\usepackage{amsthm}
\usepackage{graphicx}
\usepackage{minted}
+%Options: Sonny, Lenny, Glenn, Conny, Rejne, Bjarne, Bjornstrup
+\usepackage[Lenny]{fncychap}
\usepackage{polyglossia}
\setmainlanguage[variant=american]{english}
\usepackage{subcaption}
\usepackage{xfrac}
\usepackage{listings}
-\usepackage[intoc]{nomencl}
+\usepackage{nomencl}
\lstset{
% FIXME: Courier 9pt anbefales
\cleardoublepage
+\abstract{
+ BLEEP BLOOP.
+}
+
+\cleardoublepage
+
+\abstract{
+ BLEEP BLEEP NORSK.
+}
+
% Romerske tall på alt før selve rapporten starter er pent.
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% Arabisk (vanlige tall) sidenummerering. Starter på side 1 igjen.
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\input{theory}
\input{results}
+\cleardoublepage
+
% Bibliografi/referanseliste skal komme før appendiks
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+\markboth{\MakeUppercase\nomname}{\MakeUppercase\nomname}
+\printnomenclature[2.5cm]
+
+\cleardoublepage
% En latex-kommando for å si fra at kapitlene/seksjonene fra nå
% av skal nummereres med store bokstaver:
\appendix
+
\input{appendix}
% Indeks for rapporten. Ta bort prosenttegn hvis du vil ha det med.
amounts to switching the two eigenvalues $\sigma_1$ and $\sigma_2$ in
$\Sigma$.
-The whole transformation from the initial functional in
-\eqref{eq:first_anisotropic_functional}
-through the coarea formula and the Cauchy--Crofton formula was motivated
-by the discretization which will be described next. We will see that we
-can minimize the energy functional for each level separately, and that
-the integral over all lines $\mathcal{L}$ can be approximated by a sum
-over some discrete set of lines.
\chapter{Discrete formulation}
-This is where we discretize! It will also be an important chapter, as
-the choices and possibilities are endless. The easiest way out is to
-choose the same stencil in every point, and only let the weights depend
-on the anisotropy. This can work, but size has to be discussed (and
-tested later). Then the stencil shape can be adjusted as well.
+The whole transformation from the initial functional in
+\eqref{eq:first_anisotropic_functional} through the coarea formula and
+the Cauchy--Crofton formula was motivated by the discretization which
+will be described here. The coarea formula allows us to minimize the
+functional for each level separately, while the Cauchy--Crofton formula
+gives a feasible way of calculating the perimeter of each level set.
+
+The integrals we had in \fixme{ref} will be approximated by discrete
+sums, and we will be careful to discretize in a way which is consistent
+with the initial continuous formulation.
\section{Discretization}