Rotations, Radians and -1.#IND oh my

This is a discussion on Rotations, Radians and -1.#IND oh my within the C++ Programming forums, part of the General Programming Boards category; Hello one and all. I've been tampering with rotation matrixes and the lot, and even though i can manage the ...

  1. #1
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    Rotations, Radians and -1.#IND oh my

    Hello one and all.

    I've been tampering with rotation matrixes and the lot, and even though i can manage the more simpler rotation around the three axes. my attempts at trying it around an arbitrary fixed point (xyz) deson't work aswell as i would have hoped.

    It seems to work 80% of the time however, this seems only to be a result of the right combination of (xyz) vector for rotation and the angle chosen to rotate by. If its wrong i get a number which is > then 1 or < -1 and when used in conjunction with arcsin gives a -1.#IND output.

    my method was originall based around euler angles and quaternions found in http://en.wikipedia.org/wiki/Convers...d_Euler_angles

    essentailly computing q0-q3 and then using these to compute the euler angles

    Code:
     for (i = 0; i < PopSize; i++)
         {         
               angle = rand()%361+0.001;
               // convert to radian???
               angle =  angle * (PI / 180);
               
               cout << "Angle: " << angle << endl;
                  // convert to euler angles
                  q0 = cos(angle/2);
                  cout << "q0: " << q0 << endl;
                  q1 = sin(angle/2) * (cos(Pop[i][5][0])); // rotate around 5th atom
                  cout << "q1: " << q1 << endl;
                  q2 = sin(angle/2) * (cos(Pop[i][5][1]));
                  cout << "q2: " << q2 << endl;
                  q3 = sin(angle/2) * (cos(Pop[i][5][2]));
                  cout << "q3: " << q3 << endl;
                  cout << (q0*q2) << " - " << (q3*q1) << endl;
                  eX = atan(2*((q0*q1) + (q2*q3)) / (1 - (2*( (q1 * q1) + (q2 * q2) ) ) ) );
                  eY = asin(2*((q0*q2) - (q3*q1)));
                  eZ = atan(2*((q0*q3) + (q1*q2)) / (1 - (2*( (q2 * q2) + (q3 * q3) ) ) ) );
                  cout << "Euler X: " << eX << endl; cout << "Euler Y: " << eY << endl; cout << "Euler Z: " << eZ << endl;
                  cout << endl;
                  cout << "X " << Pop[i][5][0] << " Y " << Pop[i][5][1] << " Z " << Pop[i][5][2] << endl;
                //  cin.get();      
             for (j = 0; j < ShtResidue; j++)
             {
       //           cout << "Checking Distance Before Rotation..." << endl;
                  Xsqd = (Pop[i][j-1][0] - Pop[i][j][0]) * (Pop[i][j-1][0] - Pop[i][j][0]);
                  Ysqd = (Pop[i][j-1][1] - Pop[i][j][1]) * (Pop[i][j-1][1] - Pop[i][j][1]);
                  Zsqd = (Pop[i][j-1][2] - Pop[i][j][2]) * (Pop[i][j-1][2] - Pop[i][j][2]);
                  Sum = Xsqd + Ysqd + Zsqd;
                  Sum = sqrt (Sum);
         //         cout << "X Squared: " << Xsqd << endl; cout << "Y Squared: " << Ysqd << endl;      cout << "Z Squared: " << Zsqd << endl;
        //          cout << "Distance: " << Sum << endl;
       //           cin.get();
       //           cout << endl;
                
                  
             nX[0] = Pop[i][j][0]; // store for later use in z axis rotaion
             nY[0] = Pop[i][j][1];
             nZ[0] = Pop[i][j][2];
             
          // rotate around Z axis
        //     cout << "Rotate Z axis" << endl;
             Pop[i][j][0] = (nX[0] * (cos(eX))) - (nY[0] * (sin(eX)));
             Pop[i][j][1] = (nX[0] * (sin(eX))) + (nY[0] * (cos(eX)));
             Pop[i][j][2] = nZ[0];
        //     cout << "Atom: " << j << endl; cout << "X' = " << Pop[i][j][0] << endl; cout << "Y' = " << Pop[i][j][1] << endl; cout << "Z' = " << Pop[i][j][2] << endl;
       //      cin.get();
             oldnX[0] = Pop[i][j][0]; // store for later use in y axis rotaion
             oldnY[0] = Pop[i][j][1];
             oldnZ[0] = Pop[i][j][2];
    It's only a partial piece of the code however, and i can't seem to figure out why it works on some occassions and then not on others. To me it seems that the equations set out in the wiki correspond to what i have coded but i still occasionally get errors from this part:

    eY = asin(2*((q0*q2) - (q3*q1)));
    i.e. computing euler angle Y

    where if asin * anything greater then 1.0 or less then -1.0 it throws up the NaN -1.#IND

    Also i had originally thought i could use normal angles, but it seems that cmath uses radians instead so to be honest i don't know what effect that is having, as you can see i changed it to convert from angles to radians, but still keep getting the odd -1.#IND

    Can i use this method to calculate rotation around a vector (xyz) or i'am i out of luck.

    Any help is appreciated

    Regards Wolfe

  2. #2
    and the hat of wrongness Salem's Avatar
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    > angle = rand()%361+0.001;
    Stick to % 360 only.
    Valid integer angles would be 0 to 359 inclusive.

    > Xsqd = (Pop[i][j-1][0] - Pop[i][j][0]) * (Pop[i][j-1][0] - Pop[i][j][0]);
    Given that j starts at 0, you're stepping off the beginning of the array.
    If you dance barefoot on the broken glass of undefined behaviour, you've got to expect the occasional cut.
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  3. #3
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    With regards to j-1 section it is ony there for me to check the distances remain valid nothing else omes from it once i can finally be certain it works i will get rid of it.

    Regards Wolfe

  4. #4
    Super Moderator VirtualAce's Avatar
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    What you are looking for is an axis-angle rotation matrix. Google it.

  5. #5
    Algorithm Dissector iMalc's Avatar
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    You don't need quaternions for this. Euclidean Geometry will also work. Not meaning to imply one is a better choice here than the other. But anyway...
    See the rather controversial article: http://www.gamedev.net/reference/art...rticle1199.asp
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  6. #6
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    Quote Originally Posted by Bubba View Post
    What you are looking for is an axis-angle rotation matrix. Google it.
    I believe i already have that coded in elsewhere, if you mean by rotating around each axis. What i was trying to do know is, if oyu have a string of nodes connected as a chain in a 3D space, i want to rotate about a node ie its vector (xyz).

    thanks for the link imalc i'll have a look.

  7. #7
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    Well turns out i had also tried out what was in that link aswell , though i couldn't get that to work either lol

    Here is a snippet

    Code:
            
             nX[0] = Pop[i][j][0]; // store for later use in z axis rotaion
             nY[0] = Pop[i][j][1];
             nZ[0] = Pop[i][j][2];
                  
          //   cout << "Rotate Z axis" << endl;
             Pop[i][j][0] = ((1 - cos(angle))*(nX[0] * nX[0]) + (cos(angle))) + (1 - cos(angle)*(nX[0]*nY[0]) - (sin(angle)*nZ[0])) + (1 - cos(angle)*(nX[0]*nZ[0]) + (sin(angle)*nY[0])); 
             Pop[i][j][1] = ((1 - cos(angle))*(nX[0] * nY[0]) + (sin(angle)*nZ[0])) + (1-cos(angle)*(nY[0] * nY[0]) + (cos(angle))) + (1 - cos(angle)*(nY[0]*nZ[0]) - (sin(angle)*nX[0]));
             Pop[i][j][2] = ((1 - cos(angle))*(nX[0] * nZ[0]) - (sin(angle)*nY[0])) + (1-cos(angle)*(nY[0] * nZ[0]) + (sin(angle)*nX[0])) + (1 - cos(angle)*(nZ[0] *nZ[0]) + cos(angle));
        //     cout << "Atom: " << j << endl; cout << "X' = " << Pop[i][j][0] << endl; cout << "Y' = " << Pop[i][j][1] << endl; cout << "Z' = " << Pop[i][j][2] << endl;
            // cin.get();

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