commit 94464489d93c047d4892f54a6aefc1440e77c106
parent c41e7d8f44bc81aa76b4759f2f47d8887f3cb88d
Author: Ivan Gankevich <igankevich@ya.ru>
Date: Thu, 18 Apr 2019 17:33:23 +0300
Edit and proof-read.
Diffstat:
| main.tex | | | 266 | ++++++++++++++++++++++++++++++++++++++++--------------------------------------- |
1 file changed, 134 insertions(+), 132 deletions(-)
diff --git a/main.tex b/main.tex
@@ -71,12 +71,12 @@ IGES.
%\subsection{Digital models of ship lines and ship hull forms}
-Initial geometric model of a ship hull is very 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
+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
@@ -87,19 +87,23 @@ 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.
+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 geometric form 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}.
+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
@@ -134,29 +138,36 @@ is presented in tab.~\ref{tab:format}.
\end{tabular}
\end{table}
-\begin{figure}
- \centering
- \includegraphics[width=\textwidth]{graphics/aurora-1.png}
- \caption{Aurora cruiser digital model.\label{fig:aurora-1}}
-\end{figure}
+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[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 desired accuracy.\label{fig:aurora-2}}
+ \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 centre of gravity with respect
-to general line, centre of buoyancy, metacentre or current waterline. 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.
+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
@@ -168,6 +179,42 @@ with respect to waterline as a function of Froude number.
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}
@@ -189,31 +236,8 @@ calculate ship motion. Triangles is a better representation because they
In the following paragraphs we describe how analytically given ship hull is
transformed into a fully connected collection of triangles.
-In Vessel database each 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}
-
Ship hull is transformed from analytic to discrete form by using
-\emph{intermediate representation} in a form of two-dimensional rectangular
+\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
@@ -224,16 +248,16 @@ 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 all
-frames have to have the same number of points in order to transform them to such
-a representation.
+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 in one stage. 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.
+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
@@ -286,18 +310,19 @@ 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 vertically arranged Coons
-patches 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 effect of
-large curvature of the horizontal curve. We concatenate grids of subsequent
-frames to obtain rectangular array for bow/aft sections.
+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. Section with
- single vertical Coons patch spanning the whole vertical frame (left).
- Section with multiple smaller Coons patches arranged vertically
+ \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}
@@ -306,52 +331,12 @@ 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 triangular mesh to obtain three-dimensional
-discrete ship hull model, which is ready for use in ship motion simulation and
-visualisation.
+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}
-\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.
-
-\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}
-
-
-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/waves.png}
- \caption{Wave resistance, radiation intensity and ship waves intensity
- along the ship hull.\label{fig:waves}}
-\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.
-
-\subsection{Triangulation}
-
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
@@ -390,7 +375,7 @@ fig.~\ref{fig:models}.
\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 three-dimensional triangular
+ \caption{Final Aurora and MICW threedimensional triangular
meshes.\label{fig:models}}
\end{figure}
@@ -399,11 +384,11 @@ fig.~\ref{fig:models}.
\subsection{Advantages}
\paragraph{Faster triangulation.} Faster triangulation is advantageous for
-performing ship motion simulations on a regular workstation. This type of
-machines are usually not very powerful and does 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.
+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
@@ -421,7 +406,7 @@ used to legacy blueprints to reason about ship hull characteristics.
\subsection{Disadvantages}
-The main disadvantage of VSL format is that triangular mesh generated from it
+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
@@ -434,16 +419,17 @@ 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 geometrical vertex and in addition the type of spline surface that
+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.
+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}
@@ -469,9 +455,9 @@ 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 efficient and 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.
+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
@@ -480,4 +466,20 @@ 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}
