iccsa-19-vessel

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 \begin{document}
 
 \title{Vessel: Efficient plain text file format for ship hull geometry}
 \author{%
 Alexander Degtyarev\orcidID{0000-0003-0967-2949} \and\\
 Ivan Gankevich\textsuperscript{*}\orcidID{0000-0001-7067-6928} \and\\
 Anton Gavrikov\orcidID{0000-0003-2128-8368} \and\\
 Artemii Grigorev \and\\
 Vasily Khramushin\orcidID{0000-0002-3357-169X} \and\\
 Ivan Petriakov
 }
 
 \titlerunning{Vessel}
 \authorrunning{A.\,Degtyarev et al.}
 
 \institute{Saint Petersburg State University, Russia\\
 \email{a.degtyarev@spbu.ru},\\
 \email{i.gankevich@spbu.ru},\\
 \email{st047437@student.spbu.ru},\\
 \email{st016177@student.spbu.ru},\\
 \email{v.khramushin@spbu.ru},\\
 \email{st049350@student.spbu.ru}\\
 \url{http://www.shipdesign.ru/}}
 
 \maketitle
 
 \begin{abstract}
 
 Initially, digital geometric model of a ship hull is assumed to maintain
 continuity in solving traditional ship theory problems, ship hydromechanics and
 seakeeping in severe storm waves. In the research reported here we consider
 using a table of plaza ordinates (transversal projection of frames)
 supplemented with a description of sterns as a means of describing digital
 geometric model. This description, which we call Vessel (VSL) format, allows
 for later addition of compartments, appendages and superstructures. These more
 complicated ship structures and their characteristics (e.g. ship compartments
 and superstructures are characterised by template-based modelling) are added to
 initial ship hull model in separate files from the working directory of a
 particular experiment. We show how this model is converted into
 three-dimensional triangular mesh suitable for ship motion simulations. VSL
 format is generally more efficient than industry standard IGES format and
 is distinguished by the simplicity and capability of editing by hand.
 
 \keywords{%
 Ship lines \and
 ship blueprint \and
 ship theory \and
 ship design \and
 ship hydromechanics \and
 storm seakeeping \and
 Coons surface \and
 Hermite spline \and
 VSL \and
 IGES.
 }
 \end{abstract}
 
 
 \section{Introduction}
 
 
 %\subsection{Digital models of ship lines and ship hull forms}
 
 Initial geometric model of a ship hull is close to traditional hull blueprints
 which are naturally rendered as a table of plaza ordinates in ship theory.
 Such a model quite reliably characterises ship hull lines and above-water ship
 hull parts, while preserving continuity in hydrostatic and hydrodynamic
 calculations in ship theory and hydromechanics. This is important for
 verification of newly created numerical experiments with a multitude of
 historical series of ship calculations, model basin experiments and sea trials.
 Obvious advantage of this digital format is that it is relatively simple and
 has compact data layout, with the data prepared and refined as plain text
 strings representing stern and frame coordinate sequences. We call this format
 Vessel (or VSL for short).
 
 Numerous variants of ship hulls were systematically collected in VSL format in
 Saint Petersburg State University in Vessel database~\cite{vessel2015}. The
 database is maintained with the help of Hull software suite~\cite{hull2010}
 which allows for editing ship hull coordinates and calculates certain
 hydrostatic characteristics. In this paper we describe VSL format, compare and
 contrast its efficiency and performance with industry standard IGES format, and
 outline advatanges and disadvantages of using plain text for creating and
 editing ship hull geometry by hand.
 
 \section{Methods}
 
 \subsection{Vessel format}
 
 Formalised description of ship hull geometry is done using plain text data
 which include ship name, hull dimensions, and successive description of aft,
 main (table of plaza ordinates) and bow sections. When digital ship hull model
 is first added to Vessel database the following design characteristics are
 specified in the comments: displacement, wetted surface area, hull volume ratio
 coefficient, date and time of file creation. The diagram of a VSL file is
 presented in tab.~\ref{tab:format}, projections and threedimensional model of
 Aurora cruiser are presented in fig.~\ref{fig:aurora-1} and~\ref{fig:aurora-2}.
 
 \begin{table}
 	\centering
 	\caption{VSL file format diagram.\label{tab:format}}
 	\begin{tabular}{p{1cm}p{1cm}p{9cm}}
 		\toprule
 		\multicolumn{3}{l}{1. Technical vessel description (lines starting
 		with \texttt{//} or \texttt{;} are comments).} \\
 		\multicolumn{3}{l}{2. Format magic number (30) and hull model name in
 		angle brackets \texttt{<...>}.} \\
 		\multicolumn{3}{l}{3. The number of frames and middle frame number.} \\
 		\multicolumn{3}{l}{4. Hull dimensions (length, beam, draft).} \\
 		\cmidrule(lr){1-3}
 		\multirow{5}{*}{\rotatebox[origin=c]{90}{\parbox[t]{2.9cm}{\centering{}The
 		number of points on a curve}}} & \multicolumn{2}{l}{5. \(X(z)\)~---
 		sternpost contour abscissas as a function of applicates.} \\
 		& \multicolumn{2}{l}{6. \(Y(z)\)~--- transom width ordinates as a
 		function of applicates.} \\
 		\cmidrule(lr){2-3}
 		& \rotatebox[origin=c]{90}{\parbox[t]{1.4cm}{\centering{}Frame
 		abscissas}} & 7.  \(Y(z)\)~--- frame curves as functions of
 		applicates of general hull line. \\
 		\cmidrule(lr){2-3}
 		& \multicolumn{2}{l}{8. \(Y(z)\)~--- bulbous bow width ordinates as a
 		function of applicates.} \\
 		& \multicolumn{2}{l}{9. \(X(z)\)~--- stern contour abscissas as a
 		function of applicates.} \\
 		\cmidrule(lr){1-3}
 		\multicolumn{3}{l}{10. Design characteristics (displacement, wetted
 		surface, volume ratio coefficient).} \\
 		\bottomrule
 	\end{tabular}
 \end{table}
 
 Ship hull is divided into three sections (fig.~\ref{fig:sections}): aft, main
 and bow sections. Main section consists of frames each of which is defined by a
 collection of points lying in transverse plane. Smooth curve that goes though
 all of these points is created by cubic Hermite spline interpolation. Each
 frame may not have the same number of points (but usually do), and there are no
 additional points between endpoints of subsequent frames in longitudinal plane.
 Aft and bow sections consist of frames in transverse plane and a curve in
 longitudinal plane that defines the shape of the ship hull in this plane. This
 curve go through (usually) all frames and defines intermediate points between
 endpoints of subsequent frames.  If it does not go between some frames, then
 there are no intermediate points between them. Curves are not closed and define
 only left part of the ship hull, the full ship hull model is created by
 mirroring each point of the curve with respect to longitudinal axis and connect
 corresponding curve endpoints by straight lines.
 
 \begin{figure}
 	\centering
 	\includegraphics{build/sections.eps}
 	\caption{Three sections of a ship hull as defined by VSL
 	format.\label{fig:sections}}
 \end{figure}
 
 In accordance with initial purpose of a digital ship hull model, Hull programme
 makes basic calculations of certain characteristics of a ship hull, curved
 elements and ship stability diagrams by fixing the centre of gravity with
 respect to general line, centre of buoyancy, metacentre or current waterline
 (fig.~\ref{fig:hydrostatics}).  The programme also performs wave resistance
 calculations for arbitrary travel speeds taking into account radiation
 intensity and interference of ship waves with respect to waterline as a
 function of Froude number.
 
 \begin{figure}
 	\centering
 	\includegraphics[width=\textwidth]{graphics/hydrostatics.png}
 	\caption{Ship stability calculations for a ship with small moments of
 	inertia for the area of the current waterline (MICW-85). For a design
 	draught roll moments are small up to 30\textdegree{} wave slope, and
 	stability increases in response to any change in
 	draught.\label{fig:hydrostatics}}
 \end{figure}
 
 \subsection{Hydrostatic calculations for historic, traditional and contemporary
 ship hulls}
 
 As an illustrative example of simulating seakeeping ship characteristics we
 consider ship stability diagrams for contemporary and historical ships, and for
 a ship that is purposely optimised for improved seakeeping in storm waves.
 
 Fig.~\ref{fig:stability} shows that Aurora cruiser ship hull has excellent
 seakeeping characteristics in severe storm waves conditions, which guarantee
 safe small oscillations and smoothness of roll by reducing metacentric height~---
 initial ship hull stability. Additional positive stability appears for
 large roll angles and arbitrary heaving.
 
 \begin{figure}
 	\centering
 	\includegraphics[width=\textwidth]{graphics/stability.png}
 	\caption{Transversal projection of a ship hull (top), static ship stability
 	diagrams for a fixed centre of gravity \(Z_g\) and metacentric height equal
 	to 1\% of a beam for contemporary (a), historical (b) and improved storm
 	seakeeping (c) ships.\label{fig:stability}}
 \end{figure}
 
 More complicated usage scenario of computational model is optimisation of ship
 lines to achieve certain form of wave resistance curve
 (fig.~\ref{fig:waves}). In the calculations we build radiation intensity
 and ship waves interferences along the current waterline. By changing ship
 lines we reduce resistivity extrema for relative speeds (on Froude) on the
 order of 0.3 and 0.5 without sacrificing propulsion for minimum wave formation
 for speeds 0.4 and 0.2.
 
 \begin{figure}
 	\centering
 	\includegraphics[width=\textwidth]{graphics/waves.png}
 	\caption{Wave resistance, radiation intensity and ship waves intensity
 	along the ship hull.\label{fig:waves}}
 \end{figure}
 
 \subsection{Triangulation of a ship hull given by a collection of curves}
 
 In the original programme~\cite{hull2010} that visualises ship lines and
 calculates hydrostatic characteristics, ship hull is described by a collection
 of curves; however, for a programme that simulates ship dynamics in rough sea
 this description is not convenient. A better representation would be a
 collection of triangles (a \emph{triangular mesh}) that approximates
 analytic ship hull geometry.  At the centre of each triangle pressure
 force induced by ocean waves is applied, and then these forces are used to
 calculate ship motion. Triangles is a better representation because they
 \begin{itemize}
 	\item do not require recomputation every frame (like analytic curves), 
 	\item have simple formula for area (which is needed for pressure force
 		calculation), and
 	\item the same representation is used internally by graphical accelerators
 		that visualise simulation frames.
 \end{itemize}
 In the following paragraphs we describe how analytically given ship hull is
 transformed into a fully connected collection of triangles.
 
 Ship hull is transformed from analytic to discrete form by using
 \emph{intermediate representation}~ --- two-dimensional rectangular
 array of points, which makes it easy to obtain triangular mesh.  Each ship hull
 section is transformed to such an array, and then these arrays are
 concatenated. Each row of the resulting array represents a frame, and each
 frame is an array of points of this frame. Since the array have to be
 rectangular, the number of points equal the maximum number of points among all
 original frames in VSL file. After that, endpoints are added to make curves
 closed, and the whole array is mirrored with respect to longitudinal axis. Then
 each rectangular patch of the resulting array is divided into two triangles to
 obtain triangular mesh.  Duplicate vertices and faces, that may have been
 introduced by mirroring or making curves closed, are removed from the mesh. So,
 intermediate representation is easy to transform to a triangular mesh, but we
 have to interpolate frame curves to generate the same number of points
 in order to transform them to such a representation.
 
 It is straightforward to transform main section to a rectangular array of
 points. First, we determine the maximum number of points in a frame across all
 ship hull frames. Then for each frame we use cubic Hermite spline interpolation
 to generate the specified number of points. If each frame has the same number
 of point, we generate the same points that the original frame had, because the
 spline goes through all of them.
 
 In contrast to the main section, transformation of bow and aft sections is done
 in multiple stages. During the first stage we generate intermediate points
 between subsequent frames using the curve describing the ship hull shape in
 longitudinal plane. For that purpose we create a polygon in longitudinal plane
 that consists of all points of this curve, all points of the frame that is the
 closest to the curve endpoints, but does not cross the curve, and all endpoints
 of the frames that are between this frame and the curve (it happens when first
 and last endpoint of the curve are close to different frames).  Frame points
 that lie outside this polygon are removed.  Polygon points that lie between
 subsequent frames become intermediate points.  At this stage we decompose a
 bow/aft section into a collection of ``rectangular'' patches vertical sides of
 which are curves created from subsequent frames and horizontal sides of which
 are curves created from intermediate points (fig.~\ref{fig:bow}).
 
 \begin{figure}
 	\centering
 	\includegraphics{build/bow.eps}
 	\caption{Longitudinal slice of bow section of a ship hull that shows
 	horizontal curves with large curvature.\label{fig:bow}}
 \end{figure}
 
 A patch that is defined by four curves is called Coons
 patch~\cite{coons1967surfaces}.  Coons patch is a parametric surface \(S(u,v)\)
 between four curves \(c_0(u)\), \(c_1(u)\), \(d_0(v)\), \(d_1(v)\):
 \begin{align*}
 	& S(u,v) = C_1(u,v) + C_2(u,v) - C_3(u,v), \\
 	& C_1(u,v) = v' c_0(u) + v c_1(u), \quad v' = 1-v, \\
 	& C_2(u,v) = u' d_0(v) + u d_1(v), \quad u' = 1-u, \\
 	& C_3(u,v) = 
 		c_0(0)u'v' +
 		c_0(1)uv' +
 		c_1(0)u'v +
 		c_1(1)uv, \\
 	& c_0(0) = d_0(0),
 	\quad c_0(1) = d_1(0), \quad c_1(0) = d_0(1),
 	\quad c_1(1) = d_1(1).
 \end{align*}
 Here \(C_1\) is linear interpolation between points \(c_0\) and \(c_1\),
 \(C_2\) is linear interpolation between points \(d_0\) and \(d_1\), and
 \(C_3\) is bilinear interpolation between corner points of the patch. \(C_1\)
 and \(C_2\) are ruled surfaces~--- surfaces between two curves, that are
 generated by interpolating corresponding curve points. Bicubic interpolation
 can be used instead of bilinear to get the same derivative when joining
 multiple Coons patches together, but for a grid of interior points linear
 interpolation is enough.
 
 Using these formulae we generate a grid of interior points between curves of
 each bow/aft patch during the second stage. Our first approach was to use one
 Coons patch for each subsequent pair of frames, but we have found that some
 ship hulls have horizontal curves with large curvatures which cause linear
 interpolation to produce cusps on the resulting surface (fig.~\ref{fig:cusp}).
 We solved this problem by using multiple smaller Coons patches that were
 arranged vertically for each subsequent pair of frames. This approach removes
 the cusps, but the vertical size of the patch have to be small enough to reduce
 the effect of the large curvature of the horizontal curve. After generating
 grids of intermediate points with Coons patches for each subsequent frame, we
 concatenate them to obtain rectangular array for bow/aft sections.
 
 \begin{figure}
 	\centering
 	\includegraphics{build/micw-bow.eps}
 	\caption{Part of the bow section of the ship hull. The section with 
 	single Coons patch spanning the whole frame (left).
 	The section with multiple smaller Coons patches arranged vertically
 	(right).\label{fig:cusp}}
 \end{figure}
 
 After transforming each section of the ship hull into a rectangular array and
 concatenating them, we obtain an array of dimensions \(m\times{}n\). We then
 use two-dimensional cubic Hermite spline interpolation to generate a grid of
 \((2m-1)\times{}(2n-1)\) points. Additional points increase surface smoothness
 and provide better approximation for the original ship hull.  Finally, we
 transform the resulting grid into a triangular mesh to obtain three-dimensional
 discrete ship hull model, which is ready for the use in ship motion simulation
 and visualisation.
 
 \section{Results}
 
 To prove VSL viability for using it as an alternative to another format that
 uses analytic curves called IGES~\cite{smith1983iges}, we measured
 triangulation performance and measured how many vertices and faces are
 generated when analytic curves and surfaces are transformed into them. We do
 not have the same ship hulls in both formats, so we resorted to measuring
 performance relative to vertex and face count. To work with IGES format
 we use OpenCASCADE library~\cite{opencascade}. Benchmark results are presented
 in tab.~\ref{tab:performance}.
 
 \begin{table}
 	\centering
 	\caption{VSL performance in comparison to IGES for different ship
 	hulls.\label{tab:performance}}
 	\begin{tabular}{llrrr}
 		\toprule
 		Ship   & Format & Import time, s & No. of vertices & No. of faces \\
 		\midrule
 		MICW   & VSL    &          0.019 &            5457 &        10912 \\
 		Aurora & VSL    &          0.054 &           14653 &        29306 \\
 		5415   & IGES   &          1.300 &           21088 &        41841 \\
 		KVLCC2 & IGES   &         24.000 &           57306 &       114110 \\
 		KCS    & IGES   &         32.500 &          626188 &      1243307 \\
 		\bottomrule
 	\end{tabular}
 \end{table}
 
 We chose MICW (a hull with reduced moments of inertia for the current
 waterline) and Aurora cruiser ship hulls in VSL format and tanker (KVLCC2),
 container ship (KCS) and combat ship (5415) in IGES format that are freely
 available on the Internet\footnote{\url{https://simman2014.dk/ship-data/}}.
 VSL format showed higher performance in comparison to IGES format considering
 the number of vertices and faces. The resulting triangular meshes are shown in
 fig.~\ref{fig:models}.
 
 \begin{figure}
 	\centering
 	\includegraphics[width=0.5\textwidth]{build/{aurora.vsl}.eps}\hfill
 	\includegraphics[width=0.5\textwidth]{build/{micw.vsl}.eps}
 	\caption{Final Aurora and MICW threedimensional triangular
 	meshes.\label{fig:models}}
 \end{figure}
 
 \section{Discussion}
 
 \subsection{Advantages}
 
 \paragraph{Faster triangulation.} Faster triangulation is advantageous for
 performing ship motion simulations on a regular workstation. These machines are
 usually not very powerful and do not have a lot of memory for complicated mesh
 pre-processing. IGES importer uses multiple threads for triangulation, whereas
 VSL does everything in one thread. Yet, it achieves higher performance on a
 regular workstation.
 
 \paragraph{Ease of editing.} Most of the VSL files from Vessel database were
 written by hand. Points for frames were generated in a drawing programme by
 using legacy blueprints as an overlay and approximating curve projections by
 points. Then points were exported in plain text format and subsequently
 converted to VSL format by hand. Thus, there is no need in complicated and
 expensive CAD programme to produce Vessel files.
 
 \paragraph{Compatibility with legacy blueprints.} Legacy ship hull blueprints
 were mostly done by drawing projections of ship lines on a paper, and VSL
 incorporates longitudinal projections for bow and aft and transversal
 projection for the main section. It is easy to convert legacy blueprint to VSL
 file by overlaying frame points on the drawing. It is also easy for people who
 used to legacy blueprints to reason about ship hull characteristics.
 
 \subsection{Disadvantages}
 
 The main disadvantage of VSL format is that a triangular mesh generated from it
 approximates ship hull surface only with a certain accuracy, but cannot
 represent it exactly. This is due to the fact that we choose the same number of
 points for each frame to be able to create rectangular array of all points and
 convert it to a mesh. Obvious solution to this problem is to use
 non-rectangular array, but it does not come without disadvantages.
 Non-rectangular array complicates triangle generation as we need to compute
 intermediate points for smaller patches, and it would be more difficult to make
 the resulting surface as smooth as the original, especially at intersections of
 frames with different number of points.
 
 A simpler approach is to use rectangular array as the original ship hull
 representation, not an intermediate one. In that case each array element
 represents a geometric vertex and in addition the type of spline surface that
 represents ship hull surface \emph{exactly} is specified in the file. That way
 it is easy to create triangular mesh that would be an exact representation of
 the original analytic surface when the number of grid points tends to infinity,
 and the resulting surface would be as smooth as the original one with all
 derivatives and surface normals computed using analytic representation. Similar
 approach is followed by FastShip~\cite{fastship} in which ship hull is defined
 by a B-spline surface, that in turn is defined by control points, allowing ship
 hull designer and ship motion simulation programmes to use exactly the same
 ship hull representation. One direction of future work is to incorporate
 B-splines into existing format.
 
 \section{Conclusion}
 
 In computational experiments we used theoretical blueprints of Aurora cruiser
 which has excellent seakeeping characteristics and for which there can be no
 dangerous situations in severe storm waves. We presented the more complicated
 geometric ship hull form which is optimised for storm seakeeping. This ship
 hull has relatively small moments of inertia for the area of the current
 waterline (MICW). For this hull mutual compensation of external force
 excitations was proved in seakeeping trials in severe storm waves in model
 basin of Leningrad shipbuilding institute under the guidance of prof. Alexander
 Nikolaevich Kholodilin~\cite{khram2018}.
 
 Although, traditional plaza table of ordinates with a few frames
 has relatively small hull representation accuracy, it gives satisfactory
 representation of ship hydrostatic and hydrodynamic characteristics in
 computational experiments using multiprocessor machines and supercomputers.
 For research stages we used formalised simulation and trochoidal models
 of storm sea waves, for which digital ship hull models are quite optimal.
 
 We described efficient plain text format for three-dimensional ship hull
 geometry called VSL. This format uses longitudinal and transversal projections
 of ship lines given in analytic form. This format is easy to write by hand and
 easy to use for converting legacy ship hull blueprints into digital form. We
 demonstrated efficiency and viability of this format in comparison to IGES.
 Although, there are more precise alternatives for storing ship hull geometry,
 and VSL format gives only approximate representation of the original ship hull,
 it is distinguished by the simplicity and efficiency.
 
 \subsubsection*{Acknowledgements.}
 Research work is supported by Saint Petersburg State University (grant
 no.~26520170 and~39417213).
 
 \bibliographystyle{splncs04}
 \bibliography{references}
 
 \begin{figure}
 	\centering
 	\includegraphics[width=\textwidth]{graphics/aurora-1.png}
 	\caption{Aurora cruiser digital model.\label{fig:aurora-1}}
 \end{figure}
 
 \begin{figure}
 	\centering
 	\includegraphics[width=\textwidth]{graphics/aurora-2.png}
 	\caption{Aurora cruiser hull is prepared for a numerical ship
 	hydromechanics experiment. Although, the number of frame points
 	in the main section is relatively small, it allows for smooth
 	approximation of hull surface with the desired
 	accuracy.\label{fig:aurora-2}}
 \end{figure}
 
 \end{document}