results.tex

\chapter{Results}
\label{chapter:results}
Two types of results are presented in this chapter: screenshots showing different visual aspects of the system and benchmarks focusing on the achieved performance.

\section{Screenshots}
Screenshots from the implemented system are presented and described in each subsection below. Figure \ref{fig:researthshaded} shows the Earth shaded using a simple implementation of an atmosphere together with a daily image of surface reflectance.

\begin{figure}[h]
  \centering
  \begin{subfigure}[bt]{0.8\textwidth}
    \includegraphics[width=\textwidth]{figures/results/screenshots/specular_earth.jpg}
  \end{subfigure}
  \caption{Shaded Earth rendered with NASA GIBS VIIRS daily image \cite{gibs}}
  \label{fig:researthshaded}
\end{figure}

\clearpage
\subsection{Height Mapping}
\FloatBarrier
Figure \ref{fig:resheightmapping} shows the Earth rendered with a height dataset displacing the chunks' vertices according to the geometric shape of the ground.
\begin{figure}[h]
    \centering
    \begin{subfigure}[bt]{0.8\textwidth}
        \includegraphics[width=\textwidth]{figures/results/screenshots/height_bali.jpg}
        \caption{The volcano Gunung Agung on Bali.}
    \end{subfigure}
    \par\bigskip
    \begin{subfigure}[bt]{0.8\textwidth}
        \includegraphics[width=\textwidth]{figures/results/screenshots/height_mt_everest.jpg}
        \caption{Looking south from Mount Everest}
    \end{subfigure}
    \caption{Earth rendered with ESRI World Elevation 3D height map \cite{worldelevation3d}. Color layer: ESRI Imagery World 2D \cite{imageryworld2d}}
    \label{fig:resheightmapping}
\end{figure}

\clearpage
\subsection{Water Masking}
\FloatBarrier
Figure \ref{fig:reswatermask} shows the Earth rendered with a water mask layer enhancing specular contrasts between land and water.
\begin{figure}[h]
    \centering
    \begin{subfigure}[bt]{0.8\textwidth}
        \includegraphics[width=\textwidth]{figures/results/screenshots/specular_brazil.jpg}
        \caption{Sun's specular reflection in the Amazon River.}
    \end{subfigure}
    \par\bigskip
    \begin{subfigure}[bt]{0.8\textwidth}
        \includegraphics[width=\textwidth]{figures/results/screenshots/specular_indonesia.jpg}
        \caption{Sun's specular reflection around Bali, Indonesia.}
    \end{subfigure}
    \caption{Shaded Earth using water mask texture. Color layer: ESRI Imagery World 2D \cite{imageryworld2d}}
    \label{fig:reswatermask}
\end{figure}

\clearpage
\subsection{Night Layers}
\FloatBarrier
Figure \ref{fig:reswatermask} shows the Earth rendered with a night layer showing light from cities, which is only rendered on the night side of the planet. 

\begin{figure}[h]
    \centering
    \begin{subfigure}[bt]{0.8\textwidth}
        \includegraphics[width=\textwidth]{figures/results/screenshots/night_earth.jpg}
        \caption{Earth at night}
    \end{subfigure}
    \par\bigskip
    \begin{subfigure}[bt]{0.8\textwidth}
        \includegraphics[width=\textwidth]{figures/results/screenshots/night_new_deli.jpg}
        \caption{New Deli at night}
    \end{subfigure}
    \caption{Night layers are only rendered on the night side of the planet. Night layer: NASA GIBS VIIRS Earth at night \cite{gibs}}
\end{figure}

\clearpage
\subsection{Color Overlays}
\FloatBarrier

To demonstrate color overlays, the three examples of figure \ref{fig:coloroverlays} show how different tile providers produce references useful for debugging or locationing. 

\begin{figure}[h]
    \centering
    \begin{subfigure}[bt]{0.45\textwidth}
        \includegraphics[width=\textwidth]{figures/results/screenshots/coloroverlay1.jpg}
        \caption{Color Overlay: tile indices}
    \end{subfigure}
    ~
    \begin{subfigure}[bt]{0.45\textwidth}
        \includegraphics[width=\textwidth]{figures/results/screenshots/coloroverlay2.jpg}
        \caption{Color Overlay: size reference}
    \end{subfigure}
    
    \par\bigskip
    \begin{subfigure}[bt]{0.90\textwidth}
        \includegraphics[width=\textwidth]{figures/results/screenshots/coloroverlay3.jpg}
        \caption{Color Overlay: reference features and reference labels \cite{gibs}}
    \end{subfigure}
    \caption{Earth rendered with different color overlays used for reference. Color layer: ESRI Imagery World 2D \cite{imageryworld2d}}
    \label{fig:coloroverlays}
\end{figure}

\clearpage
\subsection{Grayscale Overlaying}
\FloatBarrier
In figure \ref{fig:hsvblending}, the great canyon Valles Marineris on Mars is rendered with a low resolution color layer combined with a higher resolution grayscale overlay.

\begin{figure}[h]
    \centering
    \begin{subfigure}[bt]{0.45\textwidth}
        \includegraphics[width=\textwidth]{figures/results/screenshots_thesis_old/valles_marineris1.jpg}
        \caption{Color layer: Viking MDIM \cite{viking}}
    \end{subfigure}
    ~
    \begin{subfigure}[bt]{0.45\textwidth}
        \includegraphics[width=\textwidth]{figures/results/screenshots_thesis_old/valles_marineris2.jpg}
        \caption{Grayscale layer: CTX Mosaic}
    \end{subfigure}
    
    \par\bigskip
    \begin{subfigure}[bt]{0.90\textwidth}
        \includegraphics[width=\textwidth]{figures/results/screenshots_thesis_old/valles_marineris3.jpg}
        \caption{CTX Mosaic HSV blended on top of Viking MDIM \cite{viking}}
    \end{subfigure}
    \caption{Valles Marineris, Mars with different layers}
    \label{fig:hsvblending}
\end{figure}

\clearpage
\subsection{Local Patches}
\label{section:localpatchesresult}
\FloatBarrier

Figure \ref{fig:localpatches} shows the approach of local DTM patches in West Candor Chasma.  

\begin{figure}[h]
    \centering
    \begin{subfigure}[t]{0.45\textwidth}
        \includegraphics[width=\textwidth]{figures/results/screenshots_thesis_old/west_candor_chasma1.jpg}
        \caption{Local Patch: CTX DTM patch}
    \end{subfigure}
    ~
    \begin{subfigure}[t]{0.45\textwidth}
        \includegraphics[width=\textwidth]{figures/results/screenshots_thesis_old/west_candor_chasma2.jpg}
        \caption{CTX mosaic, CTX DTM patch and 25 cm per pixel DTM patch}
    \end{subfigure}
    
    \par\bigskip
    \begin{subfigure}[t]{0.90\textwidth}
        \includegraphics[width=\textwidth]{figures/results/screenshots_thesis_old/west_candor_chasma3.jpg}
        \caption{CTX mosaic, CTX DTM patch and HiRISE 25 cm per pixel DTM patch closeup}
    \end{subfigure}
    \caption{Local DTM patches of West Candor Chasma, Valles Marineris, Mars. All figures use color layer: Viking MDIM \cite{viking} and height layer: MOLA \cite{mola}.}
    \label{fig:localpatches}
\end{figure}


\clearpage
\subsection{Visualizing Scientific Parameters}
\FloatBarrier

Using the vast amount of datasets provided by NASA GIBS \cite{gibs}, several scientific parameters measured by the Terra and Aqua satellites among others could be visualized as a result of layered texture rendering. Three examples are shown in figure \ref{fig:sciparam}.

\begin{figure}[h]
    \centering
    \begin{subfigure}[t]{0.45\textwidth}
        \includegraphics[width=\textwidth]{figures/results/screenshots_science_params/ozone.jpg}
        \caption{Ozone (measured in streaks)}
    \end{subfigure}
    ~
    \begin{subfigure}[t]{0.45\textwidth}
        \includegraphics[width=\textwidth]{figures/results/screenshots_science_params/land_temp.jpg}
        \caption{Land temperature}
    \end{subfigure}
    \par\bigskip
    \begin{subfigure}[t]{0.90\textwidth}
        \includegraphics[width=\textwidth]{figures/results/screenshots_science_params/sea_surface.jpg}
        \caption{Sea surface temperature}
    \end{subfigure}
    \caption{Visualization of scientific parameters on the globe. All these datasets are temporal and can be animated over time. Datasets from \cite{gibs}.}
    \label{fig:sciparam}
\end{figure}

\clearpage
\subsection{Visual Debugging: Bounding Volumes}
\FloatBarrier
Bounding polyhedra are calculated on the fly for each chunk, taking onto consideration any currently enabled height dataset. These bounding volumes are then used for by culling algorithms. Figure \ref{fig:boundingvolume} shows how smaller, more planar chunks can be encapsulated more tightly than large chunks by polyhedron shapes of eight vertices converging to rectangular blocks for high chunk levels.
\begin{figure}[h]
    \centering
    \begin{subfigure}[bt]{0.45\textwidth}
        \includegraphics[width=\textwidth]{figures/results/screenshots_thesis_old/bounds1.jpg}
        \caption{}
        \label{fig:tetrahedrablocks}
    \end{subfigure}
    ~
    \begin{subfigure}[bt]{0.45\textwidth}
        \includegraphics[width=\textwidth]{figures/results/screenshots_thesis_old/bounds2.jpg}
        \caption{}
    \end{subfigure}
    \begin{subfigure}[bt]{0.45\textwidth}
        \includegraphics[width=\textwidth]{figures/results/screenshots_thesis_old/bounds3.jpg}
        \caption{}
    \end{subfigure}
    ~
    \begin{subfigure}[bt]{0.45\textwidth}
        \includegraphics[width=\textwidth]{figures/results/screenshots_thesis_old/bounds4.jpg}
        \caption{}
        \label{fig:cuboidblocks}
    \end{subfigure}
    \caption{Rendering the bounding polyhedra for chunks at Mars. Note how the polyhedra start out as tetrahedra for the largest chunks in \ref{fig:tetrahedrablocks} and converge to rectangular blocks as seen in \ref{fig:cuboidblocks}. }
    \label{fig:boundingvolume}
\end{figure}

\clearpage
\subsection{Visual Debugging: Camera Frustum}
\FloatBarrier

Figure \ref{fig:frustummars} shows a camera frustum visualized and the affect of frustum culling on chunks together with the difference in skirt length between levels.

\begin{figure}[h]
    \centering
        \includegraphics[width=\textwidth]{figures/results/screenshots_thesis_old/frustum_mars.jpg}
    \caption{Chunks culled outside the view frustum. The skirt length of the chunks differ depending on the level. The figure also shows how some chunks are rendered in model space (green edges) and some in camera space (red edges).}
    \label{fig:frustummars}
\end{figure}

\clearpage
\section{Benchmarking}
\label{section:benchmarking}
\FloatBarrier
This section cover a range of benchmarks diagnosing the behavior and performance of the system. The specifications for the computer used for benchmarking is defined in table \ref{table:benchmark host}. 

\begin{table}[h]
  \centering
  \caption[]{Computer used for Benchmarking}
    \label{table:benchmark host}
  \begin{tabular}{| r l |}
    \hline
      \textbf{Computer Model:}  & MacBook Pro (15'' early 2011) \\
      \textbf{Processor:}       & 2GHz Intel Core i7 \\
      \textbf{RAM:}             & 8 GB 1333MHz DDR3 RAM \\
      \textbf{Graphics:}        & AMD Radeon HD 6490M 256 MB \\
    \hline
  \end{tabular}
\end{table}



\clearpage
\subsection{Top Down Views}
\FloatBarrier
The chunk rendering algorithm was evaluated for a top down view at different distances to the ground. The settings for the evaluation are presented in Table \ref{table:settingstopdown}. The camera views for the evaluation points are shown in figure \ref{fig:topdown} and the results are presented in figure \ref{fig:topdowngraph1}.
\begin{table}[h]
  \centering
  \caption[]{Globe rendering settings for top down view benchmark}
    \label{table:settingstopdown}
  \begin{tabular}{| r l |}
    \hline
      \textbf{Globe:}             & Earth \\
      \textbf{Map datasets:}      & HeightLayers = [GCS\_Elevation \cite{worldelevation3d}] \\
                                  & ColorLayers = [ESRI Imagery World 2D \cite{imageryworld2d}] \\
      \textbf{LOD Scale factor:}  & 10.0 \\
      \textbf{Chunk Selection:}    & By distance \\
      \textbf{Culling:}           & Frustum culling, Horizon culling \\
      \textbf{Level blending:}    & Enabled \\
      \textbf{Camera View:}       & Facing down, varying altitudes\\
    \hline
  \end{tabular}
\end{table}

\begin{figure}[h]
    \centering
    \begin{subfigure}[bt]{0.31\textwidth}
        \includegraphics[width=\textwidth]{figures/results/topdown/topdown5.jpg}
        \caption{Earth}
    \end{subfigure}
    ~
    \begin{subfigure}[bt]{0.31\textwidth}
        \includegraphics[width=\textwidth]{figures/results/topdown/topdown4.jpg}
        \caption{East America}
    \end{subfigure}
    ~
    \begin{subfigure}[bt]{0.31\textwidth}
        \includegraphics[width=\textwidth]{figures/results/topdown/topdown3.jpg}
        \caption{New York City}
    \end{subfigure}
    ~
    \begin{subfigure}[bt]{0.31\textwidth}
        \includegraphics[width=\textwidth]{figures/results/topdown/topdown2.jpg}
        \caption{Manhattan}
    \end{subfigure}
    ~
    \begin{subfigure}[bt]{0.31\textwidth}
        \includegraphics[width=\textwidth]{figures/results/topdown/topdown1.jpg}
        \caption{Central Park}
    \end{subfigure}
    \caption{Top down views of Earth at different altitudes}
    \label{fig:topdown}
\end{figure}

\begin{figure}[h]
\begin{tikzpicture}
    \begin{axis}[
        width  = 1.0*\textwidth,
        height = 12cm,
        major x tick style = transparent,
        ybar=2*\pgflinewidth,
        bar width=8pt,
        ymajorgrids = true,
        %ylabel = {Number of},
        symbolic x coords={Earth, East America, NYC, Manhattan, Central Park},
        xtick = data,
        scaled y ticks = false,
        enlarge x limits=0.25,
        ymin=0,
        legend cell align=left,
        legend style={
                at={(0.43, 0.66)},
                anchor=south east,
                column sep=1ex
        }
    ]

      \addplot[style={chunks_color,fill=chunks_color,mark=none}]
        coordinates { (Earth, 10) (East America, 70) (NYC, 70) (Manhattan, 110) (Central Park, 142) };

      \addplot[style={leafs_color,fill=leafs_color,mark=none}]
        coordinates { (Earth, 8) (East America, 53) (NYC, 53) (Manhattan, 83) (Central Park, 107) };
      
      \addplot[style={rendered_color,fill=rendered_color,mark=none}]
        coordinates { (Earth, 7) (East America, 14) (NYC, 13) (Manhattan, 17) (Central Park, 11) };

      \addplot[style={globe_render_time,fill=globe_render_time,mark=none}]
        coordinates { (Earth, 17) (East America, 20) (NYC, 20) (Manhattan, 21) (Central Park, 21) };

      \addplot[style={frame_render_time,fill=frame_render_time,mark=none}]
        coordinates { (Earth, 1.1) (East America, 3.4) (NYC, 3.5) (Manhattan, 5) (Central Park, 5.6) };

      \legend{Chunks, Leaf chunks, Rendered chunks, Frame time [ms], Globe render time [ms]}

    \end{axis}
\end{tikzpicture}
\caption{As the camera descends towards the ground looking straight down, the chunk tree grows but the number of rendered chunks remains relatively constant due to culling.}
\label{fig:topdowngraph1}
\end{figure}



\clearpage
\subsection{Culling for Distance Based Chunk Selection}
\label{ch:culld}
\FloatBarrier
The two culling algorithms frustum culling and horizon culling were evaluated in combination with the distance based chunk selection algorithm.
The settings used are provided in table \ref{table:cullingdsettings}. 
Figure \ref{fig:cullingdcam} shows the camera view evaluated. 
Figure \ref{fig:cullingd} shows an overview of the rendered chunks with the results shown in figure \ref{fig:cullingcomp}.


\begin{table}[h]
  \centering
  \caption[]{Globe rendering settings for evaluation of culling with distance based chunk selection}
  \label{table:cullingdsettings}
  \begin{tabular}{| r l |}
    \hline
      \textbf{Globe:}             & Earth \\
      \textbf{Map datasets:}      & HeightLayers = [GCS\_Elevation \cite{worldelevation3d}] \\
                                  & ColorLayers = [ESRI Imagery World 2D \cite{imageryworld2d}] \\
      \textbf{LOD Scale factor:}  & 7.8 \\
      \textbf{Chunk Selection:}    & By distance \\
      \textbf{Culling:}           & \textbf{Evaluated} \\
      \textbf{Level blending:}    & Enabled \\
      \textbf{Camera View:}       & Looking towards western horizon\\
      \textbf{Location:}          & New York, New Jersey\\
    \hline
  \end{tabular}
\end{table}

\begin{figure}[h]
    \centering
    \begin{subfigure}[bt]{1.0\textwidth}
        \includegraphics[width=\textwidth]{figures/results/culling/cam_d.jpg}
    \end{subfigure}
    \caption{Chunks yielded by the distance based chunk selection algorithm. Brooklyn, Manhattan and New Jersey is seen in the camera view.}
    \label{fig:cullingdcam}
\end{figure}

\clearpage
\begin{figure}[h]
    \centering
    \begin{subfigure}[t]{0.4\textwidth}
        \includegraphics[width=\textwidth]{figures/results/culling/d.jpg}
        \caption{No culling}
    \end{subfigure}
    ~
    \begin{subfigure}[t]{0.4\textwidth}
        \includegraphics[width=\textwidth]{figures/results/culling/df.jpg}
        \caption{Frustum culling}
    \end{subfigure}
    ~
    \begin{subfigure}[t]{0.4\textwidth}
        \includegraphics[width=\textwidth]{figures/results/culling/dh.jpg}
        \caption{Horizon culling}
    \end{subfigure}
    ~
    \begin{subfigure}[t]{0.4\textwidth}
        \includegraphics[width=\textwidth]{figures/results/culling/dhf.jpg}
        \caption{Frustum and horizon culling}
    \end{subfigure}
    \caption{Culling of chunks with distance based chunk selection}
    \label{fig:cullingd}
\end{figure}

\iffalse
\begin{table}[h]
\centering
\caption[]{Culling for projected area based chunk selection}
  \label{table:cullingd}
  \begin{tabular}{| r | c c c c |}
    \hline
      \textbf{Culling}            & \textbf{None}  & \textbf{Horizon} & \textbf{Frustum}  & \textbf{Both} \\ \hline
      \textbf{Chunk nodes}        & 514            & 390              & 214               & 154 \\ 
      \textbf{Leaf chunk nodes}   & 386            & 293              & 161               & 116 \\ 
      \textbf{Rendered chunks}    & 386            & 254              & 79                & 53 \\
      \textbf{Frame Time}         & 155 ms         & 53 ms            & 39 ms             & 28 ms \\
      \textbf{Globe render time}  & 119 ms         & 30 ms            & 14 ms             & 10 ms \\
    \hline
  \end{tabular}
\end{table}
\fi

\begin{figure}[h]
\begin{tikzpicture}
    \begin{axis}[
        width  = 1.0*\textwidth,
        height = 6.5cm,
        major x tick style = transparent,
        ybar=2*\pgflinewidth,
        bar width=8pt,
        ymajorgrids = true,
        %ylabel = {Number of},
        symbolic x coords={No Culling, Horizon Culling, Frustum Culling, Both},
        xtick = data,
        scaled y ticks = false,
        enlarge x limits=0.25,
        ymin=0,
        legend cell align=left,
        legend style={
                at={(0.99, 0.44)},
                anchor=south east,
                column sep=1ex
        }
    ]

      \addplot[style={chunks_color,fill=chunks_color,mark=none}]
        coordinates { (No Culling, 514) (Horizon Culling, 390) (Frustum Culling, 214) (Both, 154)};

      \addplot[style={leafs_color,fill=leafs_color,mark=none}]
        coordinates { (No Culling, 386) (Horizon Culling, 293) (Frustum Culling, 161) (Both, 116)};
      
      \addplot[style={rendered_color,fill=rendered_color,mark=none}]
        coordinates { (No Culling, 386) (Horizon Culling, 254) (Frustum Culling, 79) (Both, 53)};

      \addplot[style={frame_render_time,fill=globe_render_time,mark=none}]
        coordinates { (No Culling, 155) (Horizon Culling, 53) (Frustum Culling, 39) (Both, 28)};

      \addplot[style={globe_render_time,fill=frame_render_time,mark=none}]
        coordinates { (No Culling, 119) (Horizon Culling, 30) (Frustum Culling, 14) (Both, 10) };

      \legend{Chunks, Leaf chunks, Rendered chunks, Frame time [ms], Globe render time [ms]}

    \end{axis}
\end{tikzpicture}
\caption{The number of chunks effected by culling}
\label{fig:cullingcomp}
\end{figure}

\clearpage
\subsection{Culling for Area Based Chunk Selection}
\label{ch:culla}

\FloatBarrier
The two culling algorithms frustum culling and horizon culling were evaluated in combination with the area based chunk selection algorithm.
The settings used are provided in table \ref{table:cullingasettings}. 
Figure \ref{fig:cullingacam} shows the camera view evaluated. 
Figure \ref{fig:cullinga} shows an overview of the rendered chunks with the results shown in figure \ref{fig:topdowngrapha}.

\begin{table}[h]
  \centering
  \caption[]{Globe rendering Settings for evaluation of culling with area based chunk selection}
  \label{table:cullingasettings}
  \begin{tabular}{| r l |}
    \hline
      \textbf{Globe:}             & Earth \\
      \textbf{Map datasets:}      & HeightLayers = [GCS\_Elevation \cite{worldelevation3d}] \\
                                  & ColorLayers = [ESRI Imagery World 2D \cite{imageryworld2d}] \\
      \textbf{LOD Scale factor:}  & 7.8 \\
      \textbf{Chunk Selection:}    & By projected area \\
      \textbf{Culling:}           & \textbf{Evaluated} \\
      \textbf{Level blending:}    & Enabled \\
      \textbf{Camera View:}       & Looking towards western horizon\\
      \textbf{Location:}          & New York, New Jersey\\
    \hline
  \end{tabular}
\end{table}

\begin{figure}[h]
    \centering
    \begin{subfigure}[bt]{1.0\textwidth}
        \includegraphics[width=\textwidth]{figures/results/culling/cam_a.jpg}
    \end{subfigure}
    \caption{Chunks yielded by the projected area based chunk selection algorithm. Brooklyn, Manhattan and New Jersey is seen in the camera view.}
    \label{fig:cullingacam}
\end{figure}

\clearpage
\begin{figure}[h]
    \centering
    \begin{subfigure}[bt]{0.4\textwidth}
        \includegraphics[width=\textwidth]{figures/results/culling/a.jpg}
        \caption{No culling}
    \end{subfigure}
    ~
    \begin{subfigure}[bt]{0.4\textwidth}
        \includegraphics[width=\textwidth]{figures/results/culling/af.jpg}
        \caption{Frustum culling}
    \end{subfigure}
    ~
    \begin{subfigure}[bt]{0.4\textwidth}
        \includegraphics[width=\textwidth]{figures/results/culling/ah.jpg}
        \caption{Horizon culling}
    \end{subfigure}
    ~
    \begin{subfigure}[bt]{0.4\textwidth}
        \includegraphics[width=\textwidth]{figures/results/culling/afh.jpg}
        \caption{Frustum and Horizon culling}
    \end{subfigure}
    \caption{Culling of chunks with area based chunk selection}
    \label{fig:cullinga}
\end{figure}

\iffalse
\begin{table}[h]
\centering
\caption[]{Projected area based}
  \label{table:cullinga}
  \begin{tabular}{| r | c c c c |}
    \hline
      \textbf{Culling}            & \textbf{None} & \textbf{Horizon}  & \textbf{Frustum}  & \textbf{Both} \\ \hline
      \textbf{Chunk nodes}        & 270           & 202               & 134               & 94 \\ 
      \textbf{Leaf chunk nodes}   & 203           & 152               & 101               & 71 \\ 
      \textbf{Rendered chunks}    & 203           & 133               & 43                & 26 \\
      \textbf{Frame Time}         & 123 ms        & 41 ms             & 30 ms             & 23 ms \\
      \textbf{Globe render time}  & 62 ms         & 16 ms             & 7.9 ms            & 5.6 ms \\
    \hline
  \end{tabular}
\end{table}
\fi



\begin{figure}[h]
\begin{tikzpicture}
    \begin{axis}[
        width  = 1.0*\textwidth,
        height = 6.5cm,
        major x tick style = transparent,
        ybar=2*\pgflinewidth,
        bar width=8pt,
        ymajorgrids = true,
        %ylabel = {Number of},
        symbolic x coords={No Culling, Horizon Culling, Frustum Culling, Both},
        xtick = data,
        scaled y ticks = false,
        enlarge x limits=0.25,
        ymin=0,
        legend cell align=left,
        legend style={
                at={(0.995, 0.44)},
                anchor=south east,
                column sep=1ex
        }
    ]

      \addplot[style={chunks_color,fill=chunks_color,mark=none}]
        coordinates { (No Culling, 270) (Horizon Culling, 202) (Frustum Culling, 134) (Both, 94)};

      \addplot[style={leafs_color,fill=leafs_color,mark=none}]
        coordinates { (No Culling, 203) (Horizon Culling, 152) (Frustum Culling, 101) (Both, 71)};

      \addplot[style={rendered_color,fill=rendered_color,mark=none}]
        coordinates { (No Culling, 203) (Horizon Culling, 133) (Frustum Culling, 43) (Both, 26)};

      \addplot[style={frame_render_time,fill=globe_render_time,mark=none}]
        coordinates { (No Culling, 123) (Horizon Culling, 41) (Frustum Culling, 30) (Both, 23)};

      \addplot[style={globe_render_time,fill=frame_render_time,mark=none}]
        coordinates { (No Culling, 62) (Horizon Culling, 16) (Frustum Culling, 7.9) (Both, 5.6) };

      \legend{Chunks, Leaf chunks, Rendered chunks, Frame time [ms], Globe render time [ms]}

    \end{axis}
\end{tikzpicture}
\caption{The number of chunks effected by culling}
\label{fig:topdowngrapha}
\end{figure}

\clearpage
\subsection{LOD: Distance Based vs. Area Based}
\FloatBarrier

The benchmark results in section \ref{ch:culld} and \ref{ch:culla} were compared and evaluated in relation to each other. In figure \ref{fig:lodcomp} the two approaches are compared where both frustum culling and horizon culling were enabled.

\begin{figure}[h]
\centering
\begin{tikzpicture}
    \begin{axis}[
        width  = 0.9*\textwidth,
        height = 15cm,
        major x tick style = transparent,
        ybar=2*\pgflinewidth,
        bar width=15pt,
        ymajorgrids = true,
        ylabel = {},
        symbolic x coords={Distance based chunk selection, Area based chunk selection},
        xtick = data,
        scaled y ticks = false,
        enlarge x limits=0.55,
        ymin=0,
        legend cell align=left,
        legend style={
                at={(0.995, 0.74)},
                anchor=south east,
                column sep=1ex
        }
    ] 

      \addplot[style={chunks_color,fill=chunks_color,mark=none}]
        coordinates { (Distance based chunk selection, 154) (Area based chunk selection, 94) };

      \addplot[style={leafs_color,fill=leafs_color,mark=none}]
        coordinates { (Distance based chunk selection, 116) (Area based chunk selection, 71) };

      \addplot[style={rendered_color,fill=rendered_color,mark=none}]
        coordinates { (Distance based chunk selection, 53) (Area based chunk selection, 26) };

      \addplot[style={frame_render_time,fill=frame_render_time,mark=none}]
        coordinates { (Distance based chunk selection, 28) (Area based chunk selection, 23) };

      \addplot[style={globe_render_time,fill=globe_render_time,mark=none}]
        coordinates { (Distance based chunk selection, 10) (Area based chunk selection, 5.6) };

      \legend{Chunks, Leaf chunks, Rendered chunks, Frame time [ms], Globe render time [ms]}

    \end{axis}
\end{tikzpicture}
\caption{Comparison of distance based and area based chunk selection}
\label{fig:lodcomp}
\end{figure}

\clearpage
\subsection{Switching Using Level Blending}
\label{section:res_switching}
\FloatBarrier
The visual result of using the distance based level blending is shown in figure \ref{fig:blending2}.
\begin{figure}[h]
    \centering
    \begin{subfigure}[bt]{0.48\textwidth}
        \includegraphics[width=\textwidth]{figures/results/blending/blending_bali2_disabled.jpg}
        \caption{Blending disabled}
    \end{subfigure}
    \begin{subfigure}[bt]{0.48\textwidth}
        \includegraphics[width=\textwidth]{figures/results/blending/blending_bali2_enabled.jpg}
        \caption{Blending enabled}
    \end{subfigure}
    \caption{Comparison of using level blending and no blending. Level blending hides edges the underlying chunks}
    \label{fig:blending2}
\end{figure}

Table \ref{table:levelblending} shows the settings used to compare having level blending enabled and disabled. To show the penalty in texture detail that is paid for using level blending, the LOD scale factor was set low. Figure \ref{fig:blending} shows that the texture resolution becomes low enough to see the individual pixels when having a low LOD. The results in table \ref{table:resultblending} also show that figure \ref{fig:blendingdisabled} contains more visual information than \ref{fig:blendingenabled}. 

\begin{table}
  \centering
  \caption[]{Globe rendering settings used in benchmark}
    \label{table:levelblending}
  \begin{tabular}{| r l |}
    \hline
      \textbf{Globe:}             & Earth \\
      \textbf{Map datasets:}      & HeightLayers = [GCS\_Elevation \cite{worldelevation3d}] \\
                                  & ColorLayers = [ESRI Imagery World 2D \cite{imageryworld2d}] \\
      \textbf{LOD Scale factor:}  & 4.65 \\
      \textbf{Chunk Selection:}    & By distance \\
      \textbf{Culling:}           & Frustum culling, Horizon culling \\
      \textbf{Camera View:}       & Horizon \\
    \hline
  \end{tabular}
\end{table}

\begin{figure}[h]
    \centering
    \begin{subfigure}[bt]{0.48\textwidth}
        \includegraphics[width=\textwidth]{figures/results/blending/blending_bali_disabled.jpg}
        \caption{Blending disabled}
        \label{fig:blendingdisabled}
    \end{subfigure}
    \begin{subfigure}[bt]{0.48\textwidth}
        \includegraphics[width=\textwidth]{figures/results/blending/blending_bali_enabled.jpg}
        \caption{Blending enabled}
        \label{fig:blendingenabled}
    \end{subfigure}
    \caption{Comparison of level blending and no blending. The LOD scale factor is set low to show the resolution penalty of using blending}
    \label{fig:blending}
\end{figure}

\begin{table}
\centering
\caption[]{Level blending benchmarks. Comparing the disk space of a compressed JPG image of both cases works as a heuristic to the information contained in each image}
  \label{table:resultblending}
  \begin{tabular}{| r | c c |}
    \hline
      \textbf{Figure \ref{fig:blending}}  & \textbf{No blending} & \textbf{Level blending} \\ \hline
      \textbf{Samples per fragment} & 1 & 3 \\ 
      \textbf{Mean globe render time}  & 10.3 ms & 10.1 ms \\ 
      \textbf{Mean frame time}  & 40 ms &  49 ms \\ 
      \textbf{Screenshot jpg size} & 1,1 MB & 0,7 MB \\
    \hline
  \end{tabular}
\end{table}

\clearpage
\subsection{Polar Pinching}
\label{section:res_polarpinching}
\FloatBarrier
The impact of polar pinching on the chunk tree was evaluated using both distance based chunk selection and area based chunk selection. The results are presented in figure \ref{fig:pincheval}.

\begin{table}[h]
  \centering
  \caption[]{Globe rendering settings for evaluation of polar pinching}
  \label{table:pinchingstart}
  \begin{tabular}{| r l |}
    \hline
      \textbf{Globe:}             & Earth \\
      \textbf{Map datasets:}      & HeightLayers = [GCS\_Elevation\cite{worldelevation3d}] \\
                                  & ColorLayers = [ESRI Imagery World 2D \cite{imageryworld2d}] \\
      \textbf{LOD Scale factor:}  & 10.0 \\
      \textbf{Chunk Selection:}    & \textbf{Evaluated} \\
      \textbf{Culling:}           & Frustum culling, horizon culling \\
      \textbf{Camera View:}       & Facing down\\
      \textbf{Location:}          & Equator (at Quito, Ecuador) and North Pole\\
    \hline
  \end{tabular}
\end{table}

\iffalse
\begin{table}[h]
\centering
\caption[]{Evaluation of polar pinching with Distance based chunk selection}
  \label{table:polarpinching}
  \begin{tabular}{| r | c c |}
    \hline
      \textbf{Distance based chunk selection} & \textbf{Equator} & \textbf{North Pole} \\ \hline
      \textbf{Chunk nodes}        & 78           & 506               \\ 
      \textbf{Leaf chunk nodes}   & 59           & 380                \\ 
      \textbf{Rendered chunks}    & 6            & 151                \\
      \textbf{Frame Time}         & ? ms         & ? ms              \\
      \textbf{Globe render time}  & 2,7 ms       & 31 ms              \\
    \hline
  \end{tabular}
\end{table}
\fi


\begin{figure}[h]
\begin{tikzpicture}
    \begin{axis}[
        width  = 1.0*\textwidth,
        height = 8cm,
        major x tick style = transparent,
        ybar=2*\pgflinewidth,
        bar width=14pt,
        ymajorgrids = true,
        %ylabel = {Number of},
        symbolic x coords={D: Equator, D: Pole, A: Equator, A: Pole},
        xtick = data,
        scaled y ticks = false,
        enlarge x limits=0.25,
        ymin=0,
        legend cell align=left,
        legend style={
                at={(0.98, 0.60)},
                anchor=south east,
                column sep=1ex
        }
    ]

      \addplot[style={chunks_color,fill=chunks_color,mark=none}]
        coordinates { (D: Equator, 78) (D: Pole, 506) (A: Equator, 94) (A: Pole, 250) };

      \addplot[style={leafs_color,fill=leafs_color,mark=none}]
        coordinates { (D: Equator, 59) (D: Pole, 380) (A: Equator, 94) (A: Pole, 188) };
      
      \addplot[style={rendered_color,fill=rendered_color,mark=none}]
        coordinates { (D: Equator, 6) (D: Pole, 151) (A: Equator, 17) (A: Pole, 64) };

      \addplot[style={globe_render_time,fill=globe_render_time,mark=none}]
        coordinates { (D: Equator, 27) (D: Pole, 310) (A: Equator, 43) (A: Pole, 140) };

      \legend{Chunks, Leaf chunks, Rendered chunks, Render time [$10^{-4}$ s]}

    \end{axis}
\end{tikzpicture}
\caption{Comparison of distance based and area based chunk selection at the Equator and the North Pole. \textbf{D} = distance based, \textbf{A} = area based}
\label{fig:pincheval}
\end{figure}

\iffalse
\begin{table}[h]
\centering
\caption[]{Evaluation of polar pinching with Area based chunk selection}
  \label{table:polarpinching}
  \begin{tabular}{| r | c c |}
    \hline
      \textbf{Area based chunk selection}     & \textbf{Equator} & \textbf{North Pole} \\ \hline
      \textbf{Chunk nodes}        & 94           & 250               \\ 
      \textbf{Leaf chunk nodes}   & 71           & 188                \\ 
      \textbf{Rendered chunks}    & 17           & 64                \\
      \textbf{Frame Time}         & ? ms         & ? ms              \\
      \textbf{Globe render time}  & 4,3 ms       & 14 ms              \\
    \hline
  \end{tabular}
\end{table}
\fi

\clearpage
\subsection{Benchmark: Interactive Globe Browsing}
\FloatBarrier
The purpose of the globe browsing is to be able to interactively explore virtual globes and map datasets. In order to capture how the system behaves over time, a user interaction sequence was evaluated. The sequence is described step by step below and illustrated in Figure \ref{fig:interaction}.

\begin{enumerate}
  \item Camera views Earth from space
  \item Descend down to Naturpark Karwendel, north of Innsbruck, Austria
  \item Tilt camera up, view northern horizon
  \item Turn camera 180 degrees, view southern horizon
  \item Tilt camera down
\end{enumerate}

\begin{figure}[h]
    \centering
    \begin{subfigure}[bt]{1.0\textwidth}
        \includegraphics[width=\textwidth]{figures/results/globebrowsing.pdf}
    \end{subfigure}
    \caption{Chunk tree over time when browsing the globe}
    \label{fig:interaction}
\end{figure}

\clearpage
\subsection{Camera Space Rendering}
\FloatBarrier

Comparing the use of camera space rendering and model space rendering, vertex jittering is apparent when interacting close to the surface. Figure \ref{fig:camspacemodelspace} shows how vertex jittering is apparent when browsing a HiRISE patch close to the surface of Mars. The visual result in the image is not as striking as the artifact that appears when the camera is moving. Then the vertices are jittering only in the case of model space rendering and not for camera space rendering. 

\begin{figure}[h]
    \centering
    \begin{subfigure}[bt]{0.45\textwidth}
        \includegraphics[width=\textwidth]{figures/results/camspace.jpg}
        \caption{Camera space rendering}
    \end{subfigure}
    ~
    \begin{subfigure}[bt]{0.45\textwidth}
        \includegraphics[width=\textwidth]{figures/results/modelspace.jpg}
        \caption{Model space rendering}
    \end{subfigure}
    \caption{Vertex jittering of model space rendering}
    \label{fig:camspacemodelspace}
\end{figure}


\FloatBarrier