cylinderFunctions.txt

/*
 * Replace the function macros in cylinder?.c with the following function definitions
 * to see other kinds of surfaces. Actually, function definitions are probably better
 * than macros, as macros look clumsy with complicated functions.
 */

// The following functions extrude a base circle as in cylinder2.c, but with the
// the radius varying along the z-axis. This is seen in the formulae for FNX and FNY.
// The radius as a function of z is 1 + 5*(z-0.5)^2. Thus the radius varies as a parabola
// and the (z-0.5) is used to center the parabola at 0.5 (as j/N varies from 0 to 1!).
// You can see the parabolic section of the figure created.
GLfloat FNX(int i, int j)
{
  return ( 1 + 5 * ( (float)j/N - 0.5 )*( (float)j/N - 0.5 ) ) 
                 * cos( ( (float)i/M ) * 2 * PI);
}

GLfloat FNY(int i, int j)
{
  return ( 1 + 5 * ( (float)j/N - 0.5 )*( (float)j/N - 0.5 ) ) 
                 * sin( ( (float)i/M ) * 2 * PI);
}

GLfloat FNZ(int i, int j)
{
  return 3.0 * (float) j/N;
}

// The following functions extrude a parabola in the z-direction to 
// give a parabolic cylinder (compare parabolic-cylinder.c). The parabola
// equation is y = 1 + 5*(x-0.5)^2.
GLfloat FNX(int i, int j)
{
   return (float)i/M;
}

GLfloat FNY(int i, int j)
{
   return 1 + 5 * ( (float)i/M - 0.5 )*( (float)i/M - 0.5 );
}

GLfloat FNZ(int i, int j)
{
  return 3.0 * (float) j/N;
}

// The following functions draw a torus. The i-direction describes the latitudes
// (small circles that are sections of the torus) while the j-direction describes
// the longitudes (the larger circles that travel around the torus). Imagine a 
// torus being described by a small circle travelling (as though a ring) around
// a larger circle. Verify with trigonometry that we  map the mesh points correctly
// on to the torus.
GLfloat FNX(int i, int j)
{
   return (1 + 0.5 * cos( (float) i/M  * 2 * PI ) ) * cos( (float) j/N  * 2 * PI );
}

GLfloat FNY(int i, int j)
{
   return (1 + 0.5 * cos( (float) i/M  * 2 * PI ) ) * sin( (float) j/N  * 2 * PI );
}

GLfloat FNZ(int i, int j)
{
   return 0.5 * sin( (float) i/M  * 2 * PI );
}