diff --git a/mr/ub10/A1c/step1.png b/mr/ub10/A1c/step1.png
new file mode 100644
index 0000000..a08c90b
--- /dev/null
+++ b/mr/ub10/A1c/step1.png
Binary files differ
diff --git a/mr/ub10/A1c/step2.png b/mr/ub10/A1c/step2.png
new file mode 100644
index 0000000..a34e364
--- /dev/null
+++ b/mr/ub10/A1c/step2.png
Binary files differ
diff --git a/mr/ub10/A1c/step3.png b/mr/ub10/A1c/step3.png
new file mode 100644
index 0000000..e1360b3
--- /dev/null
+++ b/mr/ub10/A1c/step3.png
Binary files differ
diff --git a/mr/ub10/A1c/step4.png b/mr/ub10/A1c/step4.png
new file mode 100644
index 0000000..41f321c
--- /dev/null
+++ b/mr/ub10/A1c/step4.png
Binary files differ
diff --git a/mr/ub10/A1c/step5.png b/mr/ub10/A1c/step5.png
new file mode 100644
index 0000000..c2c09ac
--- /dev/null
+++ b/mr/ub10/A1c/step5.png
Binary files differ
diff --git a/mr/ub10/A1c/step6.png b/mr/ub10/A1c/step6.png
new file mode 100644
index 0000000..93930c0
--- /dev/null
+++ b/mr/ub10/A1c/step6.png
Binary files differ
diff --git a/mr/ub10/A2/A2.m b/mr/ub10/A2/A2.m
index 857790f..3c4f4de 100644
--- a/mr/ub10/A2/A2.m
+++ b/mr/ub10/A2/A2.m
@@ -1,5 +1,5 @@
 start=[3,7]
-%start= [8,2]
+start= [8,2]
 goal=[8,8]
 
 d=[-1,-1,-1,-1,-1,-1,-1,-1,-1,-1
@@ -11,9 +11,9 @@
     -1,inf,-1,inf,inf,inf,inf,inf,inf,-1
     -1,inf,-1,inf,inf,inf,inf,inf,inf,-1
     -1,-1,-1,-1,-1,-1,-1,-1,-1,-1];
-
+latexmat(d, '%g')
 d(start(1),start(2))= 0;
-d
+d;
 %make d template to show changes
 dvt= d;
 for e= 1:size(d,1)
@@ -23,8 +23,8 @@
         end
     end    
 end    
-dvt
-d
+dvt;
+d;
 changed = true;
 s2= sqrt(2);
 step=-1;
@@ -63,9 +63,9 @@
         end
     end
     forward=0
-    d
-    dv
-    latex(sym(dv))
+    d;
+    dv;
+    latexmat(dv, '%g')
     dv=dvt;
     for y = 2:size(d,1)-1%backward scan
         for x = size(d,2)-1:-1:2
@@ -97,12 +97,12 @@
     end
     backward=0
     step
-    d
-    dv
-    latex(sym(dv))
+    d;
+    dv;
+   latexmat(dv, '%g')
 end
 %plot gradient
-colormap(summer)
+colormap(gray)
 imagesc(d)
 
 %get gradient path.
@@ -129,5 +129,5 @@
        path = cat(1,cp,path);
 end    
 path
-
+latexmat(path, '%g')
 
diff --git a/mr/ub10/A2/DTA.m b/mr/ub10/A2/DTA.m
deleted file mode 100644
index de78d16..0000000
--- a/mr/ub10/A2/DTA.m
+++ /dev/null
@@ -1,82 +0,0 @@
-function [ output_args ] = DTA(map,start,aim)
-%UNTITLED4 Summary of this function goes here
-%   Detailed explanation goes here
-
-d=[-1,-1,-1,-1,-1,-1,-1,-1,-1,-1
-    -1,-1,inf,inf,-1,inf,inf,inf,inf,-1
-    -1,inf,inf,inf,-1,inf,inf,inf,inf,-1
-    -1,inf,inf,inf,-1,-1,inf,inf,inf,-1
-    -1,inf,-1,inf,inf,-1,-1,inf,-1,-1
-    -1,inf,-1,inf,-1,-1,-1,inf,-1,-1
-    -1,inf,-1,inf,inf,inf,inf,inf,inf,-1
-    -1,0,-1,inf,inf,inf,inf,inf,inf,-1
-    -1,-1,-1,-1,-1,-1,-1,-1,-1,-1]
-dvt= d
-
-changed = true;
-s2= sqrt(2);
-step=-1;
-while changed 
-    step=step+1
-    changed= false;
-    for y = size(d,1)-1:-1:2
-        for x = 2:size(d,2)-1
-            x
-            y
-            d(y,x)
-            if(d(y,x) >-1)
-                a=[d(y,x)]
-                if(d(y,x-1) >-1)
-                    a=[a d(y,x-1)+1];
-                end
-                if(d(y,x+1) >-1)
-                    a=[a d(y,x+1)+s2];
-                end
-                if(d(y+1,x)>-1)
-                    a=[a d(y+1,x)+1];
-                end
-                if d(y+1,x-1) >-1
-                    a=[a d(y+1,x-1)+s2];
-                end
-                mi = min(a);
-                if(mi~=d(y,x));
-                    changed = true;
-                end
-                d(y,x) = mi;
-                
-            end
-        end
-    end
-    forward=0
-    d
-    for y = 2:size(d,1)-1
-        for x = size(d,2)-1:-1:2
-            if(d(y,x) >-1)
-                a=[d(y,x)];
-                if(d(y,x+1) >-1)
-                    a=[a d(y,x+1)+1];
-                end
-                if(d(y-1,x-1) >-1)
-                    a=[a d(y-1,x-1)+s2];
-                end
-                if(d(y-1,x)>-1)
-                    a=[a d(y-1,x)+1];
-                end
-                if d(y-1,x+1) >-1
-                    a=[a d(y-1,x+1)+s2];
-                end
-                mi = min(a);
-                if(mi~=d(y,x))
-                    changed = true;
-                end
-                d(y,x) = mi;
-            end
-        end
-    end
-    backward=0
-    step
-    d
-end
-
-end
-
diff --git a/mr/ub10/A2/gradientAb.png b/mr/ub10/A2/gradientAb.png
new file mode 100644
index 0000000..369b082
--- /dev/null
+++ b/mr/ub10/A2/gradientAb.png
Binary files differ
diff --git a/mr/ub10/A2/gradientBb.png b/mr/ub10/A2/gradientBb.png
new file mode 100644
index 0000000..6f88db2
--- /dev/null
+++ b/mr/ub10/A2/gradientBb.png
Binary files differ
diff --git a/mr/ub10/A2/latexmat.m b/mr/ub10/A2/latexmat.m
new file mode 100644
index 0000000..ee02256
--- /dev/null
+++ b/mr/ub10/A2/latexmat.m
@@ -0,0 +1,52 @@
+function str = latexmat(mat, format)
+%LATEXMAT Generate LaTeX code for a matrix.
+%
+%   STR = LATEXMAT(MAT, FORMAT) return the LaTeX code for the matrix MAT, with
+%   the given FORMAT.
+%
+%   See HELP SPRINTF for more details about the FORMAT parameter.
+
+%   Author:      Peter John Acklam
+%   Time-stamp:  2003-07-12 22:14:14 +0200
+%   E-mail:      pjacklam@online.no
+%   URL:         http://home.online.no/~pjacklam
+
+   error(nargchk(2, 2, nargin));
+
+   if ischar(mat)
+      error('First argument can not be a string.');
+   end
+
+   if ~ischar(format)
+      error('Second argument must be a string.');
+   end
+
+   [ r, c ] = size(mat);
+
+   newline = sprintf('\n');
+
+   str = [ '\left[ \begin{array}{' ...
+               char(abs('c')*ones(1,c)) '}' newline ];
+
+   for i = 1:r
+      str = [ str ' ' ];
+      for j = 1:c
+         t = sprintf(format, real(mat(i,j)));
+         if (imag(mat(i,j)) > 0)
+            t = [ t '+' sprintf(format, imag(mat(i,j))) 'i' ];
+         elseif (imag(mat(i,j)) < 0)
+            t = [ t '-' sprintf(format, -imag(mat(i,j))) 'i' ];
+         end
+         str = [ str ' ' t ];
+         if j < c
+            str = [ str ' &' ];
+         else
+            if i < r
+               str = [ str ' \\' newline ];
+            else
+               str = [ str newline ];
+            end
+         end
+      end
+   end
+   str = [ str '\end{array} \right]' newline ];
diff --git a/mr/ub10/assignment10_presets.pdf b/mr/ub10/assignment10_presets.pdf
new file mode 100644
index 0000000..46c7208
--- /dev/null
+++ b/mr/ub10/assignment10_presets.pdf
Binary files differ
diff --git a/mr/ub10/assignment10_presets.tex b/mr/ub10/assignment10_presets.tex
new file mode 100644
index 0000000..05849ba
--- /dev/null
+++ b/mr/ub10/assignment10_presets.tex
@@ -0,0 +1,176 @@
+\documentclass[a4paper,12pt]{article}
+
+\usepackage[english]{babel}     % fuer deutsche Einstellungen
+% \usepackage[german]{babel}
+% \usepackage[T1]{fontenc}
+\usepackage[utf8]{inputenc}   % fuer Umlaute
+\usepackage{amssymb}
+\usepackage{amsfonts}
+\usepackage{epsfig}             % fuer Abbildungen
+%\usepackage{german}
+\usepackage{url}
+\usepackage{mathcomp}
+% 
+\usepackage{amssymb}
+\usepackage{amsmath}
+\usepackage{amsthm}
+\usepackage[autolanguage]{numprint}
+\usepackage{siunitx}
+
+\usepackage{tikz}
+\usepackage{tikz,fullpage}
+\usetikzlibrary{arrows,shapes}
+\usepackage{float}
+
+\usepackage{hyperref}
+\usepackage{enumerate}
+\usepackage{multicol}
+
+\clubpenalty = 10000
+\widowpenalty = 10000 \displaywidowpenalty = 10000
+
+\relpenalty=9999
+\binoppenalty=9999
+
+\newcommand*{\xMax}{24}%
+\newcommand*{\yMax}{24}%
+
+\begin{document}
+
+\newcommand{\presetDta}{
+\begin{tikzpicture}[scale=0.8]\draw[step=1.0cm,color=gray] (0,0) grid (9, 9);
+
+\draw [fill=black!50] (0, 8)rectangle (1, 9);\node at (0.5, 8.5)  {};\draw [fill=black!50] (1, 8)rectangle (2, 9);\node at (1.5, 8.5)  {};\draw [fill=black!50] (2, 8)rectangle (3, 9);\node at (2.5, 8.5)  {};\draw [fill=black!50] (3, 8)rectangle (4, 9);\node at (3.5, 8.5)  {};\draw [fill=black!50] (4, 8)rectangle (5, 9);\node at (4.5, 8.5)  {};\draw [fill=black!50] (5, 8)rectangle (6, 9);\node at (5.5, 8.5)  {};\draw [fill=black!50] (6, 8)rectangle (7, 9);\node at (6.5, 8.5)  {};\draw [fill=black!50] (7, 8)rectangle (8, 9);\node at (7.5, 8.5)  {};\draw [fill=black!50] (8, 8)rectangle (9, 9);\node at (8.5, 8.5)  {};\draw [fill=black!50] (9, 8)rectangle (10, 9);
+
+\draw [fill=black!50] (0, 7)rectangle (1, 8);\node at (0.5, 7.5)  {};\draw [fill=black!50] (1, 7)rectangle (2, 8);\node at (1.5, 7.5)  {};\draw [fill=white] (2, 7)rectangle (3, 8);\node at (2.5, 7.5)  {};\draw [fill=white] (3, 7)rectangle (4, 8);\node at (3.5, 7.5)  {};\draw [fill=black!50] (4, 7)rectangle (5, 8);\node at (4.5, 7.5)  {};\draw [fill=white] (5, 7)rectangle (6, 8);\node at (5.5, 7.5)  {};\draw [fill=white] (6, 7)rectangle (7, 8);\node at (6.5, 7.5)  {};\draw [fill=white] (7, 7)rectangle (8, 8);\node at (7.5, 7.5)  {};\draw [fill=white] (8, 7)rectangle (9, 8);\node at (8.5, 7.5)  {};\draw [fill=black!50] (9, 7)rectangle (10, 8);
+
+\draw [fill=black!50] (0, 6)rectangle (1, 7);\node at (0.5, 6.5)  {};\draw [fill=white] (1, 6)rectangle (2, 7);\node at (1.5, 6.5)  {};\draw [fill=white] (2, 6)rectangle (3, 7);\node at (2.5, 6.5)  {};\draw [fill=white] (3, 6)rectangle (4, 7);\node at (3.5, 6.5)  {};\draw [fill=black!50] (4, 6)rectangle (5, 7);\node at (4.5, 6.5)  {};\draw [fill=white] (5, 6)rectangle (6, 7);\node at (5.5, 6.5)  {};\draw [fill=yellow] (6, 6)rectangle (7, 7);\node at (6.5, 6.5)  {$B$};\draw [fill=white] (7, 6)rectangle (8, 7);\node at (7.5, 6.5)  {};\draw [fill=white] (8, 6)rectangle (9, 7);\node at (8.5, 6.5)  {};\draw [fill=black!50] (9, 6)rectangle (10, 7);
+
+\draw [fill=black!50] (0, 5)rectangle (1, 6);\node at (0.5, 5.5)  {};\draw [fill=white] (1, 5)rectangle (2, 6);\node at (1.5, 5.5)  {};\draw [fill=white] (2, 5)rectangle (3, 6);\node at (2.5, 5.5)  {};\draw [fill=white] (3, 5)rectangle (4, 6);\node at (3.5, 5.5)  {};\draw [fill=black!50] (4, 5)rectangle (5, 6);\node at (4.5, 5.5)  {};\draw [fill=black!50] (5, 5)rectangle (6, 6);\node at (5.5, 5.5)  {};\draw [fill=white] (6, 5)rectangle (7, 6);\node at (6.5, 5.5)  {};\draw [fill=white] (7, 5)rectangle (8, 6);\node at (7.5, 5.5)  {};\draw [fill=white] (8, 5)rectangle (9, 6);\node at (8.5, 5.5)  {};\draw [fill=black!50] (9, 5)rectangle (10, 6);
+
+\draw [fill=black!50] (0, 4)rectangle (1, 5);\node at (0.5, 4.5)  {};\draw [fill=white] (1, 4)rectangle (2, 5);\node at (1.5, 4.5)  {};\draw [fill=black!50] (2, 4)rectangle (3, 5);\node at (2.5, 4.5)  {};\draw [fill=white] (3, 4)rectangle (4, 5);\node at (3.5, 4.5)  {};\draw [fill=white] (4, 4)rectangle (5, 5);\node at (4.5, 4.5)  {};\draw [fill=black!50] (5, 4)rectangle (6, 5);\node at (5.5, 4.5)  {};\draw [fill=black!50] (6, 4)rectangle (7, 5);\node at (6.5, 4.5)  {};\draw [fill=white] (7, 4)rectangle (8, 5);\node at (7.5, 4.5)  {};\draw [fill=black!50] (8, 4)rectangle (9, 5);\node at (8.5, 4.5)  {};\draw [fill=black!50] (9, 4)rectangle (10, 5);
+
+\draw [fill=black!50] (0, 3)rectangle (1, 4);\node at (0.5, 3.5)  {};\draw [fill=white] (1, 3)rectangle (2, 4);\node at (1.5, 3.5)  {};\draw [fill=black!50] (2, 3)rectangle (3, 4);\node at (2.5, 3.5)  {};\draw [fill=white] (3, 3)rectangle (4, 4);\node at (3.5, 3.5)  {};\draw [fill=black!50] (4, 3)rectangle (5, 4);\node at (4.5, 3.5)  {};\draw [fill=black!50] (5, 3)rectangle (6, 4);\node at (5.5, 3.5)  {};\draw [fill=black!50] (6, 3)rectangle (7, 4);\node at (6.5, 3.5)  {};\draw [fill=white] (7, 3)rectangle (8, 4);\node at (7.5, 3.5)  {};\draw [fill=black!50] (8, 3)rectangle (9, 4);\node at (8.5, 3.5)  {};\draw [fill=black!50] (9, 3)rectangle (10, 4);
+
+\draw [fill=black!50] (0, 2)rectangle (1, 3);\node at (0.5, 2.5)  {};\draw [fill=white] (1, 2)rectangle (2, 3);\node at (1.5, 2.5)  {};\draw [fill=black!50] (2, 2)rectangle (3, 3);\node at (2.5, 2.5)  {};\draw [fill=white] (3, 2)rectangle (4, 3);\node at (3.5, 2.5)  {};\draw [fill=white] (4, 2)rectangle (5, 3);\node at (4.5, 2.5)  {};\draw [fill=white] (5, 2)rectangle (6, 3);\node at (5.5, 2.5)  {};\draw [fill=white] (6, 2)rectangle (7, 3);\node at (6.5, 2.5)  {};\draw [fill=white] (7, 2)rectangle (8, 3);\node at (7.5, 2.5)  {};\draw [fill=white] (8, 2)rectangle (9, 3);\node at (8.5, 2.5)  {};\draw [fill=black!50] (9, 2)rectangle (10, 3);
+
+\draw [fill=black!50] (0, 1)rectangle (1, 2);\node at (0.5, 1.5)  {};\draw [fill=yellow] (1, 1)rectangle (2, 2);\node at (1.5, 1.5)  {$A$};\draw [fill=black!50] (2, 1)rectangle (3, 2);\node at (2.5, 1.5)  {};\draw [fill=white] (3, 1)rectangle (4, 2);\node at (3.5, 1.5)  {};\draw [fill=white] (4, 1)rectangle (5, 2);\node at (4.5, 1.5)  {};\draw [fill=white] (5, 1)rectangle (6, 2);\node at (5.5, 1.5)  {};\draw [fill=white] (6, 1)rectangle (7, 2);\node at (6.5, 1.5)  {};\draw [fill=yellow] (7, 1)rectangle (8, 2);\node at (7.5, 1.5)  {$G$};\draw [fill=white] (8, 1)rectangle (9, 2);\node at (8.5, 1.5)  {};\draw [fill=black!50] (9, 1)rectangle (10, 2);
+
+\draw [fill=black!50] (0, 0)rectangle (1, 1);\node at (0.5, 0.5)  {};\draw [fill=black!50] (1, 0)rectangle (2, 1);\node at (1.5, 0.5)  {};\draw [fill=black!50] (2, 0)rectangle (3, 1);\node at (2.5, 0.5)  {};\draw [fill=black!50] (3, 0)rectangle (4, 1);\node at (3.5, 0.5)  {};\draw [fill=black!50] (4, 0)rectangle (5, 1);\node at (4.5, 0.5)  {};\draw [fill=black!50] (5, 0)rectangle (6, 1);\node at (5.5, 0.5)  {};\draw [fill=black!50] (6, 0)rectangle (7, 1);\node at (6.5, 0.5)  {};\draw [fill=black!50] (7, 0)rectangle (8, 1);\node at (7.5, 0.5)  {};\draw [fill=black!50] (8, 0)rectangle (9, 1);\node at (8.5, 0.5)  {};\draw [fill=black!50] (9, 0)rectangle (10, 1);
+\end{tikzpicture}
+
+\vspace{0.25cm}
+}
+
+\newcommand{\presetOone}{
+\renewcommand*{\xMax}{23}%
+\renewcommand*{\yMax}{23}%
+\begin{tikzpicture}[scale=0.3, axis/.style={very thick, ->, >=stealth'}]
+    % grid
+    \draw[very thin, gray!50] (0,0) grid (\xMax, \yMax);
+    
+    % axis
+    \draw[axis] 
+      (0,0) -> coordinate (x axis mid) (\xMax,0);
+    \draw[axis] 
+      (0,0) -> coordinate (y axis mid) (0,\yMax);
+
+    % labels
+    \foreach \i in {0,5,...,\xMax} {
+      \draw [very thick] (\i cm,5pt) -- (\i cm,-5pt) node [below] at (\i,0) {\i};
+    }
+    \foreach \i in {0,5,...,\yMax} {
+      \draw [very thick] (5pt,\i cm) -- (-5pt,\i cm) node [left] at (0,\i) {\i};
+    }
+
+    % O1
+    \draw[thick] (4, 3) -- (7, 12) -- (20, 9) -- (15, 19) -- (2, 20) -- cycle;
+\end{tikzpicture}
+}
+
+
+\newcommand{\presetOtwo}{
+\renewcommand*{\xMax}{51}%
+\renewcommand*{\yMax}{26}%
+\begin{tikzpicture}[scale=0.25, axis/.style={very thick, ->, >=stealth'}]
+    % grid
+    \draw[very thin, gray!50] (21,0) grid (\xMax, \yMax);
+    
+    % labels
+    \foreach \i in {25,30,...,\xMax} {
+      \draw [very thick] (\i cm,-0.25) -- (\i cm,0.25) node [below] at (\i,0) {\i};
+    }
+    \foreach \i in {5,10,...,\yMax} {
+      \draw [very thick] (20.75,\i cm) -- (21.25,\i cm) node [left] at (21,\i) {\i};
+    }
+    
+    % O2
+    \draw[thick] (27, 1) --
+					 (35, 1) --
+					 (38, 4) -- 
+					 (34, 9) --
+					 (44, 8) --
+					 (50, 19) --
+					 (44, 25) --
+					 (24, 25) --
+					 (30, 18) --
+					 (24, 10) -- cycle;
+					 
+					 
+\end{tikzpicture}
+\vspace{0.25cm}
+}
+\begin{multicols}{2}
+
+\presetDta
+
+\presetDta
+
+\presetDta
+
+\presetDta
+
+\presetDta
+
+\presetDta
+
+\end{multicols}
+
+\clearpage 
+
+\begin{multicols}{2}
+
+\presetOone
+
+\presetOone
+
+\presetOone
+
+\presetOone
+
+\presetOone
+
+\presetOone
+
+\end{multicols}
+
+
+\clearpage 
+
+\begin{multicols}{2}
+
+\presetOtwo
+
+\presetOtwo
+
+\presetOtwo
+
+\presetOtwo
+
+\presetOtwo
+
+\presetOtwo
+
+\end{multicols}
+
+\end{document}
diff --git a/mr/ub10/mr10.pdf b/mr/ub10/mr10.pdf
index 1f740d7..f2a3a02 100644
--- a/mr/ub10/mr10.pdf
+++ b/mr/ub10/mr10.pdf
Binary files differ
diff --git a/mr/ub10/mr10.tex b/mr/ub10/mr10.tex
index 60f0118..53adf0c 100644
--- a/mr/ub10/mr10.tex
+++ b/mr/ub10/mr10.tex
@@ -91,10 +91,213 @@
         \begin{enumerate}[(a)]
             \item done?
             \item done?
-            \item done?
+            \item ~
+
+\includegraphics[width=0.48\textwidth]{A1c/step1}
+\includegraphics[width=0.48\textwidth]{A1c/step2}
+\includegraphics[width=0.48\textwidth]{A1c/step3}
+\includegraphics[width=0.48\textwidth]{A1c/step4}
+\includegraphics[width=0.48\textwidth]{A1c/step5}
+\includegraphics[width=0.48\textwidth]{A1c/step6}
+
+
             \item Sklansky's algorithm runs in linear time, i.e. $\mathcal{O}(n)$
             \item QuickHull has a worst case runningtime of $\mathcal{O}(n^2)$, when there are no points that can be ignored. A geometric example of the worst case is a cylindric obstacle because a circle doesn't allow any point to be ignored because the drawn line is always nearer to the circles center then a point on the circle.
         \end{enumerate}
+     \Aufgabe{Path Planning by dynamic programming}{10}   
+	\begin{enumerate}[(a)]
+		\item  $\left[ \begin{array}{cccccccccc}
+		-1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\
+		-1 & -1 & Inf & Inf & -1 & Inf & Inf & Inf & Inf & -1 \\
+		-1 & Inf & Inf & Inf & -1 & Inf & Inf & Inf & Inf & -1 \\
+		-1 & Inf & Inf & Inf & -1 & -1 & Inf & Inf & Inf & -1 \\
+		-1 & Inf & -1 & Inf & Inf & -1 & -1 & Inf & -1 & -1 \\
+		-1 & Inf & -1 & Inf & -1 & -1 & -1 & Inf & -1 & -1 \\
+		-1 & Inf & -1 & Inf & Inf & Inf & Inf & Inf & Inf & -1 \\
+		-1 & Inf & -1 & Inf & Inf & Inf & Inf & Inf & Inf & -1 \\
+		-1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1
+		\end{array} \right]$
+		
+		\item Point A:\\
+		forward1:\\
+		$\left[ \begin{array}{cccccccccc}
+			-1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\
+			-1 & -1 & 6.41421 & 6.82843 & -1 & - & - & - & - & -1 \\
+			-1 & 5 & 5.41421 & 5.82843 & occ & - & - & - & - & occ \\
+			occ & 4 & 4.41421 & 5.41421 & occ & occ & - & - & - & occ \\
+			occ & 3 & occ & - & - & occ & occ & - & occ & occ \\
+			occ & 2 & occ & - & occ & occ & occ & - & occ & occ \\
+			occ & 1 & occ & - & - & - & - & - & - & occ \\
+			occ & - & occ & - & - & - & - & - & - & occ \\
+			occ & occ & occ & occ & occ & occ & occ & occ & occ & occ
+		\end{array} \right]$\\
+		backward1:\\
+		$\left[ \begin{array}{cccccccccc}
+		occ & occ & occ & occ & occ & occ & occ & occ & occ & occ \\
+		occ & occ & - & - & occ & - & - & - & - & occ \\
+		occ & - & - & - & occ & - & - & - & - & occ \\
+		occ & - & - & - & occ & occ & - & - & - & occ \\
+		occ & - & occ & 5.82843 & 6.82843 & occ & occ & - & occ & occ \\
+		occ & - & occ & 6.82843 & occ & occ & occ & - & occ & occ \\
+		occ & - & occ & 7.82843 & 8.24264 & - & - & - & - & occ \\
+		occ & - & occ & 8.82843 & 9.24264 & 9.65685 & - & - & - & occ \\
+		occ & occ & occ & occ & occ & occ & occ & occ & occ & occ
+		\end{array} \right]$\\
+		forward2:\\
+		$\left[ \begin{array}{cccccccccc}
+		occ & occ & occ & occ & occ & occ & occ & occ & occ & occ \\
+		occ & occ & - & - & occ & - & - & 15.6569 & 16.0711 & occ \\
+		occ & - & - & - & occ & - & - & 14.6569 & 15.0711 & occ \\
+		occ & - & - & - & occ & occ & - & 13.6569 & 14.0711 & occ \\
+		occ & - & occ & - & - & occ & occ & 12.6569 & occ & occ \\
+		occ & - & occ & - & occ & occ & occ & 11.6569 & occ & occ \\
+		occ & - & occ & - & - & 9.24264 & 10.2426 & 11.2426 & 12.2426 & occ \\
+		occ & - & occ & - & - & - & 10.6569 & 11.6569 & 12.6569 & occ \\
+		occ & occ & occ & occ & occ & occ & occ & occ & occ & occ
+		\end{array} \right]$\\
+		backward2:\\
+		$\left[ \begin{array}{cccccccccc}
+		occ & occ & occ & occ & occ & occ & occ & occ & occ & occ \\
+		occ & occ & - & - & occ & 17.6569 & 16.6569 & - & - & occ \\
+		occ & - & - & - & occ & 16.6569 & 15.6569 & - & - & occ \\
+		occ & - & - & - & occ & occ & 14.6569 & - & - & occ \\
+		occ & - & occ & - & - & occ & occ & - & occ & occ \\
+		occ & - & occ & - & occ & occ & occ & - & occ & occ \\
+		occ & - & occ & - & - & - & - & - & - & occ \\
+		occ & - & occ & - & - & - & - & - & - & occ \\
+		occ & occ & occ & occ & occ & occ & occ & occ & occ & occ
+		\end{array} \right]$\\
+		forward3\\
+		$\left[ \begin{array}{cccccccccc}
+		occ & occ & occ & occ & occ & occ & occ & occ & occ & occ \\
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+		occ & - & - & - & occ & occ & - & - & - & occ \\
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+		occ & - & occ & - & occ & occ & occ & - & occ & occ \\
+		occ & - & occ & - & - & - & - & - & - & occ \\
+		occ & - & occ & - & - & - & - & - & - & occ \\
+		occ & occ & occ & occ & occ & occ & occ & occ & occ & occ
+		\end{array} \right]$\\
+		backward3\\
+		$\left[ \begin{array}{cccccccccc}
+			occ & occ & occ & occ & occ & occ & occ & occ & occ & occ \\
+			occ & occ & - & - & occ & - & - & - & - & occ \\
+			occ & - & - & - & occ & - & - & - & - & occ \\
+			occ & - & - & - & occ & occ & - & - & - & occ \\
+			occ & - & occ & - & - & occ & occ & - & occ & occ \\
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+			occ & - & occ & - & - & - & - & - & - & occ \\
+			occ & - & occ & - & - & - & - & - & - & occ \\
+			occ & occ & occ & occ & occ & occ & occ & occ & occ & occ
+		\end{array} \right]$		 
+		 \\
+		 Point B:\\
+		 forward1:\\
+		 $\left[ \begin{array}{cccccccccc}
+		 occ & occ & occ & occ & occ & occ & occ & occ & occ & occ \\
+		 occ & occ & - & - & occ & 2.41421 & 1 & 1.41421 & 2.41421 & occ \\
+		 occ & - & - & - & occ & 1.41421 & - & 1 & 2 & occ \\
+		 occ & - & - & - & occ & occ & - & - & - & occ \\
+		 occ & - & occ & - & - & occ & occ & - & occ & occ \\
+		 occ & - & occ & - & occ & occ & occ & - & occ & occ \\
+		 occ & - & occ & - & - & - & - & - & - & occ \\
+		 occ & - & occ & - & - & - & - & - & - & occ \\
+		 occ & occ & occ & occ & occ & occ & occ & occ & occ & occ
+		 \end{array} \right]$\\
+		 backward1:\\
+		 $\left[ \begin{array}{cccccccccc}
+		 occ & occ & occ & occ & occ & occ & occ & occ & occ & occ \\
+		 occ & occ & - & - & occ & 2 & - & - & - & occ \\
+		 occ & - & - & - & occ & 1 & - & - & - & occ \\
+		 occ & - & - & - & occ & occ & 1 & 1.41421 & 2.41421 & occ \\
+		 occ & - & occ & - & - & occ & occ & 2.41421 & occ & occ \\
+		 occ & - & occ & - & occ & occ & occ & 3.41421 & occ & occ \\
+		 occ & - & occ & 7.82843 & 6.82843 & 5.82843 & 4.82843 & 4.41421 & 4.82843 & occ \\
+		 occ & - & occ & 8.24264 & 7.24264 & 6.24264 & 5.82843 & 5.41421 & 5.82843 & occ \\
+		 occ & occ & occ & occ & occ & occ & occ & occ & occ & occ
+		 \end{array} \right]$\\
+		 forward2:\\
+		 $\left[ \begin{array}{cccccccccc}
+		 occ & occ & occ & occ & occ & occ & occ & occ & occ & occ \\
+		 occ & occ & - & 12.8284 & occ & - & - & - & - & occ \\
+		 occ & - & - & 11.8284 & occ & - & - & - & - & occ \\
+		 occ & - & - & 10.8284 & occ & occ & - & - & - & occ \\
+		 occ & - & occ & 9.82843 & 10.2426 & occ & occ & - & occ & occ \\
+		 occ & - & occ & 8.82843 & occ & occ & occ & - & occ & occ \\
+		 occ & - & occ & - & - & - & - & - & - & occ \\
+		 occ & - & occ & - & - & - & - & - & - & occ \\
+		 occ & occ & occ & occ & occ & occ & occ & occ & occ & occ
+		 \end{array} \right]$\\
+		 backward2:\\
+		 $\left[ \begin{array}{cccccccccc}
+		 occ & occ & occ & occ & occ & occ & occ & occ & occ & occ \\
+		 occ & occ & 13.8284 & - & occ & - & - & - & - & occ \\
+		 occ & 13.8284 & 12.8284 & - & occ & - & - & - & - & occ \\
+		 occ & 12.8284 & 11.8284 & - & occ & occ & - & - & - & occ \\
+		 occ & 13.2426 & occ & - & - & occ & occ & - & occ & occ \\
+		 occ & 14.2426 & occ & - & occ & occ & occ & - & occ & occ \\
+		 occ & 15.2426 & occ & - & - & - & - & - & - & occ \\
+		 occ & 16.2426 & occ & - & - & - & - & - & - & occ \\
+		 occ & occ & occ & occ & occ & occ & occ & occ & occ & occ
+		 \end{array} \right]$\\
+		 
+		 forward3\\
+		 $\left[ \begin{array}{cccccccccc}
+		 occ & occ & occ & occ & occ & occ & occ & occ & occ & occ \\
+		 occ & occ & - & - & occ & - & - & - & - & occ \\
+		 occ & - & - & - & occ & - & - & - & - & occ \\
+		 occ & - & - & - & occ & occ & - & - & - & occ \\
+		 occ & - & occ & - & - & occ & occ & - & occ & occ \\
+		 occ & - & occ & - & occ & occ & occ & - & occ & occ \\
+		 occ & - & occ & - & - & - & - & - & - & occ \\
+		 occ & - & occ & - & - & - & - & - & - & occ \\
+		 occ & occ & occ & occ & occ & occ & occ & occ & occ & occ
+		 \end{array} \right]$\\
+		 backward3\\
+		$\left[ \begin{array}{cccccccccc}
+		occ & occ & occ & occ & occ & occ & occ & occ & occ & occ \\
+		occ & occ & - & - & occ & - & - & - & - & occ \\
+		occ & - & - & - & occ & - & - & - & - & occ \\
+		occ & - & - & - & occ & occ & - & - & - & occ \\
+		occ & - & occ & - & - & occ & occ & - & occ & occ \\
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+		occ & - & occ & - & - & - & - & - & - & occ \\
+		occ & - & occ & - & - & - & - & - & - & occ \\
+		occ & occ & occ & occ & occ & occ & occ & occ & occ & occ
+		\end{array} \right]$
+		
+\pagebreak	
+	\item ~ 
+Point A:\\
+\includegraphics[width=0.7\linewidth]{A2/gradientAb}\\
+Point B:\\
+\includegraphics[width=0.7\linewidth]{A2/gradientBb}
+\pagebreak
+\item path a:\\
+$\left[ \begin{array}{cc}
+8 & 2 \\
+7 & 2 \\
+6 & 2 \\
+5 & 2 \\
+4 & 3 \\
+5 & 4 \\
+6 & 4 \\
+7 & 5 \\
+7 & 6 \\
+7 & 7 \\
+8 & 8
+\end{array} \right]$\\
+path b:\\
+$\left[ \begin{array}{cc}
+	3 & 7 \\
+	4 & 7 \\
+	5 & 8 \\
+	6 & 8 \\
+	7 & 8 \\
+	8 & 8
+\end{array} \right]$
 
+\end{enumerate}	
 \end{document}