HOWTO: Create sphere geometry using trigonometry.

sphere.C

/* The amount to change the angle by with each step, determined by 
   resolution.*/
const float ANGLE_DELTA = (float)REVOLUTION / (float)_resolution;
/* Convert the delta to radians, since that's what C++ works in. */
const float R_ANGLE_DELTA = ANGLE_DELTA * (float)M_PI / 180.0f;

/* Allocate vertices for each step along the x-axis. */
_vertexCount = (int) ceilf(abs(X_ANGLE_STOP - X_ANGLE_START) / ANGLE_DELTA);
/* Allocate vertices for each step along the y-axis. */
_vertexCount *= (int) ceilf(abs(Y_ANGLE_STOP - Y_ANGLE_START) / ANGLE_DELTA);
/* Each step requires two triangles. */
_vertexCount *= 2;
/* Each triangle has three vertices. */
_vertexCount *= 3;

/* Each vertex has four elements. */
_positions = new float[_vertexCount * 4];

unsigned index = 0;

/* Step through x / y combinations, and use sin / cos to determine the 
   coordinates for each step. */
for (float longitude = X_ANGLE_START; longitude < X_ANGLE_STOP;
   longitude += ANGLE_DELTA)
{
   float rlong = longitude * (float)M_PI / 180.0f;
      for (float latitude = Y_ANGLE_START; latitude < Y_ANGLE_STOP;
         latitude += ANGLE_DELTA)
   {
      float rlat = latitude * (float)M_PI / 180.0f;
         /* Bottom left. */
      _positions[index + X] = sinf(rlong) * cosf(rlat);
      _positions[index + Y] = sinf(rlat);
      _positions[index + Z] = cosf(rlong) * cosf(rlat);
      _positions[index + W] = 1.0f;
      index += W + 1;

      /* Top right. */
      _positions[index + X] =
         sinf(rlong + R_ANGLE_DELTA) * cosf(rlat + R_ANGLE_DELTA);
      _positions[index + Y] =
         sinf(rlat + R_ANGLE_DELTA);
      _positions[index + Z] =
         cosf(rlong + R_ANGLE_DELTA) * cosf(rlat + R_ANGLE_DELTA);
      _positions[index + W] = 1.0f;
         index += W + 1;

      /* Top left. */
      _positions[index + X] = sinf(rlong) * cosf(rlat + R_ANGLE_DELTA);
      _positions[index + Y] = sinf(rlat + R_ANGLE_DELTA);
      _positions[index + Z] = cosf(rlong) * cosf(rlat + R_ANGLE_DELTA);
      _positions[index + W] = 1.0f;
      index += W + 1;

      /* Bottom left. */
      _positions[index + X] = sinf(rlong) * cosf(rlat);
      _positions[index + Y] = sinf(rlat);
      _positions[index + Z] = cosf(rlong) * cosf(rlat);
      _positions[index + W] = 1.0f;
      index += W + 1;

      /* Bottom right. */
      _positions[index + X] =
         sinf(rlong + R_ANGLE_DELTA) * cosf(rlat);
      _positions[index + Y] =
         sinf(rlat);
      _positions[index + Z] =
         cosf(rlong + R_ANGLE_DELTA) * cosf(rlat);
      _positions[index + W] = 1.0f;
         index += W + 1;

      /* Top right. */
      _positions[index + X] =
         sinf(rlong + R_ANGLE_DELTA) * cosf(rlat + R_ANGLE_DELTA);
      _positions[index + Y] =
         sinf(rlat + R_ANGLE_DELTA);
      _positions[index + Z] =
         cosf(rlong + R_ANGLE_DELTA) * cosf(rlat + R_ANGLE_DELTA);
      _positions[index + W] = 1.0f;
      index += W + 1;
   }
}