Yaw/Pitch/Roll matrix multiplication

[kirennian]

I'm currently having an issue with moving the camera around the z-axis (roll). For debugging purposes, I have an object with which I've tested with all 3-axis rotation and movement and it's working as expected; the object in question as well as the camera class superseed a positions class for determining their position, rotation and scale.

Having finished cycling the frame, checking for potential changes in the values, the following multiplications are in place to update the class:

//Cycles and transforms the display device around the object.
HRESULT ThreeDPositions::cycle(DeviceManager* dManager){

	//Compute matrix equations for rotation, scaling and placement.
	D3DXMatrixScaling(&mScaling, scale.x, scale.y, scale.z);
	D3DXMatrixRotationYawPitchRoll(&mRotation, rotation.y, rotation.x, rotation.z);
	D3DXMatrixTranslation(&mTranslate, placement.x, placement.y, placement.z);

	//Multiply each matrix for the final display.
	mWorld = mRotation * mScaling * mTranslate;

	//Transform the world device positioning matrix.
	dManager->getDisplayDevice()->getD3dDevice()->SetTransform(D3DTS_WORLD, &mWorld);

	return S_OK;
}

Having done that, the camera class then does the following:

//Transform the view matrix for an up to date display.
	D3DXVec3TransformCoord(&vNewDir, &vStartDirection, &currentPosition->getMRotation());
	D3DXVec3Normalize(&vNormedNewDir, &vNewDir);
	vNormedNewDir += currentPosition->getPlacement();
	D3DXMatrixLookAtLH( &mView, &currentPosition->getPlacement(), &vNewDir, &vUp);

where:

vStartDirection = D3DXVECTOR3(0.0f, 0.0f, 1.0f);
vUp = D3DXVECTOR3(0.0f, 1.0f, 0.0f);

I've checked and all of the placements for the camera, as well as rotations around the x/y axis are working correctly, strangely enough though, the z-axis rotation IS being updated (as shown by the object rotating around it correctly), yet the camera refuses to roll correctly.

Even with removing the D3DTS_WORLD transformation from the camera, no effect is seen.

Any help/pointers would be greatly appreciated.

edit:Also worthy of note is that upon testing via swapping the x/y values for rotation, z-axis rotation does happen; of course not correctly but it does point to an issue in the calculations rather then the system somehow disabling it.

[IsharaComix]

I remember having the same problem back when I was goofing off with OpenGL. I'm not sure how much it will help you, but I'll contribute this anyway. I wrote a brute-force method that allows me to rotate along any object's local axis, and then I can use that as the object's orientation dimensions.

Disclaimer: This is C code.
Further Disclaimer: This is before I learned how to write code properly.

/* 'orientation' is a 3x3 float matrix that contains a unit vector for each of the local z, x, y (in that order) axes relative to the origin. In my example, it represents the camera, and the camera looks out the z axis with the y axis representing its up vector). */

/* Rotate a number of degrees around axis 0 (z), 1 (x) or 2 (y) */
void cam_rotate(float degrees, int axis)
{
    float matrixM[3][3];
    
    float Xo, Yo, Zo, cosd, sind;
    
    int nxt = (axis+1)%3;
    float new_x,new_y,new_z, mag;
    
    /* The vector we rotate around does not change. We store its values in smaller variables to make the code more legible. */
    Xo = orientation[axis][0];
    Yo = orientation[axis][1];
    Zo = orientation[axis][2];
    cosd = cos(degrees*3.1415/180);
    sind = sin(degrees*3.1415/180);
    
    /* Multiply one of the vectors by the transformation matrix representing the degree of transformation. */
    matrixM[0][0] = Xo*Xo + cosd*(1-Xo*Xo);
    matrixM[0][1] = Xo*Yo + cosd*(0-Xo*Yo)    + sind*-Zo;
    matrixM[0][2] = Xo*Zo + cosd*(0-Xo*Zo)    + sind*Yo;
    matrixM[1][0] = Yo*Xo + cosd*(0-Yo*Xo)    + sind*Zo;
    matrixM[1][1] = Yo*Yo + cosd*(1-Yo*Yo);
    matrixM[1][2] = Yo*Zo + cosd*(0-Yo*Zo)    + sind*-Xo;
    matrixM[2][0] = Zo*Xo + cosd*(0-Zo*Xo)    + sind*-Yo;
    matrixM[2][1] = Zo*Yo + cosd*(0-Zo*Yo)    + sind*Xo;
    matrixM[2][2] = Zo*Zo + cosd*(1-Zo*Zo);
    
    new_x = matrixM[0][0]*orientation[nxt][0]+
            matrixM[0][1]*orientation[nxt][1]+
            matrixM[0][2]*orientation[nxt][2];
    new_y = matrixM[1][0]*orientation[nxt][0]+
            matrixM[1][1]*orientation[nxt][1]+
            matrixM[1][2]*orientation[nxt][2];
    new_z = matrixM[2][0]*orientation[nxt][0]+
            matrixM[2][1]*orientation[nxt][1]+
            matrixM[2][2]*orientation[nxt][2];
    mag = sqrt(new_x*new_x+new_y*new_y+new_z*new_z);
    if (new_x == 1 || new_x == -1) { new_y = 0; new_z = 0; }
    if (new_y == 1 || new_y == -1) { new_x = 0; new_z = 0; }
    if (new_z == 1 || new_z == -1) { new_x = 0; new_y = 0; }
    orientation[nxt][0] = new_x/mag;
    orientation[nxt][1] = new_y/mag;
    orientation[nxt][2] = new_z/mag;
    
    /* Take the cross product of the first two matrices to reorient the third axis. */
    nxt = (nxt+1)%3;
    new_x = matrixM[0][0]*orientation[nxt][0]+
            matrixM[0][1]*orientation[nxt][1]+
            matrixM[0][2]*orientation[nxt][2];
    new_y = matrixM[1][0]*orientation[nxt][0]+
            matrixM[1][1]*orientation[nxt][1]+
            matrixM[1][2]*orientation[nxt][2];
    new_z = matrixM[2][0]*orientation[nxt][0]+
            matrixM[2][1]*orientation[nxt][1]+
            matrixM[2][2]*orientation[nxt][2];
    mag = sqrt(new_x*new_x+new_y*new_y+new_z*new_z);
    if (new_x == 1 || new_x == -1) { new_y = 0; new_z = 0; }
    if (new_y == 1 || new_y == -1) { new_x = 0; new_z = 0; }
    if (new_z == 1 || new_z == -1) { new_x = 0; new_y = 0; }
    orientation[nxt][0] = new_x/mag;
    orientation[nxt][1] = new_y/mag;
    orientation[nxt][2] = new_z/mag;
}

So your start direction is orientation[0] and up is orientation[2].

This code is unnecessarily verbose. If you replace my hard-coded math with matrix multiplication, then you get the same effect (I did this in Python using Numpy one time). The idea is to have 3 vectors all at right angles with one another to permit arbitrary rotation along the object's local axes at any given moment.

I certainly hope this helps you - I spent days trying to figure this out, and the effect was rather nice. If you can't understand my code, the entire thing's logic was derived from the OpenGL Red Book. Here's a link to the relevant page: http://fly.cc.fer.hr/~unreal/theredbook/chapter03.html

The sines and cosines came from a Wikipedia page on the subject http://en.wikipedia.org/wiki/Transformation_matrix

[dusktreader]

I haven't used them before, but I know a lot of people use quaternions to calculate 3 axis rotations. Apparently they compose better than using Euler angles. Have a look. Like I said, I haven't used them, but they might be what you are looking for.

[kirennian]

Cheers for the pointers guys. It turns out it is caused by my misinterpretation of the D3DXMatrixLookAtLH method which I should have seen earlier. The second vector is the eye position and the third, merely the lookat position. As such, the two will only control a 2d screen positioning application, thus there is no control over the third, roll axis.

To overcome this, the up vector, fourth value has to be changed. I'll post back when I've sorted it for each camera type. :)

[dineshguru]

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