Original Post
I've been using SGI's trackball code to rotate the view around objects with the mouse but I haven't been able to get it to work around an arbitrary center of rotation. Did they hard-code their trackball stuff so it only works around the origin? (if you don't know what I'm talking about the source is below) Can anyone point me to a good resource on how to achieve this effect? I don't care if it means moving away from SGI's code as long its easy (1-2 hours max) to implement. header source
/*
* (c) Copyright 1993, 1994, Silicon Graphics, Inc.
* ALL RIGHTS RESERVED
* Permission to use, copy, modify, and distribute this software for
* any purpose and without fee is hereby granted, provided that the above
* copyright notice appear in all copies and that both the copyright notice
* and this permission notice appear in supporting documentation, and that
* the name of Silicon Graphics, Inc. not be used in advertising
* or publicity pertaining to distribution of the software without specific,
* written prior permission.
*
* THE MATERIAL EMBODIED ON THIS SOFTWARE IS PROVIDED TO YOU "AS-IS"
* AND WITHOUT WARRANTY OF ANY KIND, EXPRESS, IMPLIED OR OTHERWISE,
* INCLUDING WITHOUT LIMITATION, ANY WARRANTY OF MERCHANTABILITY OR
* FITNESS FOR A PARTICULAR PURPOSE. IN NO EVENT SHALL SILICON
* GRAPHICS, INC. BE LIABLE TO YOU OR ANYONE ELSE FOR ANY DIRECT,
* SPECIAL, INCIDENTAL, INDIRECT OR CONSEQUENTIAL DAMAGES OF ANY
* KIND, OR ANY DAMAGES WHATSOEVER, INCLUDING WITHOUT LIMITATION,
* LOSS OF PROFIT, LOSS OF USE, SAVINGS OR REVENUE, OR THE CLAIMS OF
* THIRD PARTIES, WHETHER OR NOT SILICON GRAPHICS, INC. HAS BEEN
* ADVISED OF THE POSSIBILITY OF SUCH LOSS, HOWEVER CAUSED AND ON
* ANY THEORY OF LIABILITY, ARISING OUT OF OR IN CONNECTION WITH THE
* POSSESSION, USE OR PERFORMANCE OF THIS SOFTWARE.
*
* US Government Users Restricted Rights
* Use, duplication, or disclosure by the Government is subject to
* restrictions set forth in FAR 52.227.19(c)(2) or subparagraph
* (c)(1)(ii) of the Rights in Technical Data and Computer Software
* clause at DFARS 252.227-7013 and/or in similar or successor
* clauses in the FAR or the DOD or NASA FAR Supplement.
* Unpublished-- rights reserved under the copyright laws of the
* United States. Contractor/manufacturer is Silicon Graphics,
* Inc., 2011 N. Shoreline Blvd., Mountain View, CA 94039-7311.
*
* OpenGL(TM) is a trademark of Silicon Graphics, Inc.
*/
/*
* trackball.h
* A virtual trackball implementation
* Written by Gavin Bell for Silicon Graphics, November 1988.
*/
/*
* Pass the x and y coordinates of the last and current positions of
* the mouse, scaled so they are from (-1.0 ... 1.0).
*
* The resulting rotation is returned as a quaternion rotation in the
* first paramater.
*/
void
trackball(float q[4], float p1x, float p1y, float p2x, float p2y);
/*
* Given two quaternions, add them together to get a third quaternion.
* Adding quaternions to get a compound rotation is analagous to adding
* translations to get a compound translation. When incrementally
* adding rotations, the first argument here should be the new
* rotation, the second and third the total rotation (which will be
* over-written with the resulting new total rotation).
*/
void
add_quats(float *q1, float *q2, float *dest);
/*
* A useful function, builds a rotation matrix in Matrix based on
* given quaternion.
*/
void
build_rotmatrix(float m[4][4], float q[4]);
/*
* This function computes a quaternion based on an axis (defined by
* the given vector) and an angle about which to rotate. The angle is
* expressed in radians. The result is put into the third argument.
*/
void
axis_to_quat(float a[3], float phi, float q[4]);
/*
* (c) Copyright 1993, 1994, Silicon Graphics, Inc.
* ALL RIGHTS RESERVED
* Permission to use, copy, modify, and distribute this software for
* any purpose and without fee is hereby granted, provided that the above
* copyright notice appear in all copies and that both the copyright notice
* and this permission notice appear in supporting documentation, and that
* the name of Silicon Graphics, Inc. not be used in advertising
* or publicity pertaining to distribution of the software without specific,
* written prior permission.
*
* THE MATERIAL EMBODIED ON THIS SOFTWARE IS PROVIDED TO YOU "AS-IS"
* AND WITHOUT WARRANTY OF ANY KIND, EXPRESS, IMPLIED OR OTHERWISE,
* INCLUDING WITHOUT LIMITATION, ANY WARRANTY OF MERCHANTABILITY OR
* FITNESS FOR A PARTICULAR PURPOSE. IN NO EVENT SHALL SILICON
* GRAPHICS, INC. BE LIABLE TO YOU OR ANYONE ELSE FOR ANY DIRECT,
* SPECIAL, INCIDENTAL, INDIRECT OR CONSEQUENTIAL DAMAGES OF ANY
* KIND, OR ANY DAMAGES WHATSOEVER, INCLUDING WITHOUT LIMITATION,
* LOSS OF PROFIT, LOSS OF USE, SAVINGS OR REVENUE, OR THE CLAIMS OF
* THIRD PARTIES, WHETHER OR NOT SILICON GRAPHICS, INC. HAS BEEN
* ADVISED OF THE POSSIBILITY OF SUCH LOSS, HOWEVER CAUSED AND ON
* ANY THEORY OF LIABILITY, ARISING OUT OF OR IN CONNECTION WITH THE
* POSSESSION, USE OR PERFORMANCE OF THIS SOFTWARE.
*
* US Government Users Restricted Rights
* Use, duplication, or disclosure by the Government is subject to
* restrictions set forth in FAR 52.227.19(c)(2) or subparagraph
* (c)(1)(ii) of the Rights in Technical Data and Computer Software
* clause at DFARS 252.227-7013 and/or in similar or successor
* clauses in the FAR or the DOD or NASA FAR Supplement.
* Unpublished-- rights reserved under the copyright laws of the
* United States. Contractor/manufacturer is Silicon Graphics,
* Inc., 2011 N. Shoreline Blvd., Mountain View, CA 94039-7311.
*
* OpenGL(TM) is a trademark of Silicon Graphics, Inc.
*/
/*
* Trackball code:
*
* Implementation of a virtual trackball.
* Implemented by Gavin Bell, lots of ideas from Thant Tessman and
* the August '88 issue of Siggraph's "Computer Graphics," pp. 121-129.
*
* Vector manip code:
*
* Original code from:
* David M. Ciemiewicz, Mark Grossman, Henry Moreton, and Paul Haeberli
*
* Much mucking with by:
* Gavin Bell
*/
#include <math.h>
#include "trackball.h"
/*
* This size should really be based on the distance from the center of
* rotation to the point on the object underneath the mouse. That
* point would then track the mouse as closely as possible. This is a
* simple example, though, so that is left as an Exercise for the
* Programmer.
*/
#define TRACKBALLSIZE (0.8)
/*
* Local function prototypes (not defined in trackball.h)
*/
static float tb_project_to_sphere(float, float, float);
static void normalize_quat(float [4]);
void
vzero(float *v)
{
v[0] = 0.0;
v[1] = 0.0;
v[2] = 0.0;
}
void
vset(float *v, float x, float y, float z)
{
v[0] = x;
v[1] = y;
v[2] = z;
}
void
vsub(const float *src1, const float *src2, float *dst)
{
dst[0] = src1[0] - src2[0];
dst[1] = src1[1] - src2[1];
dst[2] = src1[2] - src2[2];
}
void
vcopy(const float *v1, float *v2)
{
register int i;
for (i = 0 ; i < 3 ; i++)
v2 = v1;
}
void
vcross(const float *v1, const float *v2, float *cross)
{
float temp[3];
temp[0] = (v1[1] * v2[2]) - (v1[2] * v2[1]);
temp[1] = (v1[2] * v2[0]) - (v1[0] * v2[2]);
temp[2] = (v1[0] * v2[1]) - (v1[1] * v2[0]);
vcopy(temp, cross);
}
float
vlength(const float *v)
{
return sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]);
}
void
vscale(float *v, float div)
{
v[0] *= div;
v[1] *= div;
v[2] *= div;
}
void
vnormal(float *v)
{
vscale(v,1.0/vlength(v));
}
float
vdot(const float *v1, const float *v2)
{
return v1[0]*v2[0] + v1[1]*v2[1] + v1[2]*v2[2];
}
void
vadd(const float *src1, const float *src2, float *dst)
{
dst[0] = src1[0] + src2[0];
dst[1] = src1[1] + src2[1];
dst[2] = src1[2] + src2[2];
}
/*
* Ok, simulate a track-ball. Project the points onto the virtual
* trackball, then figure out the axis of rotation, which is the cross
* product of P1 P2 and O P1 (O is the center of the ball, 0,0,0)
* Note: This is a deformed trackball-- is a trackball in the center,
* but is deformed into a hyperbolic sheet of rotation away from the
* center. This particular function was chosen after trying out
* several variations.
*
* It is assumed that the arguments to this routine are in the range
* (-1.0 ... 1.0)
*/
void
trackball(float q[4], float p1x, float p1y, float p2x, float p2y)
{
float a[3]; /* Axis of rotation */
float phi; /* how much to rotate about axis */
float p1[3], p2[3], d[3];
float t;
if (p1x == p2x && p1y == p2y) {
/* Zero rotation */
vzero(q);
q[3] = 1.0;
return;
}
/*
* First, figure out z-coordinates for projection of P1 and P2 to
* deformed sphere
*/
vset(p1,p1x,p1y,tb_project_to_sphere(TRACKBALLSIZE,p1x,p1y));
vset(p2,p2x,p2y,tb_project_to_sphere(TRACKBALLSIZE,p2x,p2y));
/*
* Now, we want the cross product of P1 and P2
*/
vcross(p2,p1,a);
/*
* Figure out how much to rotate around that axis.
*/
vsub(p1,p2,d);
t = vlength(d) / (2.0*TRACKBALLSIZE);
/*
* Avoid problems with out-of-control values...
*/
if (t > 1.0) t = 1.0;
if (t < -1.0) t = -1.0;
phi = 2.0 * asin(t);
axis_to_quat(a,phi,q);
}
/*
* Given an axis and angle, compute quaternion.
*/
void
axis_to_quat(float a[3], float phi, float q[4])
{
vnormal(a);
vcopy(a,q);
vscale(q,sin(phi/2.0));
q[3] = cos(phi/2.0);
}
/*
* Project an x,y pair onto a sphere of radius r OR a hyperbolic sheet
* if we are away from the center of the sphere.
*/
static float
tb_project_to_sphere(float r, float x, float y)
{
float d, t, z;
d = sqrt(x*x + y*y);
if (d < r * 0.70710678118654752440) { /* Inside sphere */
z = sqrt(r*r - d*d);
} else { /* On hyperbola */
t = r / 1.41421356237309504880;
z = t*t / d;
}
return z;
}
/*
* Given two rotations, e1 and e2, expressed as quaternion rotations,
* figure out the equivalent single rotation and stuff it into dest.
*
* This routine also normalizes the result every RENORMCOUNT times it is
* called, to keep error from creeping in.
*
* NOTE: This routine is written so that q1 or q2 may be the same
* as dest (or each other).
*/
#define RENORMCOUNT 97
void
add_quats(float q1[4], float q2[4], float dest[4])
{
static int count=0;
float t1[4], t2[4], t3[4];
float tf[4];
vcopy(q1,t1);
vscale(t1,q2[3]);
vcopy(q2,t2);
vscale(t2,q1[3]);
vcross(q2,q1,t3);
vadd(t1,t2,tf);
vadd(t3,tf,tf);
tf[3] = q1[3] * q2[3] - vdot(q1,q2);
dest[0] = tf[0];
dest[1] = tf[1];
dest[2] = tf[2];
dest[3] = tf[3];
if (++count > RENORMCOUNT) {
count = 0;
normalize_quat(dest);
}
}
/*
* Quaternions always obey: a^2 + b^2 + c^2 + d^2 = 1.0
* If they don't add up to 1.0, dividing by their magnitued will
* renormalize them.
*
* Note: See the following for more information on quaternions:
*
* - Shoemake, K., Animating rotation with quaternion curves, Computer
* Graphics 19, No 3 (Proc. SIGGRAPH'85), 245-254, 1985.
* - Pletinckx, D., Quaternion calculus as a basic tool in computer
* graphics, The Visual Computer 5, 2-13, 1989.
*/
static void
normalize_quat(float q[4])
{
int i;
float mag;
mag = (q[0]*q[0] + q[1]*q[1] + q[2]*q[2] + q[3]*q[3]);
for (i = 0; i < 4; i++) q /= mag;
}
/*
* Build a rotation matrix, given a quaternion rotation.
*
*/
void
build_rotmatrix(float m[4][4], float q[4])
{
m[0][0] = 1.0 - 2.0 * (q[1] * q[1] + q[2] * q[2]);
m[0][1] = 2.0 * (q[0] * q[1] - q[2] * q[3]);
m[0][2] = 2.0 * (q[2] * q[0] + q[1] * q[3]);
m[0][3] = 0.0;
m[1][0] = 2.0 * (q[0] * q[1] + q[2] * q[3]);
m[1][1]= 1.0 - 2.0 * (q[2] * q[2] + q[0] * q[0]);
m[1][2] = 2.0 * (q[1] * q[2] - q[0] * q[3]);
m[1][3] = 0.0;
m[2][0] = 2.0 * (q[2] * q[0] - q[1] * q[3]);
m[2][1] = 2.0 * (q[1] * q[2] + q[0] * q[3]);
m[2][2] = 1.0 - 2.0 * (q[1] * q[1] + q[0] * q[0]);
m[2][3] = 0.0;
m[3][0] = 0.0;
m[3][1] = 0.0;
m[3][2] = 0.0;
m[3][3] = 1.0;
}