Rotating a multipart object

Question

I've created an object that has about 7+ parts to it including its body and smaller parts that 'attach' to it in different places. My goal is to rotate the entire object. I tried to simply call glRotatef(angle, 0, 1, 0) before constructing the entire object, but I realize that this seems to rotate 'everything' around the origin, no matter the translation. The following code was an attempt to rotate the body itself and rotate the attached parts to it.

// glRotatef(angle, 0, 1, 0); //old way of rotating the object

// body
glPushMatrix();
    // movement
    glTranslatef(subx, suby + y, subz);
    //rotating the body itself
    glRotatef(angle, 0, 1, 0); 
    // starting position of the body
    glScalef(9.0, 1.75, 1.75);
    glTranslatef(-subx, -suby, -subz);
    glTranslatef(subx, suby, subz);
    glutSolidSphere(1.0, 50, 50);
glPopMatrix();

// attached part
glPushMatrix();
    // movement
    glTranslatef(rot1x, rot1y + y, rot1z); 
    // attempting to rotate the part while 'attached to' the body
    glRotatef(angle, 0, 1, 0);
    //placing the part on the object in starting position
    glRotatef(rot1angle, rot1xrot, rot1yrot, rot1zrot);
    glTranslatef(-rot1x, -rot1y, -rot1z);
    glTranslatef(rot1x, rot1y, rot1z);
    gluPartialDisk(gluNewQuadric(), 0, 1, 50, 1, 0, 100.0);
glPopMatrix();

I can't seem to wrap my head around what needs to happen in order for the smaller parts of the object to rotate properly with the object's body (a fixed point?). Thanks for your help.

Answer 1

The operations on the matrix stack are based on one another. The reference system of each operation is the current transformation. If you want to transform a object which consists of a bunch of objects, then you have to know the relative position of each sub object to a reference position of the object union. Then you have to do the following steps:

• Move each object to a common position in the world (glTranslate).
• Orientate the objects (glRotate)
• Move each object to its relative position in the object union

// dynamic position in the world
float refPosX, refPosY, refPosZ;

// dynamic orientation
float angle;

// constant positions of the sub object relative to the object union
float subPosX[], subPosY[], subPosZ[];


for ( int i = 0 i < noOfObj, ++i ) // for each object
{
  glPushMatrix();
  glTranslatef(refPosX, refPosY, refPosZ);
  glRotatef(angle, 0, 1, 0); 
  glTranslatef(subPosX[i], subPosY[i], subPosZ[i]);
  glScalef(9.0, 1.75, 1.75);

  ..... // draw the object here

  glPopMatrix();
}

See the documentation of glTranslate:

glTranslate produces a translation by x y z . The current matrix (see glMatrixMode) is multiplied by this translation matrix, with the product replacing the current matrix,

and see the documentation of glRotate:

glRotate produces a rotation of angle degrees around the vector x y z . The current matrix (see glMatrixMode) is multiplied by a rotation matrix with the product replacing the current matrix,

Note, the translation matrix looks like this:

Matrix4x4 translate;

translate[0] : ( 1,  0,  0,  0 )
translate[1] : ( 0,  1,  0,  0 )
translate[2] : ( 0,  0,  1,  0 )
translate[3] : ( tx, ty, tz, 1 )

And the rotation matrix around Y-Axis looks like this:

Matrix4x4  rotate;
float      angle;

rotate[0] : ( cos(angle),  0, sin(angle), 0 )
rotate[1] : ( 0,           1, 0,          0 )
rotate[2] : ( -sin(angle), 0, cos(angle), 0 )
rotate[3] : ( 0,           0, 0,          1 ) 

A matrix multiplication works like this:

Matrix4x4 A, B, C;

// C = A * B
for ( int k = 0; k < 4; ++ k )
    for ( int l = 0; l < 4; ++ l )
        C[k][l] = A[0][l] * B[k][0] + A[1][l] * B[k][1] + A[2][l] * B[k][2] +  A[3][l] * B[k][3];

The result of translate * rotate is this:

model[0] : ( cos(angle),  0,  sin(angle), 0 )
model[1] : ( 0,           1,  0,          0 )
model[2] : ( -sin(angle), 0,  cos(angle), 0 )
model[3] : ( tx,          ty, tz,         1 )

Note, the result of rotate * translate would be:

model[0] : ( cos(angle),                     0,   sin(angle),                     0 )
model[1] : ( 0,                              1,   0,                              0 )
model[2] : ( -sin(angle),                    0,   cos(angle),                     0 )
model[3] : ( cos(angle)*tx - sin(angle)*tx,  ty,  sin(angle)*tz + cos(angle)*tz,  1 )

Answer 2

1. you are missing glMatrixMode calls

   If you are using only GL_MODELVIEW than it works (if lastly set active) but when your code grows longer and you add other calls you might broke this and suddenly your code will not work as expected (and very hard to debug). Therefore it is better to add glMatrixMode(GL_MODELVIEW); before any transformation chunk of code.

2. You are push/pop ing wrongly

   Your objects are nested so the matrices must be nested too. That means any part attached to owner part must start with the owners part matrix. So you need to have some hierarchy of the parts (assembly order) so you know what parts are attached to which ones and where.

   so You should have a list of parts connected to any part ... Something like:

   List<int> part[noOfObj];
   

   so any part[i], i=<0,noOfObj-1> has children parts part[i][0,1,2...,part[i].num-1] connected to it (where num is size of the list). And part[0] is the main part. That changes things a bit but simple recursion helps:

   void part_draw(int ix) // this is just recursion call used by the main function do not use it directly
    {
    glMatrixMode(GL_MODELVIEW);
    glPushMatrix();
    glTranslatef(subPosX[ix], subPosY[ix], subPosZ[ix]);
   
    glPushMatrix();            // this should not be here 
    glScalef(9.0, 1.75, 1.75); // this should not be here
    ..... // draw the object ix here
    glMatrixMode(GL_MODELVIEW);// this should not be here
    glPopMatrix();             // this should not be here
   
    for (int iy=0;iy<part[ix].num,iy++)
     part_draw(part[ix][iy]);
   
    glMatrixMode(GL_MODELVIEW);
    glPopMatrix();
    }
   
   void mesh_draw() // this is the main rendering routine which you should use
    {
    glMatrixMode(GL_MODELVIEW);
    glPushMatrix();
    glTranslatef(refPosX, refPosX, refPosZ);
    glRotatef(angle, 0, 1, 0); 
   
    part_draw(0);
   
    glMatrixMode(GL_MODELVIEW);
    glPopMatrix();
    }
   

   Now beware that subPosX/Y/Z positions must be in parent part coordinate system. Also This will not work for cyclicly nested objects (loops) as that would lead to infinite loop causing stack overflow.