I am new on this platform so please let me know if i am doing something wrong before reporting! Also, i already searched for similar problems but i could not find the answer i am looking for.
I have this problem where i need to "add" gravity component to my vector of linear accelerations, and i know this can be done with Quaternions. My vector:
Accelerations = [Xacc, Yacc, Zacc]
and a quaternions that represents my current orientation:
q = [w, x, y, z]
Let's say i start in this position:
q = [1,0,0,0]
Now of course if i move for example my smartwatch i'll get some values in my Accelerations Vector and some values in my Quaternion right?
I thought about converting my Accelerations vector into a Quaternion form:
AccQuat = [0, x, y, z]
And then make a rotation to this quaternion by the opposite of my q, so i can "translate" my Accelerations Quaternion to the Earth frame of reference q = [1,0,0,0], the converting it back into a Vector form, adding the Gravity Vector:
g = [0, 0, -9.81]
Once done, getting the "New" Vector with gravity added back into Quaternion form, rotating it to his native position and then converting it back into his vector form.
Its a little bit tricky but i think it can be done in such a way. Is this a right way to do what im trying to do? Because i have no other information other than an already Normalized Quaternion representing my position and a vector of linear Accelerations.
To multiply a Quaternions i have to apply:
qOut = q*p*q^-1
by doing 2 Quaternions multiplications right?
And if, for example, i have a quaternion representing a 90deg rotation on my Z-Axe:
q = [0.71, 0, 0, 0.71]
if i want to "Rotate back" my Accelerations Quaternion, i need to make
qOut = q*p*q^-1
but as q i need to use my "Reverse" quaternion:
qReverse = [0.71, 0, 0, -0.71]
right?
Im working with C++ to make the code work but my problem now is the mental procedure rather than coding it.
Thanks everyone for the help!
========== EDIT ==================
More informations:
i have a fixed coordinates system called World (0,0,0) always parallel to my floor, my Quaternion rotations are for a system called "0" that refers to this World, they have the same centre in (0,0,0).
Maybe this can explain better:
World is Black, 0 is Blue One.
Lets suppose that my blue axis are my 3 components in the acceleration vector.
I thought about converting them into a Quaternion by simply adding a constant = 0 as w, then rotating them with the Quaternion formula (where q is reverse of my quaternion that i got from the data):
f = q*p*q^-1
So they can coincide with the Black system.
From this add the gravity component from the Z axis as it is // to the floor, then rotating my "New Accelerations quaternion" to his original position with the same formula but inverted q. In the end i want to get my Accelerations vector with Gravity added that's all. I thought it could be done with quaternions. Hope this can explain better, forgive me if im repeating same things but im also new to this argument.
I want to compute the camera pitch and yaw values based on position and target points camera gets when it is instantiated. If I initialize pitch to 0 and yaw to -90 (as in LearnOpenGL Camera Tutorial), when the first rotate occurs, camera suddenly jumps; after that rotation works correctly. So, firstly, starting from the equations given in that tutorial I tried to get pitch and yaw values from forward vector:
float pitch = glm::degrees(glm::asin(forward.y));
float yaw = glm::degreees(glm::acos((float)x/glm::cos(glm::asin(y))));
But also
float yaw = glm::degreees(glm::asin((float)z/glm::cos(glm::asin(y))));
And cos(sin(y)) should not be 0, so y should not be 0 or -1.
I tried to implement those but the 2 values of yaw are not the same, also first value of yaw seems to be what I am looking for, but pitch does not.
After that, I tried a simple approach, knowing that pitch is the angle between forward vector and y-axis, and yaw is the angle between forward vector and x-axis, I tried to compute (on paper) the following:
const glm::vec3 yUnit(0, 1, 0);
const glm::vec3 xUnit(1, 0, 0);
float pitch = glm::degrees(glm::acos(glm::dot(forward, yUnit)));
float yaw = glm::degrees(glm::acos(glm::dot(forward, xUnit)));
With the following 2 inputs: position = (0, 0, 0), target = (0, 1, 2,5), forward = target - position = (0, 1, 2.5), normalised forward ~ (0, 0.37, 0.926), the results are pitch ~ 68 degrees and yaw = 90 degrees.
Also, i printed pitch and yaw values inside the application and the expected values should be pitch = -20 and yaw = -90.
Can you explain me if I’m wrong, why and where I made the mistake?
based on your expected values it seems like your pitch should vary between -90 and 90 degrees, so you should use asin instead of acos for pitch.
when calculating the yaw, you need to project the forward vector onto the xz plane. you can do this by setting the y component to zero and then normalizing it.
the yaw will need to vary between 0 and 360 degrees but acos only returns between 0 and 180 degrees. the yaw will be correct for the first 180 degrees, but as yaw increases from 180 to 360, the acos will decrease from 180 back to zero.
when the dot product between the forward vector and (0,0,1) is greater than zero, the yaw will be greater than 180 degrees, and so the acos value should be adjusted by subtracting it from 360.
based on your expected values, my guess for the correct yaw and pitch values is
pitch = degrees(-asin(dot(forward, y_unit)))
forward.y = 0
forward = normalize(forward)
yaw = degrees(acos(dot(forward, x_unit)))
if(dot(forward, z_unit) > 0)
yaw = 360 - yaw
Can't point at any single line to change, but suggestions:
when the first rotate occurs, camera suddenly jumps
This is a sign that something is not being initialized to what you think it is. In this case, the pitch and yaw are derived values that can be calculated from the forward vector, right? When you have derived values you should never initialise them directly, because there's a chance you'll get it wrong. If two values that are supposed to be "the same" are different, weird things will happen. Instead initialise the forward vector and immediately calculate pitch and yaw from it.
And cos(sin(y)) should not be 0
We all make this mistake from time to time. But in this case I don't think it matters for reasons later on.
However, you might want to test for what happens when the forward vector is (0, 0, 0). It's surprisingly common to somehow get an all zero vector in graphics programming.
float yaw = glm::degreees(glm::acos((float)x/glm::cos(glm::asin(y))));
Have you decided what kind of Euler angle representation you are using? In the simple case you never need to use more than one single axis coordinate value to calculate an angle, but here you are using two.
The simple case is where yaw (heading), pitch, and roll are independent angles, so yaw doesn't change if pitch does and vice versa. Your last code block with the xUnit and yUnit vectors seems to be doing that.
However in flight simulators and aerospace calculations yaw - pitch - roll are a bit more complicated because they're not independent. The yaw angle might be measured in the plane of the pitch, not absolute XZ. And aerospace yaw is often measured from "north" the Z axis, not the X. So you need to be clear about what kind of yaw and pitch you are measuring, and be consistent throughout. And you need to study any textbook examples or code to figure out how they're using pitch - yaw - roll and if it's consistent with yours.
I suggest sticking to the simple single coordinate measures for now.
float pitch = glm::degrees(glm::acos(glm::dot(forward, yUnit)));
Again, are you sure forward is normalised? LookAt is usually coded to be more forgiving than math libraries, so it's an easy mistake to make.
And, have you checked what your math library does wit values outside -180 to 180 degrees? One more thing to worry about.
Hope this helps. If you find Euler angles to be fiddly and annoying, you are not alone! That's why many 3D books and tutorials recommend learning about quaternions.
I am implementing a 3D engine for spatial visualisation, and am writing a camera with the following navigation features:
Rotate the camera (ie, analogous to rotating your head)
Rotate around an arbitrary 3D point (a point in space, which is probably not in the center of the screen; the camera needs to rotate around this keeping the same relative look direction, ie the look direction changes too. This does not look directly at the chosen rotation point)
Pan in the camera's plane (so move up/down or left/right in the plane orthogonal to the camera's look vector)
The camera is not supposed to roll - that is, 'up' remains up. Because of this I represent the camera with a location and two angles, rotations around the X and Y axes (Z would be roll.) The view matrix is then recalculated using the camera location and these two angles. This works great for pan and rotating the eye, but not for rotating around an arbitrary point. Instead I get the following behaviour:
The eye itself apparently moving further up or down than it should
The eye not moving up or down at all when m_dRotationX is 0 or pi. (Gimbal lock? How can I avoid this?)
The eye's rotation being inverted (changing the rotation makes it look further up when it should look further down, down when it should look further up) when m_dRotationX is between pi and 2pi.
(a) What is causing this 'drift' in rotation?
This may be gimbal lock. If so, the standard answer to this is 'use quaternions to represent rotation', said many times here on SO (1, 2, 3 for example), but unfortunately without concrete details (example. This is the best answer I've found so far; it's rare.) I've struggled to implemented a camera using quaternions combining the above two types of rotations. I am, in fact, building a quaternion using the two rotations, but a commenter below said there was no reason - it's fine to immediately build the matrix.
This occurs when changing the X and Y rotations (which represent the camera look direction) when rotating around a point, but does not occur simply when directly changing the rotations, i.e. rotating the camera around itself. To me, this doesn't make sense. It's the same values.
(b) Would a different approach (quaternions, for example) be better for this camera? If so, how do I implement all three camera navigation features above?
If a different approach would be better, then please consider providing a concrete implemented example of that approach. (I am using DirectX9 and C++, and the D3DX* library the SDK provides.) In this second case, I will add and award a bounty in a couple of days when I can add one to the question. This might sound like I'm jumping the gun, but I'm low on time and need to implement or solve this quickly (this is a commercial project with a tight deadline.) A detailed answer will also improve the SO archives, because most camera answers I've read so far are light on code.
Thanks for your help :)
Some clarifications
Thanks for the comments and answer so far! I'll try to clarify a few things about the problem:
The view matrix is recalculated from the camera position and the two angles whenever one of those things changes. The matrix itself is never accumulated (i.e. updated) - it is recalculated afresh. However, the camera position and the two angle variables are accumulated (whenever the mouse moves, for example, one or both of the angles will have a small amount added or subtracted, based on the number of pixels the mouse moved up-down and/or left-right onscreen.)
Commenter JCooper states I'm suffering from gimbal lock, and I need to:
add another rotation onto your transform that rotates the eyePos to be
completely in the y-z plane before you apply the transformation, and
then another rotation that moves it back afterward. Rotate around the
y axis by the following angle immediately before and after applying
the yaw-pitch-roll matrix (one of the angles will need to be negated;
trying it out is the fastest way to decide which).
double fixAngle = atan2(oEyeTranslated.z,oEyeTranslated.x);
Unfortunately, when implementing this as described, my eye shoots off above the scene at a very fast rate due to one of the rotations. I'm sure my code is simply a bad implementation of this description, but I still need something more concrete. In general, I find unspecific text descriptions of algorithms are less useful than commented, explained implementations. I am adding a bounty for a concrete, working example that integrates with the code below (i.e. with the other navigation methods, too.) This is because I would like to understand the solution, as well as have something that works, and because I need to implement something that works quickly since I am on a tight deadline.
Please, if you answer with a text description of the algorithm, make sure it is detailed enough to implement ('Rotate around Y, then transform, then rotate back' may make sense to you but lacks the details to know what you mean. Good answers are clear, signposted, will allow others to understand even with a different basis, are 'solid weatherproof information boards.')
In turn, I have tried to be clear describing the problem, and if I can make it clearer please let me know.
My current code
To implement the above three navigation features, in a mouse move event moving based on the pixels the cursor has moved:
// Adjust this to change rotation speed when dragging (units are radians per pixel mouse moves)
// This is both rotating the eye, and rotating around a point
static const double dRotatePixelScale = 0.001;
// Adjust this to change pan speed (units are meters per pixel mouse moves)
static const double dPanPixelScale = 0.15;
switch (m_eCurrentNavigation) {
case ENavigation::eRotatePoint: {
// Rotating around m_oRotateAroundPos
const double dX = (double)(m_oLastMousePos.x - roMousePos.x) * dRotatePixelScale * D3DX_PI;
const double dY = (double)(m_oLastMousePos.y - roMousePos.y) * dRotatePixelScale * D3DX_PI;
// To rotate around the point, translate so the point is at (0,0,0) (this makes the point
// the origin so the eye rotates around the origin), rotate, translate back
// However, the camera is represented as an eye plus two (X and Y) rotation angles
// This needs to keep the same relative rotation.
// Rotate the eye around the point
const D3DXVECTOR3 oEyeTranslated = m_oEyePos - m_oRotateAroundPos;
D3DXMATRIX oRotationMatrix;
D3DXMatrixRotationYawPitchRoll(&oRotationMatrix, dX, dY, 0.0);
D3DXVECTOR4 oEyeRotated;
D3DXVec3Transform(&oEyeRotated, &oEyeTranslated, &oRotationMatrix);
m_oEyePos = D3DXVECTOR3(oEyeRotated.x, oEyeRotated.y, oEyeRotated.z) + m_oRotateAroundPos;
// Increment rotation to keep the same relative look angles
RotateXAxis(dX);
RotateYAxis(dY);
break;
}
case ENavigation::ePanPlane: {
const double dX = (double)(m_oLastMousePos.x - roMousePos.x) * dPanPixelScale;
const double dY = (double)(m_oLastMousePos.y - roMousePos.y) * dPanPixelScale;
m_oEyePos += GetXAxis() * dX; // GetX/YAxis reads from the view matrix, so increments correctly
m_oEyePos += GetYAxis() * -dY; // Inverted compared to screen coords
break;
}
case ENavigation::eRotateEye: {
// Rotate in radians around local (camera not scene space) X and Y axes
const double dX = (double)(m_oLastMousePos.x - roMousePos.x) * dRotatePixelScale * D3DX_PI;
const double dY = (double)(m_oLastMousePos.y - roMousePos.y) * dRotatePixelScale * D3DX_PI;
RotateXAxis(dX);
RotateYAxis(dY);
break;
}
The RotateXAxis and RotateYAxis methods are very simple:
void Camera::RotateXAxis(const double dRadians) {
m_dRotationX += dRadians;
m_dRotationX = fmod(m_dRotationX, 2 * D3DX_PI); // Keep in valid circular range
}
void Camera::RotateYAxis(const double dRadians) {
m_dRotationY += dRadians;
// Limit it so you don't rotate around when looking up and down
m_dRotationY = std::min(m_dRotationY, D3DX_PI * 0.49); // Almost fully up
m_dRotationY = std::max(m_dRotationY, D3DX_PI * -0.49); // Almost fully down
}
And to generate the view matrix from this:
void Camera::UpdateView() const {
const D3DXVECTOR3 oEyePos(GetEyePos());
const D3DXVECTOR3 oUpVector(0.0f, 1.0f, 0.0f); // Keep up "up", always.
// Generate a rotation matrix via a quaternion
D3DXQUATERNION oRotationQuat;
D3DXQuaternionRotationYawPitchRoll(&oRotationQuat, m_dRotationX, m_dRotationY, 0.0);
D3DXMATRIX oRotationMatrix;
D3DXMatrixRotationQuaternion(&oRotationMatrix, &oRotationQuat);
// Generate view matrix by looking at a point 1 unit ahead of the eye (transformed by the above
// rotation)
D3DXVECTOR3 oForward(0.0, 0.0, 1.0);
D3DXVECTOR4 oForward4;
D3DXVec3Transform(&oForward4, &oForward, &oRotationMatrix);
D3DXVECTOR3 oTarget = oEyePos + D3DXVECTOR3(oForward4.x, oForward4.y, oForward4.z); // eye pos + look vector = look target position
D3DXMatrixLookAtLH(&m_oViewMatrix, &oEyePos, &oTarget, &oUpVector);
}
It seems to me that "Roll" shouldn't be possible given the way you form your view matrix. Regardless of all the other code (some of which does look a little funny), the call D3DXMatrixLookAtLH(&m_oViewMatrix, &oEyePos, &oTarget, &oUpVector); should create a matrix without roll when given [0,1,0] as an 'Up' vector unless oTarget-oEyePos happens to be parallel to the up vector. This doesn't seem to be the case since you're restricting m_dRotationY to be within (-.49pi,+.49pi).
Perhaps you can clarify how you know that 'roll' is happening. Do you have a ground plane and the horizon line of that ground plane is departing from horizontal?
As an aside, in UpdateView, the D3DXQuaternionRotationYawPitchRoll seems completely unnecessary since you immediately turn around and change it into a matrix. Just use D3DXMatrixRotationYawPitchRoll as you did in the mouse event. Quaternions are used in cameras because they're a convenient way to accumulate rotations happening in eye coordinates. Since you're only using two axes of rotation in a strict order, your way of accumulating angles should be fine. The vector transformation of (0,0,1) isn't really necessary either. The oRotationMatrix should already have those values in the (_31,_32,_33) entries.
Update
Given that it's not roll, here's the problem: you create a rotation matrix to move the eye in world coordinates, but you want the pitch to happen in camera coordinates. Since roll isn't allowed and yaw is performed last, yaw is always the same in both the world and camera frames of reference. Consider the images below:
Your code works fine for local pitch and yaw because those are accomplished in camera coordinates.
But when you rotate around a reference point, you are creating a rotation matrix that is in world coordinates and using that to rotate the camera center. This works okay if the camera's coordinate system happens to line up with the world's. However, if you don't check to see if you're up against the pitch limit before you rotate the camera position, you will get crazy behavior when you hit that limit. The camera will suddenly start to skate around the world--still 'rotating' around the reference point, but no longer changing orientation.
If the camera's axes don't line up with the world's, strange things will happen. In the extreme case, the camera won't move at all because you're trying to make it roll.
The above is what would normally happen, but since you handle the camera orientation separately, the camera doesn't actually roll.
Instead, it stays upright, but you get strange translation going on.
One way to handle this would be to (1)always put the camera into a canonical position and orientation relative to the reference point, (2)make your rotation, and then (3)put it back when you're done (e.g., similar to the way that you translate the reference point to the origin, apply the Yaw-Pitch rotation, and then translate back). Thinking more about it, however, this probably isn't the best way to go.
Update 2
I think that Generic Human's answer is probably the best. The question remains as to how much pitch should be applied if the rotation is off-axis, but for now, we'll ignore that. Maybe it'll give you acceptable results.
The essence of the answer is this: Before mouse movement, your camera is at c1 = m_oEyePos and being oriented by M1 = D3DXMatrixRotationYawPitchRoll(&M_1,m_dRotationX,m_dRotationY,0). Consider the reference point a = m_oRotateAroundPos. From the point of view of the camera, this point is a'=M1(a-c1).
You want to change the orientation of the camera to M2 = D3DXMatrixRotationYawPitchRoll(&M_2,m_dRotationX+dX,m_dRotationY+dY,0). [Important: Since you won't allow m_dRotationY to fall outside of a specific range, you should make sure that dY doesn't violate that constraint.] As the camera changes orientation, you also want its position to rotate around a to a new point c2. This means that a won't change from the perspective of the camera. I.e., M1(a-c1)==M2(a-c2).
So we solve for c2 (remember that the transpose of a rotation matrix is the same as the inverse):
M2TM1(a-c1)==(a-c2) =>
-M2TM1(a-c1)+a==c2
Now if we look at this as a transformation being applied to c1, then we can see that it is first negated, then translated by a, then rotated by M1, then rotated by M2T, negated again, and then translated by a again. These are transformations that graphics libraries are good at and they can all be squished into a single transformation matrix.
#Generic Human deserves credit for the answer, but here's code for it. Of course, you need to implement the function to validate a change in pitch before it's applied, but that's simple. This code probably has a couple typos since I haven't tried to compile:
case ENavigation::eRotatePoint: {
const double dX = (double)(m_oLastMousePos.x - roMousePos.x) * dRotatePixelScale * D3DX_PI;
double dY = (double)(m_oLastMousePos.y - roMousePos.y) * dRotatePixelScale * D3DX_PI;
dY = validatePitch(dY); // dY needs to be kept within bounds so that m_dRotationY is within bounds
D3DXMATRIX oRotationMatrix1; // The camera orientation before mouse-change
D3DXMatrixRotationYawPitchRoll(&oRotationMatrix1, m_dRotationX, m_dRotationY, 0.0);
D3DXMATRIX oRotationMatrix2; // The camera orientation after mouse-change
D3DXMatrixRotationYawPitchRoll(&oRotationMatrix2, m_dRotationX + dX, m_dRotationY + dY, 0.0);
D3DXMATRIX oRotationMatrix2Inv; // The inverse of the orientation
D3DXMatrixTranspose(&oRotationMatrix2Inv,&oRotationMatrix2); // Transpose is the same in this case
D3DXMATRIX oScaleMatrix; // Negative scaling matrix for negating the translation
D3DXMatrixScaling(&oScaleMatrix,-1,-1,-1);
D3DXMATRIX oTranslationMatrix; // Translation by the reference point
D3DXMatrixTranslation(&oTranslationMatrix,
m_oRotateAroundPos.x,m_oRotateAroundPos.y,m_oRotateAroundPos.z);
D3DXMATRIX oTransformMatrix; // The full transform for the eyePos.
// We assume the matrix multiply protects against variable aliasing
D3DXMatrixMultiply(&oTransformMatrix,&oScaleMatrix,&oTranslationMatrix);
D3DXMatrixMultiply(&oTransformMatrix,&oTransformMatrix,&oRotationMatrix1);
D3DXMatrixMultiply(&oTransformMatrix,&oTransformMatrix,&oRotationMatrix2Inv);
D3DXMatrixMultiply(&oTransformMatrix,&oTransformMatrix,&oScaleMatrix);
D3DXMatrixMultiply(&oTransformMatrix,&oTransformMatrix,&oTranslationMatrix);
D3DXVECTOR4 oEyeFinal;
D3DXVec3Transform(&oEyeFinal, &m_oEyePos, &oTransformMatrix);
m_oEyePos = D3DXVECTOR3(oEyeFinal.x, oEyeFinal.y, oEyeFinal.z)
// Increment rotation to keep the same relative look angles
RotateXAxis(dX);
RotateYAxis(dY);
break;
}
I think there is a much simpler solution that lets you sidestep all rotation issues.
Notation: A is the point we want to rotate around, C is the original camera location, M is the original camera rotation matrix that maps global coordinates to the camera's local viewport.
Make a note of the local coordinates of A, which are equal to A' = M × (A - C).
Rotate the camera like you would in normal "eye rotation" mode. Update the view matrix M so that it is modified to M2 and C remains unchanged.
Now we would like to find C2 such that A' = M2 × (A - C2).
This is easily done by the equation C2 = A - M2-1 × A'.
Voilà, the camera has been rotated and because the local coordinates of A are unchanged, A remains at the same location and the same scale and distance.
As an added bonus, the rotation behavior is now consistent between "eye rotation" and "point rotation" mode.
You rotate around the point by repeatedly applying small rotation matrices, this probably cause the drift (small precision errors add up) and I bet you will not really do a perfect circle after some time. Since the angles for the view use simple 1-dimension double, they have much less drift.
A possible fix would be to store a dedicated yaw/pitch and relative position from the point when you enter that view mode, and using those to do the math. This requires a bit more bookkeeping, since you need to update those when moving the camera. Note that it will also make the camera move if the point move, which I think is an improvement.
If I understand correctly, you are satisfied with the rotation component in the final matrix (save for inverted rotation controls in the problem #3), but not with the translation part, is that so?
The problem seems to come from the fact that you treating them differently: you are recalculating the rotation part from scratch every time, but accumulate the translation part (m_oEyePos). Other comments mention precision problems, but it's actually more significant than just FP precision: accumulating rotations from small yaw/pitch values is simply not the same---mathematically---as making one big rotation from the accumulated yaw/pitch. Hence the rotation/translation discrepancy. To fix this, try recalculating eye position from scratch simultaneously with the rotation part, similarly to how you find "oTarget = oEyePos + ...":
oEyePos = m_oRotateAroundPos - dist * D3DXVECTOR3(oForward4.x, oForward4.y, oForward4.z)
dist can be fixed or calculated from the old eye position. That will keep the rotation point in the screen center; in the more general case (which you are interested in), -dist * oForward here should be replaced by the old/initial m_oEyePos - m_oRotateAroundPos multiplied by the old/initial camera rotation to bring it to the camera space (finding a constant offset vector in camera's coordinate system), then multiplied by the inverted new camera rotation to get the new direction in the world.
This will, of course, be subject to gimbal lock when the pitch is straight up or down. You'll need to define precisely what behavior you expect in these cases to solve this part. On the other hand, locking at m_dRotationX=0 or =pi is rather strange (this is yaw, not pitch, right?) and might be related to the above.
I've been working on a semi flight simulator. What I am trying to do is use a pitch roll and yaw to rotate an object. I have already looked online a lot, and although they explain what the problem is I have no idea how to implement the solution. So for example I do:
glRotatef(yaw,0,1,0);
glRotatef(pitch,1,0,0);
The yaw doesn't act properly, the pitch will work fine. And from what I have been reading it seems that the objects local axis has been changed so I need to find the object's new local axis and rotate around that. So I tried that with something like:
newpitch=pitch/57.29
VectorA(0,cos(newpitch)-sin(newpitch),sin(newpitch)+cos(newpitch));
glRotatef(yaw,vec.getXAxis(),vec.getYAxis(),vec.getZAxis());
glRotatef(pitch,1,0,0);
This seems to not work either.
I've also tried making a general rotation matrix and giving it both pitch and yaw and still the same problem. And I've tried using quaternions and the same problem still exists!
Here is my code for quaternions:
void Quat::eulerToQuat(float roll,float pitch,float yaw){
float radiansY = yaw/57.2;
float radiansZ = roll/57.2;
float radiansX = pitch/57.2;
float sY = sinf(radiansY * 0.5);
float cY = cosf(radiansY * 0.5);
float sZ = sinf(radiansZ * 0.5);
float cZ = cosf(radiansZ * 0.5);
float sX = sinf(radiansX * 0.5);
float cX = cosf(radiansX * 0.5);
w = cY * cZ * cX - sY * sZ * sX;
x = sY * sZ * cX + cY * cZ * sX;
y = sY * cZ * cX + cY * sZ * sX;
z = cY * sZ * cX - sY * cZ * sX;
}
Then I converted this into a matrix and use glMultMatrix(matrix) with the modelview matrix, and this has the same problem. So I'm confident it wouldn't be gimble lock =).
So in my code I do:
float matrix[4][4];
Quat this;
this.eularToQuat(roll,pitch,yaw);
this.toMatrix(matrix);
glMultMatrix(matrix);
I think you're referring to gimbal lock? You're right that each rotation modifies the axes around which subsequent local rotations will occur. In your case that affects the yaw because the OpenGL matrix stack works so that each thing you add to it occurs conceptually before whatever is already on the stack (ie, it's post multiplication in matrix terms).
Your solution, however, won't solve the problem even if implemented correctly. What you're trying to do is get the global y axis in local coordinate space so that you can rotate around the global y even after you've rotated around the global z, shifting the local axes. But that just buys you much the same problems as if you'd stuck with global axes throughout and applied the rotations in the other order. The second rotation will now interfere with the first rather than vice versa.
Another way to convince yourself that what you're doing is wrong is to look at how much information you have. You're trying to describe the orientation of an object with two numbers. Two numbers isn't enough to describe any rotation whatsoever, so there's obviously some other rule in there to convert two numbers into a complete orientation. Whatever you do to modify that rule, you're going to end up limiting the orientations you can reach. But with an aeroplane you really want to be able to reach any orientation, so that's a fundamental contradiction.
The confusion comes because, if you have a suitable way of storing orientation, it's completely valid to work forward from that by saying 'what is the orientation if I modify that by rotating around local y by 5, then around local z by 10?', etc. The problem is trying to aggregate all those transformations into a single pair of rotations. It isn't possible.
The easiest solution if you're already generally up on OpenGL tends to be to store the orientation as a complete matrix. You accumulate pitch and yaw rotations by applying them as they occur to that matrix. You pass that matrix to OpenGL via glMultMatrix to perform your drawing.
It's not an optimal solution but a quick fix test solution would be to use glLoadMatrix and glGet to apply transformations by loading your matrix to and then retrieving it from the OpenGL matrix stack, separately from your drawing. It's not really what the stack is for so you'll probably get some performance problems and over time rounding errors will cause odd behaviour but you can fix those once you're persuaded by the approach. The OpenGL man pages give the formulas for all transformation matrices and you should look up matrix normalisation (you'll probably be using an orthonormal matrix whether you realise it or not, which should help with Google) to deal with cumulative rounding.
EDIT: with respect to the code you've posted while I was rambling, quaternions are another valid way of representing orientation and another thing that you can apply incremental updates to safely. They're also compact very easy to protect from rounding errors. However I think your problem may be that you aren't using quaternions as the storage for orientation, merely as an intermediate container. So adding them to the chain doesn't fix any of your problems.
EDIT2: a further bit of hand-waving explanation to push the idea that directly storing pitch and yaw isn't good enough: imagine that, from the point of view of the pilot, you apply a yaw of 90 degrees, then a pitch of 30 degrees, then a yaw of -90 degrees. Then you end up exactly as if you'd applied a roll of 30 degrees. But if you're just storing pitch and yaw then you've no way of storing roll. Furthermore, if you just add up the total yaw and total pitch you end up thinking you've applied a pitch of 30 degrees rather than a roll. So it doesn't matter what order you apply pitch and yaw, or whether you use global or local axes, you get the wrong result.
You should yaw, pitch and roll using one transformation. Cause when you don't, you'll pushing yourself towards gimbal lock. Excerpt:
Gimbal lock is the loss of one degree of freedom in a
three-dimensional space that occurs when the axes of two of the three
gimbals are driven into a parallel configuration, "locking" the system
into rotation in a degenerate two-dimensional space.
Consider this example of Gimbal locked airplane:
When the pitch (green) and yaw (magenta)
gimbals become aligned, changes to roll (blue) and yaw apply the same
rotation to the airplane
This one has been eating up my entire night, and I'm finally throwing up my hands for some assistance. Basically, it's fairly straightforward to calculate the Pitch and Yaw from the View Matrix right after you do a camera update:
D3DXMatrixLookAtLH(&m_View, &sCam.pos, &vLookAt, &sCam.up);
pDev->SetTransform(D3DTS_VIEW, &m_View);
// Set the camera axes from the view matrix
sCam.right.x = m_View._11;
sCam.right.y = m_View._21;
sCam.right.z = m_View._31;
sCam.up.x = m_View._12;
sCam.up.y = m_View._22;
sCam.up.z = m_View._32;
sCam.look.x = m_View._13;
sCam.look.y = m_View._23;
sCam.look.z = m_View._33;
// Calculate yaw and pitch and roll
float lookLengthOnXZ = sqrtf( sCam.look.z^2 + sCam.look.x^2 );
fPitch = atan2f( sCam.look.y, lookLengthOnXZ );
fYaw = atan2f( sCam.look.x, sCam.look.z );
So my problem is: there must be some way to obtain the Roll in radians similar to how the Pitch and Yaw are being obtained at the end of the code there. I've tried several dozen algorithms that seemed to make sense to me, but none of them gave quite the desired result. I realize that many developers don't track these values, however I am writing some re-centering routines and setting clipping based on the values, and manual tracking breaks down as you apply mixed rotations to the View Matrix. So, does anyone have the formula for getting the Roll in radians (or degrees, I don't care) from the View Matrix?
Woohoo, got it! Thank you stacker for the link to the Euler Angles entry on Wikipedia, the gamma formula at the end was indeed the correct solution! So, to calculate Roll in radians from a "vertical plane" I'm using the following line of C++ code:
fRoll = atan2f( sCam.up.y, sCam.right.y ) - D3DX_PI/2;
As Euler pointed out, you're looking for the arc tangent of the Y (up) matrix's Z value against the X (right) matrix's Z value - though in this case I tried the Z values and they did not yield the desired result so I tried the Y values on a whim and I got a value which was off by +PI/2 radians (right angle to the desired value), which is easily compensated for. Finally I have a gryscopically accurate and stable 3D camera platform with self-correcting balance. =)
It seems the Wikipedia article about Euler angles contains the formula you're lookin for at the end.