Recompile plots to properly align legend

ch/EmbeddingRepresentation/DataStructure.tex

@@ -41,6 +41,6 @@ While it would be possible to add additional pointers between meta mesh and base
 
 Note that meta faces are not connected to base faces, since the costs outweigh the benefit. Connecting base faces to their respective meta face would require iterating over a lot of base faces every time a new meta edge is traced, whereas in applications so far it was rare that the meta face of a base face needed to be addressed. As such it is computationally cheaper to computationally determine the meta face associated to a base face by doing an outward search until a meta edge is reached.
 
-However, one important restriction on meta faces $f^\mathcal{M}_i\in F^\mathcal{M}$ is that they, and by extension their embeddings $\Phi\left(f^\mathcal{M}_i\right)$, are \textit{always simple}. An embedded face $\Phi\left(f^\mathcal{M}_i\right)$ is a set of faces $\Phi\left(f^\mathcal{M}_i\right)=\left\{f^\mathcal{B}_j\in F^\mathcal{B'} \big|  F^\mathcal{B'}\subseteq F^\mathcal{B}\right\}$ on the surface of $\mathcal{B}$, and is called simple if it has no handles and exactly one external boundary. Restricting meta faces to simple faces has the advantages of making tracing new edges a lot easier, since we don't have to consider how to navigate around handles. 
+However, one important restriction on meta faces $f^\mathcal{M}_i\in F^\mathcal{M}$ is that they, and by extension their embeddings $\Phi\left(f^\mathcal{M}_i\right)$, are \textit{always simple}. An embedded face $\Phi\left(f^\mathcal{M}_i\right)$ is a set of faces $\Phi\left(f^\mathcal{M}_i\right)=\left\{f^\mathcal{B}_j\in F^\mathcal{B'} \big|  F^\mathcal{B'}\subseteq F^\mathcal{B}\right\}$ on the surface of $\mathcal{B}$, and is called simple if it has no handles and exactly one external boundary. Restricting meta faces to simple faces has the advantage of making tracing new edges a lot easier, since we don't have to consider how to navigate around handles. 
 
 In this implementation the meta mesh has an explicit representation as a mesh which is then connected with its underlying base mesh via pointers, as seen in Figure \ref{fig:catmetamesh}. But it would also be possible to represent the meta mesh entirely implicitly via properties on base mesh elements. It can however be argued that having an explicit representation is worth it since it makes the structure more transparent and operations on the meta mesh easier to apply. Another big advantage of having an explicit representation of the meta mesh is the speed of mesh traversal. To traverse from one meta vertex to another on the base mesh would require the traversal of a potentially long sequence of base halfedges, whereas by traversing meta mesh halfedges a lot of operations can be skipped. This increases the speed and comfort of operations on the meta mesh at the cost of the space required to represent the meta mesh as a second mesh connected to the base mesh.
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