Groups | Search | Server Info | Login | Register

Groups > comp.sys.ibm.pc.demos > #27

Re: figured part out; new questions

Cross-posted to 2 groups.

Show all headers | View raw

In comp.graphics.algorithms David Melik <dchmelik@hipplanet.com> wrote:
> //cube.cpp
> //This is my new code. Apparently I had derived the rotation matrices
> wrong,

There's a real elegant solution at
  http://paulbourke.net/geometry/rotate/
including C code. I successfully used his stuff
to generate the rotating figure on the banner
near the top of the page
  http://www.forkosh.com/lineart.html
Here's the function for those rotations, with
structs POINT3D and LINE3D defined in the obvious way.
See how very easy that is with Bourke's stuff?
I wonder if there's a yet easier way.

/* ==========================================================================
 * Function:    rotate3dpt ( POINT3D p, LINE3D axis, double theta )
 * Purpose:     rotate point p around axis by angle theta (in degrees)
 * --------------------------------------------------------------------------
 * Arguments:   p (I)           POINT3D p={double x,y,z} containing coords
 *                              of point to be rotated.
 *              axis (I)        LINE3D axis={POINT3D pt1,pt2} defines the
 *                              rotation axis, with pt1 its "tail", and
 *                              pt2 its "head", such that positive rotation
 *                              angles are interpreted by the right-hand
 *                              screw rule, pointing toward the head.
 *              theta (I)       double containing rotation in degrees.
 * --------------------------------------------------------------------------
 * Returns:     ( POINT3D )     {double x,y,z} of rotated coords,
 *                              or just returning p's coords for any error
 * --------------------------------------------------------------------------
 * Notes:     o See http://paulbourke.net/geometry/rotate/
 *              for discussion/derivation and original source code.
 *            o we could interpret axislen as theta, thus eliminating
 *              that arg, but we're now just normalizing axis.
 * ======================================================================= */
/* --- entry point --- */
POINT3D rotate3dpt ( POINT3D p, LINE3D axis, double theta )
{
POINT3D r = p;                          /*p rotated by theta back to caller*/
double  costheta=1.0, sintheta=0.0,     /* cos,sin(theta in radians) */
        pi = 3.14159265359;             /* pi (convert theta to radians) */
POINT3D axispt = {0.0,0.0,0.0}; /*axis.pt2 after axis.pt1 xlated to origin*/
double  axislen = 1.0;                  /* to normalize axispt */
/* ---
 * xlate p and axispt=axis.pt2 so that axis.pt1 goes to origin
 * (note: axis.pt1 is tail, and axis.pt2 is head of rotation vector)
 * ----------------------------------------------------------------- */
axispt.x = axis.pt2.x - axis.pt1.x;
axispt.y = axis.pt2.y - axis.pt1.y;
axispt.z = axis.pt2.z - axis.pt1.z;
p.x -= axis.pt1.x;
p.y -= axis.pt1.y;
p.z -= axis.pt1.z;
/* ---
 * normalize axispt
 * ---------------- */
axislen = sqrt( ((axispt.x)*(axispt.x))
          + ((axispt.y)*(axispt.y)) + ((axispt.z)*(axispt.z)) );
if ( axislen < 0.0000001 ) goto end_of_job; /* axis.pt2=axis.pt1 */
axispt.x /= axislen;
axispt.y /= axislen;
axispt.z /= axislen;
/* ---
 * apply rotation
 * -------------- */
costheta = cos(pi*theta/180.);
sintheta = sin(pi*theta/180);
r.x = r.y = r.z = 0.0;                  /* initialization */
/* --- x --- */
r.x += (costheta + (1.-costheta) * axispt.x * axispt.x)* p.x;
r.x += ((1.-costheta) * axispt.x * axispt.y - axispt.z * sintheta) * p.y;
r.x += ((1.-costheta) * axispt.x * axispt.z + axispt.y * sintheta) * p.z;
/* --- y --- */
r.y += ((1.-costheta) * axispt.x * axispt.y + axispt.z * sintheta) * p.x;
r.y += (costheta + (1.-costheta) * axispt.y * axispt.y)* p.y;
r.y += ((1.-costheta) * axispt.y * axispt.z - axispt.x * sintheta) * p.z;
/* --- z --- */
r.z += ((1.-costheta) * axispt.x * axispt.z - axispt.y * sintheta) * p.x;
r.z += ((1.-costheta) * axispt.y * axispt.z + axispt.x * sintheta) * p.y;
r.z += (costheta + (1.-costheta) * axispt.z * axispt.z)* p.z;
/* ---
 * translate rotated point back to original coords
 * ----------------------------------------------- */
r.x += axis.pt1.x;
r.y += axis.pt1.y;
r.z += axis.pt1.z;
/* ---
 * return rotated point to caller
 * ------------------------------ */
end_of_job:
  return ( r );
} /* --- end-of-function rotate3dpt --- */

-- 
John Forkosh  ( mailto:  j@f.com  where j=john and f=forkosh )

Back to comp.sys.ibm.pc.demos | Previous | Next — Previous in thread | Next in thread | Find similar

Thread

questions about rotating cube graphics in C++ (aiming for C) David Melik <dchmelik@hipplanet.com> - 2012-06-22 00:53 -0700
  figured part out; new questions David Melik <dchmelik@hipplanet.com> - 2012-06-22 03:19 -0700
    Re: figured part out; new questions David Melik <dchmelik@hipplanet.com> - 2012-06-22 04:33 -0700
      Re: figured part out; new questions Johann Klammer <klammerj@NOSPAM.a1.net> - 2012-06-24 00:40 +0200
        Re: figured part out; new questions David Melik <dchmelik@hipplanet.com> - 2012-06-23 19:29 -0700
          Re: figured part out; new questions Nobody <nobody@nowhere.com> - 2012-06-25 22:40 +0100
            Re: figured part out; new questions Hans-Bernhard Bröker <HBBroeker@t-online.de> - 2012-06-26 00:20 +0200
          Re: figured part out; new questions legalize+jeeves@mail.xmission.com (Richard) - 2012-06-29 18:59 +0000
        Re: figured part out; new questions David Melik <dchmelik@hipplanet.com> - 2012-06-23 19:36 -0700
          Re: figured part out; new questions JohnF <john@please.see.sig.for.email.com> - 2012-07-01 13:50 +0000
            Re: figured part out; new questions David Melik <dchmelik@hipplanet.com> - 2012-07-08 22:36 -0700

csiph-web