From cd09f137d1e5df4a5937e4a103f83348a18138bc Mon Sep 17 00:00:00 2001
From: Stefan Sava <stefansava21@gmail.com>
Date: Sat, 20 Oct 2018 17:28:30 +0300
Subject: [PATCH] Implement the deCasteljau Algorithm and plot the Bezier Curve
 using the resulted points

---
 matlab/interpolations/Bezier.m      | 13 ++++++++++++
 matlab/interpolations/deCasteljau.m | 33 +++++++++++++++++++++++++++++
 2 files changed, 46 insertions(+)
 create mode 100644 matlab/interpolations/Bezier.m
 create mode 100644 matlab/interpolations/deCasteljau.m

diff --git a/matlab/interpolations/Bezier.m b/matlab/interpolations/Bezier.m
new file mode 100644
index 0000000..348490f
--- /dev/null
+++ b/matlab/interpolations/Bezier.m
@@ -0,0 +1,13 @@
+function [] = Bezier(v, dim)
+  result = zeros(dim, 2);
+  i = 1;
+  for u = linspace(0,1,dim) 
+    result(i,:) = deCasteljau(v, length(v) - 1, 0, u);
+    i++;
+  endfor
+ 
+ plot (result(1:dim,1), result(1:dim,2), 'r','LineWidth',2)
+ hold
+ plot(v(:,1), v(:,2),'LineWidth',2)
+ title('Bezier Curve for given points')
+endfunction
\ No newline at end of file
diff --git a/matlab/interpolations/deCasteljau.m b/matlab/interpolations/deCasteljau.m
new file mode 100644
index 0000000..7b4318a
--- /dev/null
+++ b/matlab/interpolations/deCasteljau.m
@@ -0,0 +1,33 @@
+## Copyright (C) 2018 Stefan
+## 
+## This program is free software; you can redistribute it and/or modify it
+## under the terms of the GNU General Public License as published by
+## the Free Software Foundation; either version 3 of the License, or
+## (at your option) any later version.
+## 
+## This program is distributed in the hope that it will be useful,
+## but WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+## GNU General Public License for more details.
+## 
+## You should have received a copy of the GNU General Public License
+## along with this program.  If not, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*- 
+## @deftypefn {Function File} {@var{retval} =} Bezier (@var{input1}, @var{input2})
+##
+## @seealso{}
+## @end deftypefn
+
+## Author: Stefan <stefan@Specter>
+## Created: 2018-10-20
+
+#Finding a point on a Bezier Curve: DeCasteljau's Algorithm
+function [result] = deCasteljau (v,i,j,t)
+  if i == 0
+    result = v(j + 1, :);
+    %v(j,0) = x coordinate; v(j,1) = y coordinate;
+  else
+    result = (1 - t) * deCasteljau(v,i - 1,j,t) + t * deCasteljau(v,i - 1, j + 1,t);   
+  endif
+endfunction