Math Forum / Math Software / MATLAB / July 2008

Hello,

I am trying to write a script that will become a function
for calculating the angular error between two lines, where
one line is the reference line.  My script takes three
points that need not be located near the origin and then
translates them so that "start" is located at the origin,
shifting "actual" and "target" with it.

I then want to rotate all three lines around the orgin, with
"start" fixed at (0,0), so that the line defined by start
and actual lies along the positive x-axis, still preserving
the original triangle.  

Now, the line from start-target should lie either above or
below the x-axis.  If it lies above, I want to calculate the
angle between the (start-target) line and the (start-actual)
line and get a NEGATIVE angle.  If the start-target line
lies below, I want to get a POSITIVE angle between the two
lines.  Basically, I want to see if people walked to the
left (negative error) or right (positive error) of a target,
and how many degrees off they were.

I think there is something wrong with my rotation formula in
the (incomplete) if statement at the end of the script.  It
doesn't quite rotate the start-actual line to lie along the
positive x-axis.  It should give me a finalactualx = 3, and
a finalactualy = 0, but it's off by a bit.

Any ideas?  Any suggestions on how to set up a good if
statement would be helpful too...

Thanks,
Jon

=======

clear all
close all

start  = [-1 -1]
actual = [-1 -4]
target = [-3 -2]

% create a translator matrix based on the start location
translator = [start(1)*-1 start(2)*-1];

% translate all the points so that start is at the origin
newstart = start + translator;
newactual = actual + translator;
newtarget = target + translator;

% plot the original points
figure
scatter(start(1),start(2), 'go');
axis ([-15 15 -15 15]);
hold on
scatter (actual(1),actual(2), 'bo');
scatter (target(1),target(2), 'ro');

% plot the translated points
figure
scatter (newstart(1),newstart(2), 'go');
axis ([-15 15 -15 15]);
hold on
scatter (newactual(1), newactual(2),'bo');
scatter (newtarget(1), newtarget(2),'ro');

% rotate the translated points so that the actual point is
on +x-axis
newactualrads = cart2pol(actual(1),actual(2)) % get polar
coord theta (radians) for actual location
newactualdegs = rad2deg(newactualrads)        % convert the
polar coord to a degree value

if newactualdegs < 0
   
   newactualdegs = abs(newactualdegs)
   
   finalactualx = newactual(1) * cosd(newactualdegs) -
newactual(2) * sind(newactualdegs);
   finalactualy = newactual(2) * cosd(newactualdegs) +
newactual(1) * sind(newactualdegs);
   
elseif newactualdegs > 0
   ...
else
   continue
end