I'm not quite sure if my question has been asked before in general terms. Whenever it has been asked, it is in terms of a specific language.
Let's say I have an objects rotation represented as a quaternion q = {w, x, y, z}.
I want to rotate this quaternion A radians around the y axis.
Since quaternions are already a measure of rotation, should I just add (or multiply) another quaternion representing the desired rotation to q? How would one go about this?
Thanks for your help.
You are right
Since quaternions are already a measure of rotation, should I just add (or multiply) another quaternion representing the desired rotation to q?
You should multiply current rotation quaternion with desired rotation quaternion. Depending on, local frame "Y" or global frame "Y" you should multiply from left to right or right to left.
Related
For a game i'm trying to calculate the angle between where i'm looking at and the position of another object in the scene. I got the angle by using the following code:
Vec3 out_sub;
Math.Subtract(pEnt->vOrigin, pLocalEnt->vOrigin, out_sub);
float angle = Math.DotProductAcos(out_sub, vec3LookAt);
This code does give me the angle between where im looking at and an object in the scene. But there's a small problem.
When i don't directly look at the object but slightly to the left of it, then it says i have to rotate 10 degrees in order to directly look at the object. Which is perfectly correct.
But, when i look slightly to the right of the object, it also says i have to rotate 10 degrees in order to look directly to the object.
The problem here is, the i have no way to tell which way to rotate to. I only know its 10 degrees. But do i have to rotate to the left or right? That's what i need to find out.
How can i figure that out?
I feel the need to elaborate on Ignacio's answer...
In general, your question is not well-founded, since "turn left" and "turn right" only have meaning after you decide which way is "up".
The cross product of two vectors is a vector that tells you which way is "up". That is, A x B is the "up" that you have to use if you want to turn left to get from A to B. (And the magnitude of the cross product tells you how far you have to turn, more or less...)
For 3D vectors, the cross product has a z component of x1 * y2 - y1 * x2. If the vectors themselves are 2D (i.e., have zero z components), then this is the only thing you have to compute to get the cross product; the x and y components of the cross product are zero. So in 2D, if this number is positive, then "up" is the positive z direction and you have to turn left. If this number is negative, then "up" is the negative z direction and you have to turn left while upside-down; i.e., turn right.
You also need to perform the cross product on the vectors. You can then get the direction of the rotate by the direction of the resultant vector.
I know there are plenty of questions about 3d rotation that have been answered here but all of them seem to deal with rotational matrices and quaternions in OpenGL (and I don't really care if I get gimbal lock). I need to get 3d coordinates EX:(x,y,z) of a point that always must be the same distance, I'll call it "d" for now, from the origin. The only information I have as input is the deltax and deltay of the mouse across the screen. So far here is what I have tried:
First:
thetaxz+=(omousex-mouseX)/( width );
thetaxy+=(omousey-mouseY)/( height);
(thetaxy is the angle in radians on the x,y axis and thetaxz on the x,z axis)
(I limit both angles so that if they are less than or equal to 0 they equal 2*PI)
Second:
pointX=cos(thetaxz)*d;
pointY=sin(thetaxy)*d;
(pointX is the point's x coordinate and pointY is the y)
Third:
if(thetaxz)<PI){
pointZ=sqrt(sq(d)-sq(eyeX/d)-sq(eyeY/d));
}else{
pointZ=-sqrt(abs(sq(d)-sq(eyeX/d)-sq(eyeY/d)));
}
(sq() is a function that squares and abs() is an absolute value function)
(pointZ should be the point's z coordinate and it is except at crossing between the positive z hemisphere and negative z hemisphere. As it approaches the edge the point gets stretched further than the distance that it is always supposed to be at in the x and y and seemingly randomly around 0.1-0.2 radians of thetaxz the z coordinate becomes NAN or undefined)
I have thought about this for awhile, and truthfully I'm having difficulty warping my head around the concept of quaternions and rotational matrices however if you can show me how to use them to generate actual coordinates I would be glad to learn. I would still prefer it if I could just use some trigonometry in a few axis. Thank you in advance for any help and if you need more information please just ask.
Hint/last minute idea: I think it may have something to do with the z position affecting the x and y positions back but I am not sure.
EDIT: I drew a diagram:
If you truly want any success in this, you're going to have to bite the bullet and learn about rotation matrices and / or quaternion rotations. There may be other ways to do what you want, but rotation matrices and quaternion rotations are used simply because they are widely understood and among the simplest means of expressing and applying rotations to vectors. Any other representation somebody can come up with will probably be a more complex reformulation of one or both of these. In fact it can be shown rotation is a linear transformation and so can be expressed as a matrix. Quaternion rotations are just a simplified means of rotating vectors in 3D, and therefore have equivalent matrix representations.
That said, it sounds like you're interested in grabbing an object in your scene with a mouse click and rotating in a natural sort of way. If that's the case, you should look at the ArcBall method (there are numerous examples you may want to look over). This still requires you know something of quaternions. You will also find that an at least minimal comprehension of the basic aspects of linear algebra will be helpful.
Update: Based on your diagram and the comments it contains, it looks like all you are really trying to do is to convert Spherical Coordinates to Cartesian Coordinates. As long as we agree on the the notation, that's easy. Let θ be the angle you're calling XY, that is, the angle between the X axis rotated about the Z axis; this is called the azimuth angle and will be in the range [0, 2π) radians or [0°, 360°). Let Φ be an angle between the XY plane and your vector; this is called the elevation angle and will be in the range [-π/2, +π/2] or [-90°, +90°] and it corresponds to the angle you're calling the XZ angle (rotation in the XZ plane about the Y axis). There are other conventions, so make sure you're consistent. Anyway, the conversion is simply:
x = d∙cos(Φ)∙cos(θ)
y = d∙cos(Φ)∙sin(θ)
z = d∙sin(Φ)
I'm currently working with libQGLViewer, and I'm receiving a stream of data from my sensor, holding azimuth, elevation and roll values, 3 euler angles.
The problem can be considered as the camera representing an aeroplane, and the changes in azimuth, elevation and roll the plane moving.
I need a general set of transformation matrices to transform the camera point and the up vector to represent this, but I'm unsure how to calculate them since the axis to rotate about changes after each rotation ( I think? ).
Either that, or just someway to pass the azimuth, elevation, roll values to the camera and have some function do it for me? I understand that cameraPosition.setOrientation(Quaterion something) might work, but I couldn't really understand it. Any ideas?
For example you could just take the three matrices for rotation about the coordinate axes, plug in your angles respectively, and multiply these three matrices together to get the final roation matrix (but use the correct multiplication order).
You can also just compute a quaternion from the euler angles. Look here for ideas. Just keep in mind that you always have to use the correct order of the euler angles (whatever your three values mean), perhaps with some experimentation (those different euler conventions always make me crazy).
EDIT: In response to your comment: This is accounted by the order of rotations. The matrices applied like v' = XYZv correspond to roation about z, unchanged y and then unchanged x, which is equal to x, y' and then z''. So you have to keep an eye on the axes (what your words like azimuth mean) and the order in which you rotate about these axes.
By using left hand rule, I rotate one object left and right using y axis, and rotate up/down using x axis.
After first object is rotated to the right, the up/down rotation should be using z axis.
However, when I try to rotate using z axis, after the first rotation, it has the same effect when I rotate using y axis.
Anyone has any ideas?
Thanks
The proper order of rotations in order to keep everything straight is roll, pitch, yaw. That is, rotation around the X axis, rotation around the Y axis, rotation around the Z axis.
Not sure what your question is, but if you're asking why this happens, the answer is that rotations are not commutative. That is, a rotation of theta about axis A followed by a rotation of phi around axis B is not the same as rotation of phi around axis B followed by a rotation of theta around axis A.
If you're asking why a sequence of operations that seems okay when you visualise it fails to work in code, be sure you're using a right-handed coordinate system. Also, it might be helpful to work through your various rotation matrices for the x, y and z axes using the unit vector (1,0,0) - in fact, if you do it on paper you'll get a better intuition for what's happening.
Thanks for all the answers:
Sorry I didn't state the problem clearly.
That's the typical gimbal lock problem.
and my solution is to use quaternion rotation
I'm trying to figure out some calculations using arcs in 3d space but am a bit lost. Lets say that I want to animate an arc in 3d space to connect 2 x,y,z coordinates (both coordinates have a z value of 0, and are just points on a plane). I'm controlling the arc by sending it a starting x,y,z position, a rotation, a velocity, and a gravity value. If I know both the x,y,z coordinates that need to be connected, is there a way to calculate what the necessary rotation, velocity, and gravity values to connect it from the starting x,y,z coordinate to the ending one?
Thanks.
EDIT: Thanks tom10. To clarify, I'm making "arcs" by creating a parabola with particles. I'm trying to figure out how to ( by starting a parabola formed by a series particles with an beginning x,y,z,velocity,rotation,and gravity) determine where it will in end(the last x,y,z coordinates). So if it if these are the two coordinates that need to be connected:
x1=240;
y1=140;
z1=0;
x2=300;
y2=200;
z2=0;
how can the rotation, velocity, and gravity of this parabola be calculated using only these variables start the formation of the parabola:
x1=240;
y1=140;
z1=0;
rotation;
velocity;
gravity;
I am trying to keep the angle a constant value.
This link describes the ballistic trajectory to "hit a target at range x and altitude y when fired from (0,0) and with initial velocity v the required angle(s) of launch θ", which is what you want, right? To get your variables into the right form, set the rotation angle (in the x-y plane) so you're pointing in the right direction, that is atan(y/x), and from then on out, to match the usual terminology for 2D problem, rewrite your z to y, and the horizontal distance to the target (which is sqrt(xx + yy)) as x, and then you can directly use the formula in link.
Do the same as you'd do in 2D. You just have to convert your figures to an affine space by rotating the axis, so one of them becomes zero; then solve and undo the rotation.