43 lines
1.6 KiB
TeX
43 lines
1.6 KiB
TeX
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\subsection{Extremities}
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After computing the mesh around the splines we need to draw the extremities using subdivisions to obtain smoother extremities.
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The first step is to calculate the projection of the extremity circle on the correspondent sphere. Then for a subdivision of depth 0 we link this projection with the mesh points along the extrem circle (see Figure \ref{projection}). For one subdivision we take the middle of each segments computed earlier and we project it on the sphere (see Figure \ref{sub}). Finally we made a triangular mesh the way you can see on Figure \ref{mesh}).
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The rendering of our extremities on dino.skl for example can be seen on Figures \ref{extremity2} (2 subdivisions) and \ref{extremity10}
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(10 subdivisions).
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\begin{figure}[H]
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\begin{center}
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\includegraphics[scale=0.2]{img/projection}
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\caption{\label{projection}Projection of the extrem circle center on the sphere}
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\end{center}
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\end{figure}
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\begin{figure}[H]
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\begin{center}
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\includegraphics[scale=0.2]{img/Subdivision}
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\caption{\label{sub}One subdivision}
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\end{center}
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\end{figure}
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\begin{figure}[H]
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\begin{center}
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\includegraphics[scale=0.2]{img/meshExtremity}
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\caption{\label{mesh}The final extremity mesh for one subdivision}
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\end{center}
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\end{figure}
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\begin{figure}[H]
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\begin{minipage}[b]{0.45\linewidth}
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\centering
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\includegraphics[scale=0.5]{img/2}
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\caption{\label{extremity2}The final extremity mesh for 2 subdivisions}
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\end{minipage}
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\hspace{0.5cm}
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\begin{minipage}[b]{0.45\linewidth}
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\centering
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\includegraphics[scale=0.5]{img/10}
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\caption{\label{extremity10}The final extremity mesh for 10 subdivisions}
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\end{minipage}
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\end{figure}
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