Question

I need to write a small program which to test whether a line (position vector) does strictly clockwise or CCLW movement. I tried to use atand to find the angle, but it could jump from negative to positive value when it pass thought 90 deg, it will have the same thing if I use slope method.

However, the motion does not have to cut at 90 deg, it could jump from 89 to 91. Then a big slope jump could happen. Any idea please

Thanks

Answer 1

One way to do this would be to calculate the cross-product of consecutive position vectors. If all the cross-products are positive then the line moved with a strictly clockwise. Similarly, if they are all negative then the line moved counter-clockwise. If the signs are mixed then the line did not move strictly in one angular direction:

function checkRotation(pos)

pos(:,3) = 0;
pos = unique(sum(sign(cross(pos(1:end-1,:), pos(2:end,:))), 2));
if isequal(pos, 1)
    disp('Rotation was counter-clockwise');
elseif isequal(pos, -1)
    disp('Rotation was clockwise');
else
    disp('No strict rotation direction');
end

Create some random position vectors on -10<=x<=10 and -10<=y<=10 and test rotation:

>> pos = 20 * rand([10, 2]) - 10

pos =

         -8.28968405819912          9.26177078573826
         -4.75035530603335         0.936114374779359
          6.02029245539477         0.422716616080031
         -9.41559444875707         -5.36811226582952
          8.57708278956089        -0.222045121596661
          4.60661725710906          2.48120176347379
        -0.227820523928417          3.58271081731495
          1.57050122046878         -2.08969568662814
         -5.25432840456957         -2.65126702911047
        -0.823023436401378          9.75964006323266

>> checkRotation(pos)
No strict rotation direction

Create position vectors that move only CCW and test:

>> theta = 0:15:180;
>> pos = [cosd(theta)' sind(theta)'];
>> checkRotation(pos)
Rotation was counter-clockwise

and similarly for CW rotation:

>> theta = 180:-15:0;
>> pos = [cosd(theta)' sind(theta)'];
>> checkRotation(pos)
Rotation was clockwise

Note that the success of rotation detection is limited by your sampling rate. If the line rotates counter-clockwise by more than 180 degrees in successive samplings of the line position, it is indistinguishable from a rotation less than 180 degrees in the clockwise direction. This is an example of aliasing.