of Other the map elements are not of cartographicthe map are and not arecartographic thus subject and to differentare thus rulessubject or to do different not represent rules anyor do real not life represent objects. Ref.any [ 21real] mentionslife objects. an [21] example mentions of the an mapexam titleple of and the legend. map title Those and legend. descriptive Those elements descrip- aretive controlled elements byare natural controlled language by natural rules, langua and theirge rules, location and on their the lo mapcation is controlledon the map by is aestheticcontrolled rules by ofaesthetic the map rules creator. of the Thematic map creato mapsr. Thematic belong to maps the group belong of to geographical the group of maps.geographical Friendly maps. [22] states Friendly that they[22] states are effective that they in discoveringare effective and in discovering exploring spatial and explor- data. Theing theme spatial is data. related The to thetheme chosen is related phenomena to the (e.g.,chosen economic, phenomena demographical (e.g., economic, or cultural). demo- Accordinggraphical toor Slocumcultural). et al.According [12] and Tynerto Slocum [7], in et many al. [12] cases and thematic Tyner [7], maps in many are defined cases the- by thematic special maps technique are defined used by for the the special map’s techniqu creation.e Those used techniquesfor the map’s are, creation. among others,Those tech- dot andniques flow are, maps, among diagrams, others, proportionaldot and flow maps, symbols diagrams, or isolines propor [23].tional Subjects symbols related or isolines to the preparation,[23]. Subjects development related to the and preparation, production dev of thematicelopment maps and areproduction well addressed of thematic in global maps literatureare well addressed [3,14]. The in division global li ofterature thematic [3,14]. maps, The according division of to thematic their purpose, maps, isaccording shown in to Figuretheir 1purpose,. is shown in Figure 1.

FigureFigure 1. 1.The The division division of of thematic thematic maps. maps.

It should be emphasized that thematic maps are made in a two-dimensional space based on strictly deﬁned cartographic principles, requiring the creator to have a basic knowledge of geography. Simpliﬁed forms of presentation used on maps (cartographic Appl. Sci. 2021, 11, 7016 3 of 12

Appl. Sci. 2021, 11, 7016 It should be emphasized that thematic maps are made in a two-dimensional3 space of 12 based on strictly defined cartographic principles, requiring the creator to have a basic knowledge of geography. Simplified forms of presentation used on maps (cartographic signs,signs, markings, markings, coordinate coordinate system system and and others) others) constitute constitute the the main main limitations limitations of of their their use use byby average average map map users. users. InIn addition addition toto thethe issueissue ofof generalizationgeneralization of content content presented presented on on maps, maps, the the need need to tovisualize visualize three-dimensional three-dimensional data data is is increasingly increasingly noteworthy. In thisthis case,case, thethe existing existing mappingmapping convention convention is is not not enough. enough. Ref. [24] [24 gives] gives an ananalysis analysis on on user user perception, perception, where where he hestates states that that the the flexibility flexibility of of representation representation of of 3D 3D map is greatergreater comparedcompared withwith that that of of traditionaltraditional planar planar maps. maps. Human Human perception perception of of the the world world and and how how 3D 3D representations representations ap- ap- pealpeal to to the the brain brain causes causes relatively relatively high high intuitiveness intuitiveness and and natural natural ease ofease understanding of understanding [25]. Musliman[25]. Musliman et al. [et26 ]al. state [26] that state 3D that human 3D huma visionn vision perceptions perceptions are processed are processed faster becausefaster be- morecause brain more neurons brain neurons are used are in used the in process. the process. Three-dimensional Three-dimensional projections projections resemble resemble the realthe worldreal world more more than than traditional traditional 2D mappings 2D mappings and and are thusare thus more more natural natural and and easier easier to decodeto decode bythe by humanthe human brain brain [27]. [27]. Additionally, Additional thely, studiesthe studies of GeoVEs of GeoVEs prove prove the usefulness the useful- ofness 3D representationof 3D representation [28]. [28]. OneOne of of the the specific specific types types of of thematic thematic three-dimensional three-dimensional maps maps are are projections projections in in the the formform of of plans plans for for informational informational purposes purposes (Figure (Figure2). 2). Their Their main main feature feature is is the the visualization visualization ofof a a specific specific area area in in a a 3D 3D perspective, perspective, where where all all objects objects are are presented presented in in near-real near-real shapes shapes andand dimensions dimensions and and where where the the source source data data for for the the mapping mapping has has been been obtained obtained by by various various surveyingsurveying techniques. techniques. A A model model example example is Google is Google Earth’s Earth’s Street Street View. View. They areThey often are usedoften asused a cartographic as a cartographic presentation presentation of the areaof the and area objects and inobjects the area in the such area as touristsuch as guides, tourist skiguides, resorts ski maps, resorts as wellmaps, as as plans well of as yacht plans ports. of yacht These ports. types These of maps types play of anmaps important play an roleimportant in everyday role lifein everyday because, apartlife because, from the apart information from the they information include, they they allow include, the user they toallow create the a spatialuser to orientationcreate a spatial of a orientation human relative of a human to the surroundingrelative to the space. surrounding Hence, space. they areHence, often they used are for often navigation used for purposes, navigation i.e., purposes, moving ini.e., a moving defined in direction a defined or direction towards aor specifictowards target. a specific target.

FigureFigure 2. 2.Examples Examples of of three-dimensional three-dimensional plans plans (sources: (sources: https://www.europe-mountains.com/ https://www.europe-mountains.com/,, http://www.dubaiattractions.biz/ accessed on 3 May 2020). http://www.dubaiattractions.biz/ accessed on 3 May 2020).

InIn addition addition to to the the issue issue of of generalization generalization of of the the content content presented presented on on maps, maps, the the need need toto visualize visualize three-dimensional three-dimensional data data is is increasingly increasingly important. important. In In this this case, case, the the existing existing mappingmapping convention convention isis notnot enough.enough. The motivation to to conduct conduct the the study study was was the the need need to tojointly jointly present present the the results results of of the the measurement measurement campaign campaign carried carried out out in inApril April 2019 2019 at atthe theNational National Sailing Sailing Centre Centre (NSC) (NSC) of the of theGdansk Gdansk University University of Physical of Physical Education Education and Sport and Sport(Poland) (Poland) [29]. [Taking29]. Taking into account into account the meas the measurementurement methods methods used usedand the and various the various types typesof spatial of spatial information information generated, generated, the authors the authors set themselves set themselves the thetask task of verifying of verifying the the fol- followinglowing research research hypothesis: hypothesis: “it “itis possible is possible to create to create a new a newtype typeof map of imaging map imaging that adapts that adaptsselected selected features features and functions and functions of the themat of the thematicic map to mapthree-dimensional to three-dimensional space”. space”.The vis- Theualization visualization presented presented in the in paper the paper maintains maintains the uniqueness the uniqueness of the of thecoordinates coordinates of offlat ﬂatpoints points based based on the on thecartographic cartographic projection projection used. used. An important An important added added value value of the of study the studyis the is increase the increase in the in thenumber number of ofdimensions dimensions from from two two to to three three and and the useuse ofof semiotic semiotic thematicthematic maps maps to to present present one one image image spatial spatia andl and descriptive descriptive data data of of various various types. types.

2. Materials and Methods The research data used to create three-dimensional thematic map imaging (T3DMI) were GNSS (Global Navigation Satellite System) technology measurements, terrestrial laser Appl. Sci. 2021, 11, 7016 4 of 12

Appl. Sci. 2021, 11, 7016 2. Materials and Methods 4 of 12 The research data used to create three-dimensional thematic map imaging (T3DMI) were GNSS (Global Navigation Satellite System) technology measurements, terrestrial laser scanning (TLS) point cloud and bathymetric survey performed using an unmanned scanning (TLS) point cloud and bathymetric survey performed using an unmanned surface surface vehicle (USV) equipped with a single beam echosounder (SBES). Observations vehicle (USV) equipped with a single beam echosounder (SBES). Observations recorded recorded by the devices had separate coordinate systems, hence it was necessary to har- by the devices had separate coordinate systems, hence it was necessary to harmonize the monize the spatial data into one reference system. The transformation parameters were spatial data into one reference system. The transformation parameters were determined determined after identifying the coordinates of points representing the location of the after identifying the coordinates of points representing the location of the same object same object in different data sets. After processing the source data, a perspective view was in different data sets. After processing the source data, a perspective view was used to useddisplay to display them in them the three-dimensional in the three-dimensional Euclidean Euclidean space. Its space. advantage Its advantage is obtaining is obtaining a depth aeffect depth by effect assigning by assigning size to objects size to conditioned objects conditioned by their distances by their distances from the projectionfrom the projec- center. tionDepending center. onDepending the adopted on the solution, adopted the solution perspective, the projection perspective can projection be created can based be created on one, basedtwo or on three one, points two inor space three [ 30points]. Unlike in space orthogonal [30]. Unlike projection, orthogonal there are projection, signiﬁcant there distance are significantdistortions distance in the perspective distortions view. in the The perspective mathematical view. foundationsThe mathematical of both foundations solutions are of bothpresented, solutions among are otherspresented, in Carlbom among others and Paciorek in Carlbom [31] and and Naus Paciorek [32]. [31] and Naus [32].

2.1. Measurement Data The terrestrial laser scanning method was usedused to obtain spatial data about the land objects of the marina of the NSC and objects on the water surface. The three-dimensional representation of infrastructu infrastructuralral elements supplemented the bathymetric data. The The instru- instru- ment used, the Trimble TX8 scanner, waswas equippedequipped withwith anan opticaloptical modulemodule that enabled picture-taking of the environment and a designationdesignation of a color toto individualindividual measuredmeasured points at the stage of data processing. 16 scannerscanner stations were establishedestablished in the marina area (Figure (Figure 33).). For For each each point point from from the the point point cloud, cloud, the the horizontal horizontal and and vertical vertical angles angles and theand distance the distance between between the thetarget target and and the the dev deviceice were were measured. measured. Based Based on on the the obtained observations, the coordinates of individual points in the local coordinate system of the station were calculated.calculated. ItIt isis worthworth notingnoting that that each each measuring measuring station station had had a a separate separate coor- co- ordinatedinate system system with with an an origin origin point point in in the the laser laser emission emissionand and receptionreception center.center. TheThe planar orientation of the coordinate system resulted from the method (direction) of mounting the instrument on a tripod.

Figure 3. Location of 16 stations on the background of the point cloud (a) and the Trimble TX-8 laser scanner during a Figure 3. Location of 16 stations on the background of the point cloud (a) and the Trimble TX-8 laser scanner during a measurement (b). measurement (b).

Each of the scans registered at the stations had a local coordinate system. To create a uniform pointpoint cloudcloud for for the the entire entire marina, marina, one one of the of localthe local systems systems was adoptedwas adopted as the globalas the globalsystem system for all for the all point the clouds.point clouds. To perform To perform this operation, this operation, it was it necessarywas necessary to replicate to rep- licatethe same the same elements elements of the of the real real world world in thein the three-dimensional three-dimensional space space of of adjacent adjacent pointpoint clouds. The transformati transformationon control points were the coordinates of the centers of spherical markers (polystyrene (polystyrene spheres) spheres) located located in in the the marina, marina, ensuring ensuring optimal optimal visibility visibility from from the measurementthe measurement stations. stations. Coordinates Coordinates of ofpoints points (centers (centers of of spheres) spheres) in in local coordinatecoordinate systems of the stations were used to determine the transformation parameters of every point cloud. The effect of the registration (connection) of point clouds was a coherent and geometrically correct set of spatial data representing the measured object. Registration Appl. Sci. 2021, 11, 7016 5 of 12 Appl. Sci. 2021, 11, 7016 5 of 12

Appl. Sci. 2021, 11, 7016 5 of 12 systems of the stations were used to determine the transformation parameters of every systems of the stations were used to determine the transformation parameters of every point cloud. The effect of the registration (connection) of point clouds was a coherent and point cloud. The effect of the registration (connection) of point clouds was a coherent and geometrically correct set of spatial data representing the measured object. Registration errorgeometrically of 16-point correct clouds set did of not spatial exceed data 1 cm. repr Theesenting resulting the spatial measured data setobject. was aRegistration numerical error of 16-point clouds did not exceed 1 cm. The resulting spatial data set was a numerical representationerror of 16-point of clouds the marina did not technical exceed infrastructure 1 cm. The resulting (Figure spatial4). data set was a numerical representation of the marina technical infrastructure (Figure 4). representation of the marina technical infrastructure (Figure 4).

Figure 4. Perspective view of the registered point cloud of the marina. FigureFigure 4. 4.Perspective Perspective view view of of the the registered registered point point cloud cloud of of the the marina. marina. The second equally important spatial data set were bathymetric observations rec- TheThe second second equally equally important important spatial spatial data data set wereset were bathymetric bathymetric observations observations recorded recorded by a single-beam echosounder SonarMite mounted on an unmanned surface vessel. byorded a single-beam by a single-beam echosounder echosounder SonarMite SonarMite mounted mounted on an unmanned on an unmanned surface vessel.surface Depthvessel. Depth readings received a spatial and temporal assignment based on the positioning re- readingsDepth readings received received a spatial a spatial and temporal and temporal assignment assignment based based on the on positioning the positioning results results of the Trimble R10 GNSS receiver. Satellite measurements carried out by the receiver ofsults the of Trimble the Trimble R10 GNSSR10 GNSS receiver. receiver. Satellite Satellite measurements measurements carried carried out out by by the the receiver receiver were performed in the GNSS RTK differential mode using the VRSNet.pl active geodetic were performed in the GNSS RTK differential mode using the VRSNet.pl active geodetic network. BathymetricBathymetric measurementsmeasurements were were carried carried out out in both in both manual manual and automatic and automatic mode, network. Bathymetric measurements were carried out in both manual and automatic mode,including including setting setting the drone the drone to follow to follow given proﬁles.given profiles. The method The meth ofod manual of manual navigation navi- mode, including setting the drone to follow given profiles. The method of manual navi- gationof the USVof the was USV used was in used the casein the of case narrow of narrow and hard-to-reach and hard-to-reach areas ofareas the of marina the marina basin. gation of the USV was used in the case of narrow and hard-to-reach areas of the marina basin.Bathymetric Bathymetric data recording data recording locations locations are shown are shown in Figure in 5Figure. 5. basin. Bathymetric data recording locations are shown in Figure 5.

Figure 5. Depth measurement locations (a) and devices used in the bathymetric survey (b). FigureFigure 5. 5.Depth Depth measurementmeasurement locations locations ( a(a)) and and devices devices used used in in the the bathymetric bathymetric survey survey ( b(b).). The GNSS RTK differential measurement method was also used to measure charac- TheThe GNSSGNSS RTKRTK differentialdifferential measurementmeasurement methodmethod waswas alsoalso usedused toto measuremeasure charac-characteristic marina landmarks. The determined vertices coordinates of the border of selected teristicteristic marinamarina landmarks. landmarks. TheThe determineddetermined verticesvertices coordinatescoordinates ofof the the border border of of selected selected elements of the quay infrastructure were reference points for the registered TLS point elementselements ofof thethe quayquay infrastructureinfrastructure werewere referencereference pointspoints forfor thethe registeredregistered TLSTLSpoint point cloud. To determine the transformation parameters (scale parameter, rotation angle, and cloud.cloud. ToTo determine determine thethe transformation transformation parametersparameters (scale(scale parameter,parameter, rotation rotation angle, angle, and and translation vector), selected quay elements measured with a GNSS receiver were identi- translationtranslation vector), vector), selected selected quay quay elements elements measured measured with with a GNSS a GNSS receiver receiver were were identiﬁed identi- fied in the point cloud space. The purpose of the operation, unlike the registration of TLS infied the in point the point cloud cloud space. space. The purpose The purpose of the of operation, the operation, unlike unlike the registration the registration of TLS of point TLS point clouds described above, was georeferencing the obtained spatial data set. The loca- cloudspoint clouds described described above, above, was georeferencing was georeferenci theng obtained the obtained spatial spatial data set. data The set. location The loca- of tion of the measured control points of the characteristic points of the marina quay is thetion measured of the measured control points control of points the characteristic of the characteristic points of thepoints marina of the quay marina is shown quay in is shown in Figure 6. Figureshown6 .in Figure 6. Appl. Sci. 2021, 11, 7016 6 of 12 Appl. Sci. 2021, 11, 7016 6 of 12

FigureFigure 6.6. CharacteristicCharacteristic control pointspoints ofof thethe marinamarina quayquay ((aa)) measuredmeasured byby thethe GNSSGNSS RTKRTK methodmethod withwith thethe TrimbleTrimble R10R10 receiverreceiver ((bb)) (source: (source: www.geotronics.com.plwww.geotronics.com.pl accessed accessed on on 4 4 May May 2020). 2020).

2.2.2.2. Data Processing TheThe spatial datadata obtained inin the measurement processprocess hadhad toto bebe referencedreferenced toto aa singlesingle uniformuniform coordinatecoordinate system.system. This process,process, alsoalso knownknown asas harmonization,harmonization, isis anan importantimportant elementelement ofof geospatialgeospatial analysisanalysis inin thethe currentcurrent state-of-the-artstate-of-the-art measuringmeasuring techniques.techniques. TheThe studystudy used the Polish national plane plane coordina coordinatete system system PL-2000. PL-2000. The The PL-2000 PL-2000 system system is is a amodification modiﬁcation of of the the Gauss-Krüger Gauss-Krüger projection, projection, in in which which the mapping functions havehave thethe followingfollowing formform [[33]:33]: h i xkNA==+−++−++−+ (()1− TCA+ ) 33225 / 6+ () 5− 18 TT+ 2 + 72 C− 580 e2 '5 A /120 x k00N A1 T C A /6 5 18T T 72C 58e A /120 (1)(1)

2 2 4 y = k0 M − M0 + N tan ϕ 224A /2 + 5 − T + 9C + 4C A /24 ykMM=−+{tan/2594/24 Nϕ  A +−++() T C C A o + (2) 00+ 61− 58T + T2 + 600C − 330e02 A6/720 (2) +− ++226 − where: ()61 58TT 600 C 330 e ' A / 720} 2 e0 = e2/ 1 − e2 , where: 2 2 2 1/2 e'N==ea//()11−−ee2 ,sin 2 φ ,

T = 2 2 2 1/ 2 N = a /()1− e tansinφφ, , 02 2 C2 = e cos φ, T = tan φ , A = (λ − λ0) cos φ, 2 2 C = e' cos φ , M = a[(1 − e2/4 − 3e4/64 − 5e6/256 − ...)φ − (3e2/8 + 3e4/32 + 45e6/1024 + ...) sin 2φ +( 4 + 6 + =)()λ − λ − ( φ6 + ) + ] 15e /256 45e /1024 A... sin 4φ0 cos35e ,/3072 ... sin 6φ ... Modification of the original projection coordinates consists of changing the coefficient M = a[(1− e2 / 4 − 3e4 / 64 − 5e6 / 256 −)φ − (3e2 / 8 + 3e4 / 32 + 45e6 /1024 +)sin 2φ + of scale change k0 from 1 to 0.999923 and the use of four meridional zones with a width of 3◦ and longitude+ (15e4 / 256 of+ axial45e6 meridians/1024 +)sinλ04 ofφ − 15(35◦ eE,6 / 183072◦ E,+ 21)◦sinE6 andφ + 24]◦ E, respectively. To distinguish the eastern coordinates in individual zones, the value of 500,000 m + (λ0/3◦) Modification of the original projection coordinates consists of changing the coeffi- ··· 1,000,000 m is added to the coordinate values. The Gauss-Krüger projection is shown incient Figure of scale7. change k0 from 1 to 0.999923 and the use of four meridional zones with a widthThe of length3° and andlongitude ellipsoidal of axial width meridians of the Geocentric λ0 of 15° E, curvilinear 18° E, 21° coordinates E and 24° E, obtained respec- bytively. the GNSSTo distinguish RTK measurement the eastern werecoordinates transformed in individual into the zones, PL-2000 the system. value of Ellipsoidal 500,000 m heights+ (λ0/3°) were · 1,000,000 corrected m foris added undulation to the of coordinate the PL-geoid-2011 values. The geoid, Gauss-Krüger which complements projection and is refinesshown thein Figure global 7. geopotential model EGM2008 [34]. Selected characteristic points of the NCZ˙ AWFiS marina were assigned coordinates, taking into account georeference (Figure6) and coordinates in the local coordinate system of the point cloud (Figures3 and4). Based on the ICP method [35] and the SVD algorithm [36], the parameters of the transformation of the TLS point cloud coordinates were determined. The transformation matrix coefficients Appl. Sci. 2021, 11, 7016 7 of 12

included the change in the scale of s, the translation vector T, and the rotation angle θ. The obtained parameter values were, respectively, s = 0.999998, TT = [6,550,742.821 m, 6,026,644.338 m, 1.878 m], θ = 291.8782◦. The procedure of transformation of the TLS point cloud from the local coordinate system into the PL-2000 and normal height systems was carried out using the formula: ” 0 P = RZ(ϑ) · P + T (3) where: 0 P , P”—point coordinates vectors before and after transformation, respectively, RZ(ϑ)—rotation matrix by the angle θ around the vertical axis OZ of the coordinate system, T—translation vector. Bathymetric data, in the form of depth measured with a single-beam echosounder, obtained positional data based on the coordinates determined by the Trimble R10 receiver. As in the case of determining the location of the characteristic points of the NSC marina quay, the receiver used the RTK GNSS differential measurement method. The known vertical offset between the GNSS receiver and the transducer, as well as the known depth of the SBES transducer, enabled the determination of the bottom elevation in the normal heights system. Thus, the second set of measured spatial data was harmonized to the coordinate system of the previous dataset. The next stage of bathymetric data processing Appl. Sci. 2021, 11, 7016 was the preparation of a numerical seabed model using the Nearest Neighbor method7 of [37 12]. Based on this method, the marina isobaths were also generated.

Figure 7. Gauss-Krüger projection of the world (a)) and CentralCentral andand EasternEastern EuropeEurope forfor thethe 1919°◦ E meridian (b).).

TheAn inseparablelength and ellipsoidal element of width the maps of the is Geocentric a grid of imagescurvilinear showing coordinates meridians obtained and byparallels. the GNSS Based RTK on measurement this grid, the were coordinates transformed can be into read the and PL-2000 the impact system. of Ellipsoidal projection heightsdistortions were on corrected the content for ofundulation the map canof the be PL-geoid-2011 assessed. To presentgeoid, which the georeference complements of andspatial refines data the in theglobal T3DMI geopotential visualization, model a EGM grid image2008 [34]. of meridians Selected characteristic and parallels points with anof theinterval NCŻ of AWFiS 5 arc seconds marina waswere used. assigned The propertycoordinates, of points taking located into account on the samegeoreference meridian (Fig- is a ureconstant 6) and longitude coordinates value. in the Similarly, local coordinate for the parallel, system the of latitude the point value cloud is constant. (Figures Based3 and on4). Basedthese relationships,on the ICP method the Gauss-Krüger [35] and the projectionSVD algorithm and PL-2000 [36], the coordinate parameters system of the formulastransfor- weremation used of the on theTLS generated point cloud grid coordinates lines coordinates. were determined. The obtained The points transformation were assigned matrix a coefficientszero-height included value. Such the a change procedure in the was scale justiﬁed of s, the due translation to the presentation vector T,of and the the coastal rotation sea anglebasin, θ therefore. The obtained the height parameter values values in the object’swere, respectively, area are close s = to 0.999998, zero. Therefore, TT = [6,550,742.821 there is no m,problem 6,026,644.338 of a signiﬁcant m, 1.878 vertical m], θ distance= 291.8782°. between The procedure ground level of transformation and height reference of the level. TLS point cloud from the local coordinate system into the PL-2000 and normal height systems was3. Results carried and out Discussion using the formula: The result of the procedure for the harmonization= ()ϑ ⋅ + of the laser scanning and bathymetric survey spatial data is shown in FigureP" R8.Z Due toP' theT thematic nature of the study, the(3) T3DMI visualization has been provided with an appropriate legend, presenting important where: objects from the viewpoint of the marina’s management. The grid of meridian and parallel P', P" —point coordinates vectors before and after transformation, respectively, images()ϑ allow for the orientation of the presented content. The numerical model of the bottomRZ —rotation of the basin matrix has been by the enriched angle θ witharound labeled the vertical isobaths. axis OZ of the coordinate system, T—translation vector. Bathymetric data, in the form of depth measured with a single-beam echosounder, obtained positional data based on the coordinates determined by the Trimble R10 receiver. As in the case of determining the location of the characteristic points of the NSC marina quay, the receiver used the RTK GNSS differential measurement method. The known vertical offset between the GNSS receiver and the transducer, as well as the known depth of the SBES transducer, enabled the determination of the bottom elevation in the normal heights system. Thus, the second set of measured spatial data was harmonized to the coordinate system of the previous dataset. The next stage of bathymetric data processing was the preparation of a numerical seabed model using the Nearest Neighbor method [37]. Based on this method, the marina isobaths were also generated. An inseparable element of the maps is a grid of images showing meridians and parallels. Based on this grid, the coordinates can be read and the impact of projection distortions on the content of the map can be assessed. To present the georeference of spatial data in the T3DMI visualization, a grid image of meridians and parallels with an interval of 5 arc seconds was used. The property of points located on the same meridian is a constant longitude value. Similarly, for the parallel, the latitude value is constant. Based on these relationships, the Gauss-Krüger projection and PL-2000 coordinate system formulas were used on the generated grid lines coordinates. The obtained points were assigned a zero- height value. Such a procedure was justified due to the presentation of the coastal sea basin, therefore the height values in the object’s area are close to zero. Therefore, there is no problem of a significant vertical distance between ground level and height reference level. Appl. Sci. 2021, 11, 7016 8 of 12

3. Results and Discussion The result of the procedure for the harmonization of the laser scanning and bathymetric survey spatial data is shown in Figure 8. Due to the thematic nature of the study, the T3DMI visualization has been provided with an appropriate legend, presenting im- Appl. Sci. 2021, 11, 7016 portant objects from the viewpoint of the marina’s management. The grid of meridian8 ofand 12 parallel images allow for the orientation of the presented content. The numerical model of the bottom of the basin has been enriched with labeled isobaths.

Figure 8. Three-dimensional map imaging (T3DMI)(T3DMI) visualizationvisualization ofof thethe NationalNational SailingSailing CentreCentre (NSC)(NSC) marina.marina.

The above form of data presentation signiﬁcantlysignificantly increases the possibilities of inter- pretation. Three-dimensional spacespace ofof thethe mappingmapping andand itsits contentcontent areare adaptedadapted toto currentcurrent needs. The unique features of the presented typetype ofof 3D space imaging show a much higher degree of realismrealism inin theirtheir projection.projection. TheThe useuse ofof state-of-the-artstate-of-the-art measurementmeasurement techniquestechniques ensured a highhigh reliabilityreliability ofof thethe sourcesource datadata andand faithfulfaithful representationrepresentation ofof objects.objects. AsAs aa result, thethe elementselements presentedpresented inin thethe T3DMIT3DMI imageimage dodo notnot comecome fromfrom manualmanual insertioninsertion inin a graphics program, but fromfrom measurement.measurement. TheThe exception here areare labelslabels indicatingindicating thethe location of selected marina points. Another feature of T3DMI imaging is the presence of elements that are unusual for other mappings. In this case, they are scanned parts of the yachts. The grid of meridians and parallels situated below the surveyed data provides the mapping user with geographical orientation in space. The above elements can also be a valuable material for presenting the environment in other navigational applications, e.g., car or tourist. Appl. Sci. 2021, 11, 7016 9 of 12

A feature of the T3DMI is the user-customizable view. Depending on needs of the viewer, the orthogonal or perspective projection is available. The top orthogonal view of the T3DMI model, combined with the parametric lines of the coordinate system and after adding the optional element of a linear scale, permits the creation of an image which corresponds with classic thematic maps [13]. The added value of the T3DMI to a two-dimensional map is the possibility of changing to a perspective view with the desired position of the projection center [38]. Adding the possibility of placing additional descriptive objects in the three-dimensional space of the model, the user gains the option of creating projections focused on a specific aspect of space. In both cases, based on the three-dimensional model, the obtained graphic datasets can be used in analog paper form or electronic graphic files. When discussing the features and benefits of T3DMI, it is important to mention the related matter of Virtual Reality (VR). The rapid development of the technology of measuring devices, hardware computer components, firmware, and software has contributed to the creation of a new way of presenting graphic data— to replace monitors with VR head- sets. Combined with the appropriate inertial sensors, a user obtains a unique experience that significantly differs from viewing the screen of a typical monitor. Many researchers were involved in the comparison and evaluation of VR sets, eg. Papachristos et al. [39] or Froehlich and Azhar [40]. Throughout the literature, there are publications which present the methodology behind creating three-dimensional models and displaying them in VR technology. Walm- sley and Kersten [41] presented the results of the study using a combination of TLS and photogrammetric technologies. An important element of the study was the creation of models based on point clouds. As a result, three-dimensional visualizations of the object were obtained, whereby the user can virtually relocate in the area with the use of a VR headset. In another study, Edler et al. [42] presented the application of this technology in a revitalized post-industrial area. An important element of the work was the use of GIS data to reconstruct the terrain model. The work [43] is also noteworthy, where an important direction in the development of VR technology was observed, consisting of adding sound to the visual data. In the context of state-of-the-art, it should be noted that T3DMI is a three-dimensional model, so it can also be used for real-time presentation of the temporal situation of the area in VR technology. This is a potential direction for future work. An important limitation of real-time visualization is the large size of point clouds, which makes it advisable to create three-dimensional models, as presented in [41]. The added value of the T3DMI is the presence of the bathymetric model and the georeferencing of all spatial data included in the model.

4. Conclusions The study proved the effectiveness of the proposed methods for spatial imaging of the terrain surface and the bottom of the marina. In many cases, classic maps, due to their two-dimensional nature, do not allow for a clear representation of several elements on a single image. This problem is particularly notable from the perspective of the current and future development of measuring devices collecting spatial data. The authors in the study combined the current state of knowledge and technology to create three-dimensional thematic map visualization (T3DMI). The resulting harmonized dataset, consisting of the TLS point cloud, bathymetric survey, and the bottom model with isobaths is a comprehensive representation of both the seabed and land objects. The three-dimensional numerical properties of the data enable wide access to spatial information about the marina. Working in the georeferenced point cloud space not only allows for the calculation of geometric measures (distance, area, volume) but also the reading of the values of horizontal and vertical orthogonal coordinates. An additional grid of images of meridians and parallels indicate the values of the curvilinear coordinates of latitude and longitude. Appl. Sci. 2021, 11, 7016 10 of 12

Given the feature of a wide spectrum of thematic map applications, T3DMI imaging has been profiled for the information needs of the NSC marina. The location of the key objects for marina management was defined using selected projections. The use of a perspective view is a new quality of map imaging that serves as a kind of three-dimensional thematic map. It should be clearly emphasized here that the classic map definition only applies to two-dimensional imaging, hence the terming T3DMI as a map would be incorrect. The combined representation of separate elements of the real world in the form of a single spatial dataset is a new quality of imaging. Further research directions of the proposed solution could be the creation of an interactive database, which should be updated at regular intervals. An important functional element would be providing access to the database in the form of a mobile application. Using the example of the T3DMI of the marina described in the publication, the user would be able to assess the possibility and safety of mooring to the quay. The application could have additional functionality in the form of free berths. An important limitation for internet data transmission is the large size of point clouds. However, the preparation and implementation of three-dimensional models in the database would significantly minimize this problem. The added value of the study is to suggest a new way of presenting both the Earth’s surface and natural or anthropogenic objects. The solution presented by the authors combines both theoretical and practical aspects of the issue. The process of creating T3DMI visualization uses, among other mathematical properties of cartographic projections, the theory of height systems, three-dimensional coordinate transformations, and advanced methods of spatial modeling. The spatial dataset can be used as a universal basis for creating other products dedicated to the individual needs of recipients. Given the rapid development of measurement technologies, the presented methodology of spatial data processing is an important direction in object visualization, using selected features of cartographic mappings.

Author Contributions: Conceptualization, C.S. and P.S.D.; Methodology, P.S.D.; Software, P.S.D.; Validation, C.S., M.S. and A.M.; Formal Analysis, P.S.D.; Investigation, P.S.D.; Resources, A.M., M.S. and P.S.D.; Data Curation, A.M., M.S. and P.S.D.; Writing—Original Draft Preparation, P.S.D.; Writing—Review & Editing, P.S.D., C.S., M.S. and A.M.; Visualization, P.S.D.; Supervision, C.S. and A.M.; Project Administration, C.S.; Funding Acquisition, C.S. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded from the statutory activities of Gdynia Maritime University, grant number WN/2021/PZ/05. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. Conﬂicts of Interest: The authors declare no conﬂict of interest.

References 1. Bagrow, L. History of Cartography; Routledge: New York, NY, USA, 2017. 2. Bugayevskiy, L.M.; Snyder, J. Map Projections: A Reference Manual; CRC Press: Boca Raton, FL, USA, 1995. 3. Robinson, A.H. Elements of Cartography; John and Wiley and Sons: Hoboken, NJ, USA, 1995. 4. Maling, D.H. Coordinate Systems and Map Projections; Elsevier: Amsterdam, The Netherlands, 2013. 5. Hooijberg, M. Practical Geodesy: Using Computers; Springer Science & Business Media: Berlin/Heidelberg, Germany, 2012. 6. Peterson, G.N. GIS Cartography: A Guide to Effective Map Design; CRC Press: Boca Raton, FL, USA, 2014. 7. Tyner, J.A. Principles of Map Design; Guilford Publications: New York, NY, USA, 2014. 8. Monmonier, M. Rhumb Lines and Map Wars: A Social History of the Mercator Projection; University of Chicago Press: Chicago, IL, USA, 2010. 9. Morga´s,W.; Kopacz, Z. Conversion of geodetic coordinates into ﬂat (2-dimensional) coordinates PL-UTM for the purposes of navigation. Sci. J. Pol. Nav. Acad. 2017, 208, 45–60. Appl. Sci. 2021, 11, 7016 11 of 12

10. Deakin, R.E.; Hunter, M.N.; Karney, C.F.F. The Gauss-Krüger projection. In Proceedings of the 23rd Victorian Regional Survey Conference, Warrnambool, Australia, 10–12 September 2010; pp. 1–20. 11. Dent, B.D.; Torguson, J.S.; Holder, T.W. Cartography: Thematic Map Design; McGraw Hill Higher Education: Boston, MA, USA, 2009. 12. Slocum, T.A.; MacMaster, R.B.; Kessler, F.C.; Howard, H.H. Thematic Cartography and Geovisualization, 3rd ed.; Pearson Prentice Hall: Hoboken, NJ, USA, 2009. 13. Zyszkowska,˙ W. Levels and properties of map perception. Pol. Cartogr. Rev. 2017, 49, 17–26. [CrossRef] 14. Kraak, M.J.; Ormeling, F. Cartography: Visualization of Spatial Data; Guilford Press: New York, NY, USA, 2011. 15. DiBiase, D. Visualization in the earth sciences. Earth Miner. Sci. 1990, 59, 13–18. 16. Dabrowski, P.S.; Specht, C. Spatial expansion of the symmetrical objects point clouds to the lateral surface of the cylinder— Mathematical model. Measurement 2019, 134, 40–47. [CrossRef] 17. Specht, M.; Specht, C.; Mindykowski, J.; D ˛abrowski, P.; Ma´snicki,R.; Makar, A. Geospatial Modeling of the Tombolo Phenomenon in Sopot using Integrated Geodetic and Hydrographic Measurement Methods. Remote Sens. 2020, 12, 737. [CrossRef] 18. D ˛abrowski, P.S.; Specht, C.; Felski, A.; Koc, W.; Wilk, A.; Czaplewski, K.; Karwowski, K.; Jaskólski, K.; Specht, M.; Chrostowski, P.; et al. The Accuracy of a Marine Satellite Compass under Terrestrial Urban Conditions. J. Mar. Sci. Eng. 2020, 8, 18. [CrossRef] 19. Specht, C.; Lewicka, O.; Specht, M.; D ˛abrowski, P.; Burdziakowski, P. Methodology for Carrying Out Measurements of the Tombolo Geomorphic Landform Using Unmanned Aerial and Surface Vehicles near Sopot Pier, Poland. J. Mar. Sci. Eng. 2020, 8, 384. [CrossRef] 20. Specht, C.; D ˛abrowski, P.; Dumalski, A.; Hejbudzka, K. Modeling 3D Objects for Navigation Purposes Using Laser Scanning. TransNav: Int. J. Mar. Navig. Saf. Sea Transp. 2016, 10.[CrossRef] 21. Vasilev, S. Who is Who’ on the Map? In Proceedings of the 1st International Trade Fair of Geodesy, Cartography, Navigation and Geoinformatics GEOS 2006, Prague, Czech Republic, 1–3 March 2007. 22. Friendly, M. 1995. Milestones in the History of Thematic Cartography, Statistical Graphics, and Data Visualization. In Proceedings of the 13th International Conference on Database and Expert Systmes Applications (DEXA 2002), Aix-en-Provence, France, 2–6 September 2002; pp. 59–66. 23. Tennekes, M. Tmap: Thematic Maps in R. J. Stat. Softw. 2018, 84, 1–39. [CrossRef] 24. Góralski, R. Three-Dimensional Interactive Maps Theory and Practice, A Submission Presented in Partial Fulﬁlment of the Requirements of the University of Glamorgan/Prifysgol Morgannwg for the Degree of Doctor of Philosophy. 2009. Available online: https://core.ac.uk/reader/9653382 (accessed on 4 May 2020). 25. Van Driel, N.J. Three dimensional display of geologic data. In Three Dimensional Applications in Geographical Information Systems; Raper, J., Ed.; CRC Press: Boca Raton, FL, USA, 1989. 26. Musliman, I.A.; Abdul-Rahman, A.; Coors, V. 3D Navigation for 3D-GIS—Initial Requirements. In Innovations in 3D Geo Information Systems; Abdul-Rahman, A., Zlatanova, S., Coors, V., Eds.; Springer: Berlin/Heidelberg, Germany, 2006. 27. Schilling, A.; Coors, V.; Giersich, M.; Aasgaard, R. Introducing 3D GIS for the Mobile Community—Technical Aspects in the Case of TellMaris; IMC Workshop on Assistance, Mobility, Applications: Stuttgart, Germany, 2003. 28. Kraak, M.J. Visual exploration of virtual environments. In Virtual Reality in Geography; Unwin, D., Fisher, P., Eds.; Taylor & Francis: Abingdon, UK, 2002. 29. Makar, A.; Specht, C.; Specht, M.; D ˛abrowski, P.; Szafran, M. Integrated Geodetic and Hydrographic Measurements of the Yacht Port for Nautical Charts and Dynamic Spatial Presentation. Geosciences 2020, 10, 203. [CrossRef] 30. Mitchell, W.J.; McCullough, M. Digital Design Media; John Wiley & Sons: Hoboken, NJ, USA, 1995. 31. Carlbom, I.; Paciorek, J. Planar geometric projections and viewing transformations. ACM Comput. Surv. (CSUR) 1978, 10, 465–502. [CrossRef] 32. Naus, K. Electronic navigational chart as an equivalent to image produced by hypercatadioptric camera system. Pol. Marit. Res. 2015, 22, 3–9. [CrossRef] 33. Snyder, J.P. Map Projections—A Working Manual; US Government Printing Ofﬁce: Washington, DC, USA, 1987; Volume 1395. 34. Pavlis, N.K.; Holmes, S.A.; Kenyon, S.C.; Factor, J.K. An earth gravitational model to degree 2160: EGM2008. EGU Gen. Assem. 2008, 10, 13–18. 35. Pomerleau, F.; Colas, F.; Siegwart, R.; Magnenat, S. Comparing ICP variants on real-world data sets. Auton. Robot. 2013, 34, 133–148. [CrossRef] 36. Kalman, D. A singularly valuable decomposition: The SVD of a matrix. Coll. Math. J. 1996, 27, 2–23. [CrossRef] 37. Olivier, R.; Hanqiang, C. Nearest neighbor value interpolation. Int. J. Adv. Comput. Sci. Appl. 2012, 3, 25–30. [CrossRef] 38. Wolf, P.R.; Dewitt, B.A.; Wilkinson, B.E. Elements of Photogrammetry with Applications in GIS; McGraw-Hill Education: New York, NY, USA, 2014. 39. Papachristos, N.M.; Vrellis, I.; Mikropoulos, T.A. A comparison between oculus rift and a low-cost smartphone VR headset: Immersive user experience and learning. In Proceedings of the 2017 IEEE 17th International Conference on Advanced Learning Technologies (ICALT), Timisoara, Romania, 3–7 July 2017; IEEE: New York, NY, USA, 2017; pp. 477–481. 40. Froehlich, M.A.; Azhar, S. Investigating virtual reality headset applications in construction. In Proceedings of the 52nd Associated Schools of Construction Annual International Conference, Provo, UT, USA, 13–16 April 2016; Volume 52, pp. 13–16. 41. Walmsley, A.P.; Kersten, T.P. The IMPERIAL Cathedral in Königslutter (Germany) as an immersive experience in virtual reality with integrated 360 panoramic photography. Appl. Sci. 2020, 10, 1517. [CrossRef] Appl. Sci. 2021, 11, 7016 12 of 12

42. Edler, D.; Keil, J.; Wiedenlübbert, T.; Sossna, M.; Kühne, O.; Dickmann, F. Immersive VR experience of redeveloped post-industrial sites: The example of “Zeche Holland” in Bochum-Wattenscheid. KN-J. Cartogr. Geogr. Inf. 2019, 69, 267–284. [CrossRef] 43. Hruby, F. The sound of being there: Audiovisual cartography with immersive virtual environments. KN-J. Cartogr. Geogr. Inf. 2019, 69, 19–28. [CrossRef]