paella
/
paella
1
0
Fork 0
Code Issues Pull Requests Projects Releases Wiki Activity

modif circles.tex et license.tex

This commit is contained in:
Amandinella 2015-03-12 20:39:34 +01:00
parent a3b625b1ae
commit 3dbf50a4d1
2 changed files with 59 additions and 9 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

34
report/chapters/license.tex
View File

@ -1,2 +1,36 @@
\chapter{License}
We decided to add a license to our project in order to allow the client using
our project without any problems of properties. We chose the Zlib license
which allow a free-use of our project. You can see our lisence in the listing \ref{license}.\\
\begin{lstlisting}[caption=Zlib license, label=license]
Paella - Copyright (C) 2015 - Thomas FORGIONE, Emilie JALRAS, Marion LENFANT, Thierry MALON, Amandine PAILLOUX
This software is provided 'as-is', without any express or implied warranty.
In no event will the authors be held liable for any damages arising from the use of this software.
Permission is granted to anyone to use this software for any purpose,
including commercial applications, and to alter it and redistribute it freely,
subject to the following restrictions:
1. The origin of this software must not be misrepresented;
you must not claim that you wrote the original software.
If you use this software in a product, an acknowledgment
in the product documentation would be appreciated but is not required.
2. Altered source versions must be plainly marked as such,
and must not be misrepresented as being the original software.
3. This notice may not be removed or altered from any source distribution.
External-libraries
------------------
Boost is under the boost software license
Eigen is under the MPL2
OpenCV is under the BSD License
SFML is under the zlib/libpng license
\end{lstlisting}

34
report/subsections/circles.tex
View File

@ -2,25 +2,41 @@
At the beginning of this part we have a set of 3D splines. We sample this splines and calculate the characteristic circle associated to each sampled point. Then we match the points between successive circles and use a triangular mesh.
\paragraph{Characteristic circles computation}
\subsubsection{Characteristic circles computation}
We take a point sampled on the spline. It gives us information about the sphere located on this point : $\overrightarrow{C}(t)$ the sphere center coordinates and r(t) its radius. We also have their derivatives : $\overrightarrow{C'}(t)$ and r'(t). The idea is to find the intersection between this sphere and the characteristic plane, which would give us the characteristic circle.
If a point P is on the circle, then we can write this formula : \\
$<\overrightarrow{C'}(t),\overrightarrow{PC}(t)> -r'(t)r(t) = 0$
If a point P is on the circle, then we can write the formula \ref{eq1} :
\begin{equation}
<\overrightarrow{C'}(t),\overrightarrow{PC}(t)> -r'(t)r(t) = 0
\label{eq1}
\end{equation}
and then we calculate the center of the characteristic circle with this formula :
$\overrightarrow{Cp}(t) = \overrightarrow{C}(t) - r'(t)r(t)/ /| \overrightarrow{C'}(t)/| ^{2} * \overrightarrow{C'}(t)$
and then we calculate the center of the characteristic circle with the formula \ref{eq2}:
\begin{equation}
\overrightarrow{Cp}(t) = \overrightarrow{C}(t) - \frac{r'(t)r(t)}{\| \overrightarrow{C'}(t)\| ^{2}} \times \overrightarrow{C'}(t)
\label{eq2}
\end{equation}
\begin{figure}[H]
\begin{center}
\includegraphics[scale=0.5]{img/characteristicCircle}
\includegraphics[scale=0.8]{img/characteristicCircle}
\caption{\label{initialSchedule} Characteristic circle calculation}
\end{center}
\end{figure}
\paragraph{meshing}
\subsubsection{Meshing}
After obtaining characteristic circles we sample them. Then we need to find matching points. We decided to make points sampling start in one direction of our mark. When this is done we project the mark on the new circle and sample again. Then we link each point to the point of the same index on the next circle.
After obtaining characteristic circles we sample them.
Then we need to find matching points. We decided to make points sampling start in one direction of our mark.
When this is done we project the mark on the new circle and sample again. Then we link each point to the point of the same index on the next circle.
The final mesh can be seen Figure \ref{regularMesh}.
\begin{figure}[H]
\begin{center}
\includegraphics[scale=0.8]{img/regularMesh}
\caption{\label{regularMesh} The regular mesh}
\end{center}
\end{figure}
%TODO