2D Euclidean vector rotations
Solution 1
you should remove the vars from the function:
x = x * cs - y * sn; // now x is something different than original vector x
y = x * sn + y * cs;
create new coordinates becomes, to avoid calculation of x before it reaches the second line:
px = x * cs - y * sn;
py = x * sn + y * cs;
Solution 2
Rotating a vector 90 degrees is particularily simple.
(x, y)
rotated 90 degrees around (0, 0)
is (-y, x)
.
If you want to rotate clockwise, you simply do it the other way around, getting (y, -x)
.
Solution 3
Rotate by 90 degress around 0,0:
x' = -y
y' = x
Rotate by 90 degress around px,py:
x' = -(y - py) + px
y' = (x - px) + py
Solution 4
Sounds easier to do with the standard classes:
std::complex<double> vecA(0,1);
std::complex<double> i(0,1); // 90 degrees
std::complex<double> r45(sqrt(2.0),sqrt(2.0));
vecA *= i;
vecA *= r45;
Vector rotation is a subset of complex multiplication. To rotate over an angle alpha
, you multiply by std::complex<double> { cos(alpha), sin(alpha) }
Solution 5
You're calculating the y-part of your new coordinate based on the 'new' x-part of the new coordinate. Basically this means your calculating the new output in terms of the new output...
Try to rewrite in terms of input and output:
vector2<double> multiply( vector2<double> input, double cs, double sn ) {
vector2<double> result;
result.x = input.x * cs - input.y * sn;
result.y = input.x * sn + input.y * cs;
return result;
}
Then you can do this:
vector2<double> input(0,1);
vector2<double> transformed = multiply( input, cs, sn );
Note how choosing proper names for your variables can avoid this problem alltogether!
deceleratedcaviar
Updated on July 09, 2022Comments
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deceleratedcaviar almost 2 years
I have a euclidean vector
a
sitting at the coordinates(0, 1)
. I want to rotatea
by 90 degrees (clockwise) around the origin:(0, 0)
.If I have a proper understanding of how this should work, the resultant (x, y) coordinates after the rotation should be
(1, 0)
. If I were to rotate it by 45 degrees (still clockwise) instead, I would have expected the resultant coordinates to be(0.707, 0.707)
.theta = deg2rad(angle); cs = cos(theta); sn = sin(theta); x = x * cs - y * sn; y = x * sn + y * cs;
Using the above code, with an
angle
value of 90.0 degrees, the resultant coordinates are:(-1, 1)
. And I am so damn confused. The examples seen in the following links represent the same formula shown above surely?What have I done wrong? Or have I misunderstood how a vector is to be rotated?
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deceleratedcaviar over 13 yearsOh god, I needed fresh eyes... again something so obvious... Thanks mate (works a beaut, 2 hours later... haha)
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Caspar Kleijne over 13 yearswhen you execute x = x * cs - y * sn;, it gives a different value to x in y = x * sn + y * cs, so the x will "derail"
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Keith Irwin over 13 years@Daniel: The x in the second statement had had its value changed by the time you used it to calculate the value for y. So, essentially, you calculated the x coordinate for rotating (0,1) (which is -1). Then you stored this in the x coordinate giving (-1,1) and then you calculated the y coordinate for rotating (-1,1) (which should actually be -1, so I'm not sure how you got (-1,1) rather than (-1,-1) ). The correct answer, by the way, isn't (1,0), it's (-1,0) since rotation by positive angles is counterclockwise when view from above.
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Jeff Linahan almost 10 yearsnote that this method does not need to compute sines or cosines
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MSalters almost 10 yearsTBH that's because
r45
is precalculated. -
Jordan Miner almost 8 years+1. To anyone rotating a 2D vector for a computer screen: this answer assumes the y axis is pointing up as in math. If it is points down as on computer screens, then clockwise and counterclockwise are reversed.
(-y, x)
is clockwise and(y, -x)
is counterclockwise. -
CPayne over 6 yearsThis YouTube series will give you a deep an intuitive understanding for rotation/change of basis!