Added matlab code samples.

All of these code samples currently are mis-identified in my repositories. I'm
donating them to the cause.

samples/Matlab/lane_change.m

@@ -0,0 +1,56 @@
+function [x, y, t] = lane_change(start, width, slope, pathLength, speed, num, ...
+                                 type, varargin)
+% Generates the time and coordinates for either a single or double lane change
+% manuever at a particular speed.
+%
+% Parameters
+% ----------
+% start : float
+%   The starting point along the x axis in meters.
+% width : float
+%   The width of the lane deviation.
+% slope : float
+%   The slope of the lane change.
+% pathLength : float
+%   The length of path.
+% speed : float
+%   Speed of travel.
+% num : integer
+%   Number of time steps.
+% type : string
+%   Either 'single' or 'double'. A double lane change return to x = 0.
+% laneLength : float, optional
+%   Length of the lane for a double lane change.
+%
+% Returns
+% -------
+% x : matrix, (num, 1)
+%   The longitudinal path.
+% y : matrix, (num, 1)
+%   The lateral path.
+% t : matrix, (num, 1)
+%   Time.
+
+x = 0:pathLength / num:pathLength;
+x = x';
+t = x / speed;
+
+y = zeros(length(x), 1);
+endOfSlope = width / slope + start;
+slopeInd = find((x > start) & (x <= endOfSlope));
+y(slopeInd) = slope * (x(slopeInd) - start);
+if strcmp(type, 'single')
+    theRest = slopeInd(end) + 1:length(y);
+    y(theRest) = width * ones(length(theRest), 1);
+elseif strcmp(type, 'double');
+    if length(varargin) < 1
+        error('Double lane change needs length of lane.')
+    else
+        laneLength = varargin{1};
+        startOfSlope = start + laneLength - width / slope;
+        lane = find((x > endOfSlope) & (x <= startOfSlope));
+        y(lane) = width * ones(length(lane), 1);
+        downSlope = find((x > startOfSlope) & (x <= start + laneLength));
+        y(downSlope) = slope * (start + laneLength - x(downSlope));
+    end
+end