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diff --git a/assets/TILTED_METHOD_verynarrow.svg b/assets/TILTED_METHOD_verynarrow.svg
diff --git a/assets/TILTED_method.svg b/assets/TILTED_method.svg
diff --git a/assets/TILTED_method_narrow.svg b/assets/TILTED_method_narrow.svg
diff --git a/assets/TILTED_method_v5.pdf b/assets/TILTED_method_v5.pdf
diff --git a/assets/aligned_giannini_norm.jpg b/assets/aligned_giannini_norm.jpg
diff --git a/assets/aligned_giannini_norm.png b/assets/aligned_giannini_norm.png
diff --git a/assets/aligned_giannini_pca.jpg b/assets/aligned_giannini_pca.jpg
diff --git a/assets/aligned_giannini_pca.png b/assets/aligned_giannini_pca.png
diff --git a/assets/aligned_giannini_rgb.jpg b/assets/aligned_giannini_rgb.jpg
diff --git a/assets/aligned_giannini_rgb.png b/assets/aligned_giannini_rgb.png
diff --git a/assets/aligned_kitchen_norm.jpg b/assets/aligned_kitchen_norm.jpg
diff --git a/assets/aligned_kitchen_norm.png b/assets/aligned_kitchen_norm.png
diff --git a/assets/aligned_kitchen_pca.jpg b/assets/aligned_kitchen_pca.jpg
diff --git a/assets/aligned_kitchen_pca.png b/assets/aligned_kitchen_pca.png
diff --git a/assets/aligned_kitchen_rgb.jpg b/assets/aligned_kitchen_rgb.jpg
diff --git a/assets/aligned_kitchen_rgb.png b/assets/aligned_kitchen_rgb.png
diff --git a/assets/aligned_storefront_norm.jpg b/assets/aligned_storefront_norm.jpg
diff --git a/assets/aligned_storefront_norm.png b/assets/aligned_storefront_norm.png
diff --git a/assets/aligned_storefront_pca.jpg b/assets/aligned_storefront_pca.jpg
diff --git a/assets/aligned_storefront_pca.png b/assets/aligned_storefront_pca.png
diff --git a/assets/aligned_storefront_rgb.jpg b/assets/aligned_storefront_rgb.jpg
diff --git a/assets/aligned_storefront_rgb.png b/assets/aligned_storefront_rgb.png
diff --git a/assets/aligned_stump_norm.jpg b/assets/aligned_stump_norm.jpg
diff --git a/assets/aligned_stump_norm.png b/assets/aligned_stump_norm.png
diff --git a/assets/aligned_stump_pca.jpg b/assets/aligned_stump_pca.jpg
diff --git a/assets/aligned_stump_pca.png b/assets/aligned_stump_pca.png
diff --git a/assets/aligned_stump_rgb.jpg b/assets/aligned_stump_rgb.jpg
diff --git a/assets/aligned_stump_rgb.png b/assets/aligned_stump_rgb.png
diff --git a/assets/diamond.svg b/assets/diamond.svg
diff --git a/assets/diamond_16_slow.gif b/assets/diamond_16_slow.gif
diff --git a/assets/diamond_alignment.gif b/assets/diamond_alignment.gif
diff --git a/assets/diamond_slow.gif b/assets/diamond_slow.gif
diff --git a/assets/fox_alignment.gif b/assets/fox_alignment.gif
diff --git a/assets/fox_alignment_smaller.gif b/assets/fox_alignment_smaller.gif
diff --git a/assets/sdf_aligned.jpg b/assets/sdf_aligned.jpg
diff --git a/assets/sdf_aligned.png b/assets/sdf_aligned.png
diff --git a/assets/sdf_tilted.jpg b/assets/sdf_tilted.jpg
diff --git a/assets/sdf_tilted.png b/assets/sdf_tilted.png
diff --git a/assets/square.svg b/assets/square.svg
diff --git a/assets/tikz/README b/assets/tikz/README
@@ -0,0 +1,9 @@
+Compiling figure sources on MacOS (MacTex 2023):
+
+1. Convert to .dvi:
+
+   latex <source_file>.tex
+
+2. Run dvisvgm with options:
+
+   dvisvgm -e --no-fonts <source_file>.dvi
diff --git a/assets/tikz/diamond.tex b/assets/tikz/diamond.tex
@@ -0,0 +1,89 @@
+\documentclass[border=0in]{standalone}
+
+\usepackage[T1]{fontenc}
+\usepackage{opensans}
+\usepackage{bm}
+\usepackage{mathrsfs}
+
+\usepackage{tikz}
+\usepackage{pgfplots}
+\pgfplotsset{compat=1.18}
+\usepackage{amsmath}
+\usepackage{amsfonts}
+\usepackage{amssymb}
+\usepackage{xcolor}
+\usepackage{newtxsf}
+
+\usepgfplotslibrary{fillbetween}
+
+\definecolor{c0}{HTML}{f0f9e8}
+\definecolor{c1}{HTML}{bae4bc}
+\definecolor{c2}{HTML}{7bccc4}
+\definecolor{c3}{HTML}{43a2ca}
+\definecolor{c4}{HTML}{0868ac}
+\definecolor{lightgray}{HTML}{d3d3d3}
+\newcommand{\grtr}{\natural}
+
+
+\setcounter{MaxMatrixCols}{20}
+
+
+\begin{document}
+
+\begin{tikzpicture}
+
+  % bounding box
+  \draw[black, fill=white, line width=1pt] (-2.2,-2.2) rectangle (2.2,2.2); % Adjust the dimensions as needed
+
+  % Black Square
+  \fill[black, rotate=45] (-1.2,-1.2) rectangle (1.2,1.2); % Adjust the coordinates to position the square
+
+  % first approx sign
+  \node [anchor=center] at (2.97, 0) {{\Huge $\approx$ }};
+
+
+  % discretized matrix
+\node [anchor=center] at (6.25, 0) {
+    \Large
+    $\begin{bmatrix}
+      \textcolor{lightgray}{0} &\hspace{-0.45em}& \textcolor{lightgray}{0} &\hspace{-0.45em}& \textcolor{lightgray}{0} &\hspace{-0.45em}& \textcolor{lightgray}{0} &\hspace{-0.45em}& \textcolor{lightgray}{0} &\hspace{-0.45em}& \textcolor{lightgray}{0} &\hspace{-0.45em}& \textcolor{lightgray}{0} \\
+      \textcolor{lightgray}{0} &\hspace{-0.45em}& \textcolor{lightgray}{0} &\hspace{-0.45em}& \textcolor{lightgray}{0} &\hspace{-0.45em}& \textcolor{black}{1} &\hspace{-0.45em}& \textcolor{lightgray}{0} &\hspace{-0.45em}& \textcolor{lightgray}{0} &\hspace{-0.45em}& \textcolor{lightgray}{0} \\
+      \textcolor{lightgray}{0} &\hspace{-0.45em}& \textcolor{lightgray}{0} &\hspace{-0.45em}& \textcolor{black}{1} &\hspace{-0.45em}& \textcolor{black}{1} &\hspace{-0.45em}& \textcolor{black}{1} &\hspace{-0.45em}& \textcolor{lightgray}{0} &\hspace{-0.45em}& \textcolor{lightgray}{0} \\
+      \textcolor{lightgray}{0} &\hspace{-0.45em}& \textcolor{black}{1} &\hspace{-0.45em}& \textcolor{black}{1} &\hspace{-0.45em}&
+      \textcolor{black}{1} &\hspace{-0.45em}& \textcolor{black}{1} &\hspace{-0.45em}& \textcolor{black}{1} &\hspace{-0.45em}&
+      \textcolor{lightgray}{0} \\
+      \textcolor{lightgray}{0} &\hspace{-0.45em}& \textcolor{lightgray}{0} &\hspace{-0.45em}& \textcolor{black}{1} &\hspace{-0.45em}& \textcolor{black}{1} &\hspace{-0.45em}& \textcolor{black}{1} &\hspace{-0.45em}& \textcolor{lightgray}{0} &\hspace{-0.45em}& \textcolor{lightgray}{0} \\
+      \textcolor{lightgray}{0} &\hspace{-0.45em}& \textcolor{lightgray}{0} &\hspace{-0.45em}& \textcolor{lightgray}{0} &\hspace{-0.45em}& \textcolor{black}{1} &\hspace{-0.45em}& \textcolor{lightgray}{0} &\hspace{-0.45em}& \textcolor{lightgray}{0} &\hspace{-0.45em}& \textcolor{lightgray}{0} \\
+      \textcolor{lightgray}{0} &\hspace{-0.45em}& \textcolor{lightgray}{0} &\hspace{-0.45em}& \textcolor{lightgray}{0} &\hspace{-0.45em}& \textcolor{lightgray}{0} &\hspace{-0.45em}& \textcolor{lightgray}{0} &\hspace{-0.45em}& \textcolor{lightgray}{0} &\hspace{-0.45em}& \textcolor{lightgray}{0} \\
+    \end{bmatrix}$};
+
+  % second approx sign
+  \node [anchor=center] at (9.5, 0) {{\Huge $\approx$ }};
+
+
+  % discretized matrix 2
+  \node [anchor=center] at (12.75, 0) {
+    \large
+    $\begin{bmatrix}
+      \textcolor{lightgray}{0} & \textcolor{lightgray}{0} & \textcolor{lightgray}{0} & \textcolor{lightgray}{0} & \textcolor{lightgray}{0} & \textcolor{lightgray}{0} & \textcolor{lightgray}{0} & \textcolor{lightgray}{0} & \textcolor{lightgray}{0} \\
+      \textcolor{lightgray}{0} & \textcolor{lightgray}{0} & \textcolor{lightgray}{0} & \textcolor{lightgray}{0} & \textcolor{black}{1} & \textcolor{lightgray}{0} & \textcolor{lightgray}{0} & \textcolor{lightgray}{0} & \textcolor{lightgray}{0} \\
+      \textcolor{lightgray}{0} & \textcolor{lightgray}{0} & \textcolor{lightgray}{0} & \textcolor{black}{1} & \textcolor{black}{1} & \textcolor{black}{1} & \textcolor{lightgray}{0} & \textcolor{lightgray}{0} & \textcolor{lightgray}{0} \\
+      \textcolor{lightgray}{0} & \textcolor{lightgray}{0} & \textcolor{black}{1} & \textcolor{black}{1} & \textcolor{black}{1} & \textcolor{black}{1} & \textcolor{black}{1} & \textcolor{lightgray}{0} & \textcolor{lightgray}{0} \\
+      \textcolor{lightgray}{0} & \textcolor{black}{1} & \textcolor{black}{1} & \textcolor{black}{1} & \textcolor{black}{1} & \textcolor{black}{1} & \textcolor{black}{1} & \textcolor{black}{1} & \textcolor{lightgray}{0} \\
+      \textcolor{lightgray}{0} & \textcolor{lightgray}{0} & \textcolor{black}{1} & \textcolor{black}{1} & \textcolor{black}{1} & \textcolor{black}{1} & \textcolor{black}{1} & \textcolor{lightgray}{0} & \textcolor{lightgray}{0} \\
+      \textcolor{lightgray}{0} & \textcolor{lightgray}{0} &
+      \textcolor{lightgray}{0} & \textcolor{black}{1} & \textcolor{black}{1} &
+      \textcolor{black}{1} & \textcolor{lightgray}{0} & \textcolor{lightgray}{0} & \textcolor{lightgray}{0} \\
+      \textcolor{lightgray}{0} & \textcolor{lightgray}{0} &
+      \textcolor{lightgray}{0} & \textcolor{lightgray}{0} & \textcolor{black}{1} &
+      \textcolor{lightgray}{0} & \textcolor{lightgray}{0} & \textcolor{lightgray}{0} & \textcolor{lightgray}{0} \\
+      \textcolor{lightgray}{0} & \textcolor{lightgray}{0} &
+      \textcolor{lightgray}{0} & \textcolor{lightgray}{0} &
+      \textcolor{lightgray}{0} & \textcolor{lightgray}{0} & \textcolor{lightgray}{0} & \textcolor{lightgray}{0} & \textcolor{lightgray}{0} \\
+    \end{bmatrix}$};
+  % \node [anchor=center] at (6, 0) {$abcd$};
+
+
+\end{tikzpicture}
+
+\end{document}
diff --git a/assets/tikz/square.tex b/assets/tikz/square.tex
@@ -0,0 +1,151 @@
+\documentclass[border=0in]{standalone}
+
+\usepackage[T1]{fontenc}
+\usepackage{opensans}
+\usepackage{bm}
+\usepackage{mathrsfs}
+
+\usepackage{tikz}
+\usepackage{pgfplots}
+\pgfplotsset{compat=1.18}
+\usepackage{amsmath}
+\usepackage{amsfonts}
+\usepackage{amssymb}
+\usepackage{xcolor}
+\usepackage{newtxsf}
+
+\usepgfplotslibrary{fillbetween}
+
+\definecolor{c0}{HTML}{f0f9e8}
+\definecolor{c1}{HTML}{bae4bc}
+\definecolor{c2}{HTML}{7bccc4}
+\definecolor{c3}{HTML}{43a2ca}
+\definecolor{c4}{HTML}{0868ac}
+\definecolor{lightgray}{HTML}{d3d3d3}
+\newcommand{\grtr}{\natural}
+
+
+\begin{document}
+
+\begin{tikzpicture}
+
+  % bounding box
+  \draw[black, fill=white, line width=1pt] (-2.2,-2.2) rectangle (2.2,2.2); % Adjust the dimensions as needed
+
+  % Black Square
+  \fill[black] (-1.2,-1.2) rectangle (1.2,1.2); % Adjust the coordinates to position the square
+
+  % first approx sign
+  \node [anchor=center] at (2.97, 0) {{\Huge $\approx$ }};
+
+
+  % discretized matrix
+  \node [anchor=center] at (6.25, 0) {{\huge $\begin{bmatrix}
+          {\color{lightgray} 0} && {\color{lightgray} 0} && {\color{lightgray}
+          0} && {\color{lightgray} 0} && {\color{lightgray} 0} \\
+          {\color{lightgray} 0} && 1 && 1 && 1 && {\color{lightgray} 0} \\
+          {\color{lightgray} 0} && 1 && 1 && 1 && {\color{lightgray} 0} \\
+          {\color{lightgray} 0} && 1 && 1 && 1 && {\color{lightgray} 0} \\
+          {\color{lightgray} 0} && {\color{lightgray} 0} && {\color{lightgray}
+          0} && {\color{lightgray} 0} && {\color{lightgray} 0}
+  \end{bmatrix}$}};
+
+
+  % second approx sign
+  \node [anchor=center] at (9.5, 0) {{\Huge $\approx$ }};
+
+
+  % discretized matrix 2
+  \node [anchor=center] at (12.75, 0) { $\begin{bmatrix}
+  \begin{matrix}
+    \color{lightgray} 0 & \color{lightgray} 0 \\
+    \color{lightgray} 0 & \color{lightgray} 0 \\
+  \end{matrix} & \begin{matrix}
+    \color{lightgray} 0 & \color{lightgray} 0 \\
+    \color{lightgray} 0 & \color{lightgray} 0 \\
+  \end{matrix} & \begin{matrix}
+    \color{lightgray} 0 & \color{lightgray} 0 \\
+    \color{lightgray} 0 & \color{lightgray} 0 \\
+  \end{matrix} & \begin{matrix}
+    \color{lightgray} 0 & \color{lightgray} 0 \\
+    \color{lightgray} 0 & \color{lightgray} 0 \\
+  \end{matrix} & \begin{matrix}
+    \color{lightgray} 0 & \color{lightgray} 0 \\
+    \color{lightgray} 0 & \color{lightgray} 0 \\
+  \end{matrix} \\
+  
+  \begin{matrix}
+    \color{lightgray} 0 & \color{lightgray} 0 \\
+    \color{lightgray} 0 & \color{lightgray} 0 \\
+  \end{matrix} & \begin{matrix}
+    1 & 1 \\
+    1 & 1 \\
+  \end{matrix} & \begin{matrix}
+    1 & 1 \\
+    1 & 1 \\
+  \end{matrix} & \begin{matrix}
+    1 & 1 \\
+    1 & 1 \\
+  \end{matrix} & \begin{matrix}
+    \color{lightgray} 0 & \color{lightgray} 0 \\
+    \color{lightgray} 0 & \color{lightgray} 0 \\
+  \end{matrix} \\
+  
+  \begin{matrix}
+    \color{lightgray} 0 & \color{lightgray} 0 \\
+    \color{lightgray} 0 & \color{lightgray} 0 \\
+  \end{matrix} & \begin{matrix}
+    1 & 1 \\
+    1 & 1 \\
+  \end{matrix} & \begin{matrix}
+    1 & 1 \\
+    1 & 1 \\
+  \end{matrix} & \begin{matrix}
+    1 & 1 \\
+    1 & 1 \\
+  \end{matrix} & \begin{matrix}
+    \color{lightgray} 0 & \color{lightgray} 0 \\
+    \color{lightgray} 0 & \color{lightgray} 0 \\
+  \end{matrix} \\
+  
+  \begin{matrix}
+    \color{lightgray} 0 & \color{lightgray} 0 \\
+    \color{lightgray} 0 & \color{lightgray} 0 \\
+  \end{matrix} & \begin{matrix}
+    1 & 1 \\
+    1 & 1 \\
+  \end{matrix} & \begin{matrix}
+    1 & 1 \\
+    1 & 1 \\
+  \end{matrix} & \begin{matrix}
+    1 & 1 \\
+    1 & 1 \\
+  \end{matrix} & \begin{matrix}
+    \color{lightgray} 0 & \color{lightgray} 0 \\
+    \color{lightgray} 0 & \color{lightgray} 0 \\
+  \end{matrix} \\
+  
+  \begin{matrix}
+    \color{lightgray} 0 & \color{lightgray} 0 \\
+    \color{lightgray} 0 & \color{lightgray} 0 \\
+  \end{matrix} & \begin{matrix}
+    \color{lightgray} 0 & \color{lightgray} 0 \\
+    \color{lightgray} 0 & \color{lightgray} 0 \\
+  \end{matrix} & \begin{matrix}
+    \color{lightgray} 0 & \color{lightgray} 0 \\
+    \color{lightgray} 0 & \color{lightgray} 0 \\
+  \end{matrix} & \begin{matrix}
+    \color{lightgray} 0 & \color{lightgray} 0 \\
+    \color{lightgray} 0 & \color{lightgray} 0 \\
+  \end{matrix} & \begin{matrix}
+    \color{lightgray} 0 & \color{lightgray} 0 \\
+    \color{lightgray} 0 & \color{lightgray} 0 \\
+  \end{matrix}
+\end{bmatrix}$};
+
+  % \node [anchor=center] at (6, 0) {$abcd$};
+
+
+\end{tikzpicture}
+
+\end{document}
diff --git a/assets/tilted_gianini_pca.jpg b/assets/tilted_gianini_pca.jpg
diff --git a/assets/tilted_gianini_pca.png b/assets/tilted_gianini_pca.png
diff --git a/assets/tilted_giannini_norm.jpg b/assets/tilted_giannini_norm.jpg
diff --git a/assets/tilted_giannini_norm.png b/assets/tilted_giannini_norm.png
diff --git a/assets/tilted_giannini_pca.jpg b/assets/tilted_giannini_pca.jpg
diff --git a/assets/tilted_giannini_pca.png b/assets/tilted_giannini_pca.png
diff --git a/assets/tilted_giannini_rgb.jpg b/assets/tilted_giannini_rgb.jpg
diff --git a/assets/tilted_giannini_rgb.png b/assets/tilted_giannini_rgb.png
diff --git a/assets/tilted_kitchen_norm.jpg b/assets/tilted_kitchen_norm.jpg
diff --git a/assets/tilted_kitchen_norm.png b/assets/tilted_kitchen_norm.png
diff --git a/assets/tilted_kitchen_pca.jpg b/assets/tilted_kitchen_pca.jpg
diff --git a/assets/tilted_kitchen_pca.png b/assets/tilted_kitchen_pca.png
diff --git a/assets/tilted_kitchen_rgb.jpg b/assets/tilted_kitchen_rgb.jpg
diff --git a/assets/tilted_kitchen_rgb.png b/assets/tilted_kitchen_rgb.png
diff --git a/assets/tilted_storefront.jpg b/assets/tilted_storefront.jpg
diff --git a/assets/tilted_storefront.png b/assets/tilted_storefront.png
diff --git a/assets/tilted_storefront_norm.jpg b/assets/tilted_storefront_norm.jpg
diff --git a/assets/tilted_storefront_norm.png b/assets/tilted_storefront_norm.png
diff --git a/assets/tilted_storefront_pca.jpg b/assets/tilted_storefront_pca.jpg
diff --git a/assets/tilted_storefront_pca.png b/assets/tilted_storefront_pca.png
diff --git a/assets/tilted_storefront_rgb.jpg b/assets/tilted_storefront_rgb.jpg
diff --git a/assets/tilted_storefront_rgb.png b/assets/tilted_storefront_rgb.png
diff --git a/assets/tilted_stump_norm.jpg b/assets/tilted_stump_norm.jpg
diff --git a/assets/tilted_stump_norm.png b/assets/tilted_stump_norm.png
diff --git a/assets/tilted_stump_pca.jpg b/assets/tilted_stump_pca.jpg
diff --git a/assets/tilted_stump_pca.png b/assets/tilted_stump_pca.png
diff --git a/assets/tilted_stump_rgb.jpg b/assets/tilted_stump_rgb.jpg
diff --git a/assets/tilted_stump_rgb.png b/assets/tilted_stump_rgb.png