Here's the short version: multiply your source vector by a 3d rotation matrix. Zaxo's snippet is nifty, but not quite sufficient as it doesn't do matrix math.

The extra complexity that comes with moving from 2d rotations to 3d rotations is the fact that, in 3d, you don't really have a canonical axis to rotate around. In the x-y plane, when you do a rotation by r radians, you pretty much have to rotate around the z axis. In 3d space, you can rotate around the x, y, or z axis, or around an arbitrary vector (if that gives you problems, think of it as rotating around several canonical axes at once). So you can't easily describe a 3d rotation with a single parameter; you basically need a matrix (or a quaternion, but let's not go there).

Sorry for bumping an old thread.. i hope this saves a bit of someones time: Ry is wrong, it should be:

cos(th) 0 sin(th)
0 1 0
-sin(th) 0 cos(th)
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rgds, Mitja

how do you find the angles è, ö, and ø between two vectors?

To find the angle between the two vectors, you need to normalize them (so they have length of 1 unit) by doing this (v is the vector you want to normalize):

float distance = sqrt(v.x*v.x + v.y*v.y + v.z*v.z);
v.x = v.x/distance;
v.y = v.y/distance;
v.z = v.z/distance;
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Then find the dot product of the two normalized vectors (Va and Vb):

float dotProduct = Va.x*Vb.x + Va.y*Vb.y + Va.z*Vb.z;
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This gives you the cosine of the angle, so simple do:

acos(dotProduct);
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This will give you the angle. I think this post was a bit late :S

If you only need to rotate around the Z axis then it is a simple 2D trig problem. The z co-ordinate is invariant as this is our rotational plane.

sub rotate {
    my ( $x,$y,$z,$angle ) = @_;
    $angle = deg2rad($angle);
    my $x_new = cos($angle)*$x - sin($angle)*$y;
    my $y_new = sin($angle)*$x + cos($angle)*$y;
  return $x_new, $y_new, $z;
}
sub deg2rad { return 3.14159265358979*$_[0]/180 };
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Here is a nice article with a pretty applet Update Corrected error noted by johnnywang

cheers

tachyon

The beauty of concrete! Thanks so much for a perfect example tachyon. Also, a good page about the topic: 2D Math
jtrue

just want to point out it's not quite right. You need to first find the polar angle for the original point (x,y), then add the $angle to that for the new polar angle.

Updated. I'm only refering to the geometric meaning. There is a formula: multiplying by the rotation matrix given by ((cos, -sin),(sin, cos)) (not perl notation!)

Well, the quick-and-dirty way to do it is to scale your x component by cos(t) and your y component by sin(t). You might be happier with a matrix-based solution in the long run, though.

Edit: The math above is, of course, totally bogus. I plead momentary imbecility. johnnywang has the correct solution. D'oh!

What kind of program are you writing, btw?

--
Yours in pedantry,
F o x t r o t U n i f o r m
"Lines of code don't matter as long as I'm not writing them." -- merlyn

# 2 points on a plane
my $x = 2;
my $y = 1;
#yang is the y-angle 0-360 i want to rotate by
my $yang = 45;
#convert yang to radians
$yang = 3.14159265358979*$yang/180;
#rad is the radius of my sphere
my $rad = sqrt($x**2 + $y**2);
my $x = cos($yang)*$rad;
my $y = sin($yang)*$rad;
print "x=$x\ny=$y\n";
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Just a little change, the formula was not correct (as I pointed out in my previous post in this thread)

# 2 points on a plane
my $x = 2;
my $y = 1;
#yang is the y-angle 0-360 i want to rotate by
my $yang = 45;
#convert yang to radians
$yang = 3.14159265358979*$yang/180;
my $xnew = cos($yang)*$x - sin($yang)*y;
my $ynew = sin($yang)*$x + cos($yang)*y;
print "x=$xnew, y=$ynew\n";
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