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* (c) Copyright 1993, 1994, Silicon Graphics, Inc.
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* Permission to use, copy, modify, and distribute this software for
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* any purpose and without fee is hereby granted, provided that the above
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* copyright notice appear in all copies and that both the copyright notice
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* and this permission notice appear in supporting documentation, and that
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* the name of Silicon Graphics, Inc. not be used in advertising
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* or publicity pertaining to distribution of the software without specific,
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* written prior permission.
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* THE MATERIAL EMBODIED ON THIS SOFTWARE IS PROVIDED TO YOU "AS-IS"
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* AND WITHOUT WARRANTY OF ANY KIND, EXPRESS, IMPLIED OR OTHERWISE,
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* INCLUDING WITHOUT LIMITATION, ANY WARRANTY OF MERCHANTABILITY OR
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* FITNESS FOR A PARTICULAR PURPOSE. IN NO EVENT SHALL SILICON
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* GRAPHICS, INC. BE LIABLE TO YOU OR ANYONE ELSE FOR ANY DIRECT,
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* SPECIAL, INCIDENTAL, INDIRECT OR CONSEQUENTIAL DAMAGES OF ANY
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* KIND, OR ANY DAMAGES WHATSOEVER, INCLUDING WITHOUT LIMITATION,
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* LOSS OF PROFIT, LOSS OF USE, SAVINGS OR REVENUE, OR THE CLAIMS OF
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* THIRD PARTIES, WHETHER OR NOT SILICON GRAPHICS, INC. HAS BEEN
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* ADVISED OF THE POSSIBILITY OF SUCH LOSS, HOWEVER CAUSED AND ON
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* ANY THEORY OF LIABILITY, ARISING OUT OF OR IN CONNECTION WITH THE
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* POSSESSION, USE OR PERFORMANCE OF THIS SOFTWARE.
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* US Government Users Restricted Rights
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* Use, duplication, or disclosure by the Government is subject to
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* restrictions set forth in FAR 52.227.19(c)(2) or subparagraph
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* (c)(1)(ii) of the Rights in Technical Data and Computer Software
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* clause at DFARS 252.227-7013 and/or in similar or successor
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* clauses in the FAR or the DOD or NASA FAR Supplement.
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* Unpublished-- rights reserved under the copyright laws of the
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* United States. Contractor/manufacturer is Silicon Graphics,
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* Inc., 2011 N. Shoreline Blvd., Mountain View, CA 94039-7311.
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* OpenGL(TM) is a trademark of Silicon Graphics, Inc.
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* Implementation of a virtual trackball.
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* Implemented by Gavin Bell, lots of ideas from Thant Tessman and
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* the August '88 issue of Siggraph's "Computer Graphics," pp. 121-129.
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* David M. Ciemiewicz, Mark Grossman, Henry Moreton, and Paul Haeberli
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* Much mucking with by:
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#pragma warning (disable:4244) /* disable bogus conversion warnings */
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#include "trackball.h"
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* This size should really be based on the distance from the center of
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* rotation to the point on the object underneath the mouse. That
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* point would then track the mouse as closely as possible. This is a
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* simple example, though, so that is left as an Exercise for the
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#define TRACKBALLSIZE (0.8f)
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* Local function prototypes (not defined in trackball.h)
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static float tb_project_to_sphere(float, float, float);
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static void normalize_quat(float [4]);
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vset(float v[3], float x, float y, float z)
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vsub(const float src1[3], const float src2[3], float dst[3])
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dst[0] = src1[0] - src2[0];
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dst[1] = src1[1] - src2[1];
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dst[2] = src1[2] - src2[2];
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vcopy(const float v1[3], float v2[3])
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for (i = 0 ; i < 3 ; i++)
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vcross(const float v1[3], const float v2[3], float cross[3])
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temp[0] = (v1[1] * v2[2]) - (v1[2] * v2[1]);
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temp[1] = (v1[2] * v2[0]) - (v1[0] * v2[2]);
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temp[2] = (v1[0] * v2[1]) - (v1[1] * v2[0]);
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vlength(const float v[3])
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return sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]);
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vscale(float v[3], float div)
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vscale(v,1.0/vlength(v));
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vdot(const float v1[3], const float v2[3])
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return v1[0]*v2[0] + v1[1]*v2[1] + v1[2]*v2[2];
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vadd(const float src1[3], const float src2[3], float dst[3])
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dst[0] = src1[0] + src2[0];
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dst[1] = src1[1] + src2[1];
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dst[2] = src1[2] + src2[2];
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* Ok, simulate a track-ball. Project the points onto the virtual
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* trackball, then figure out the axis of rotation, which is the cross
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* product of P1 P2 and O P1 (O is the center of the ball, 0,0,0)
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* Note: This is a deformed trackball-- is a trackball in the center,
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* but is deformed into a hyperbolic sheet of rotation away from the
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* center. This particular function was chosen after trying out
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* several variations.
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* It is assumed that the arguments to this routine are in the range
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trackball(float q[4], float p1x, float p1y, float p2x, float p2y)
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float a[3]; /* Axis of rotation */
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float phi; /* how much to rotate about axis */
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float p1[3], p2[3], d[3];
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if (p1x == p2x && p1y == p2y) {
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* First, figure out z-coordinates for projection of P1 and P2 to
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vset(p1,p1x,p1y,tb_project_to_sphere(TRACKBALLSIZE,p1x,p1y));
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vset(p2,p2x,p2y,tb_project_to_sphere(TRACKBALLSIZE,p2x,p2y));
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* Now, we want the cross product of P1 and P2
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* Figure out how much to rotate around that axis.
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t = vlength(d) / (2.0*TRACKBALLSIZE);
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* Avoid problems with out-of-control values...
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if (t > 1.0) t = 1.0;
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if (t < -1.0) t = -1.0;
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axis_to_quat(a,phi,q);
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* Given an axis and angle, compute quaternion.
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axis_to_quat(const float a[3], float phi, float q[4])
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vscale(q, sin(phi/2.0));
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* Project an x,y pair onto a sphere of radius r OR a hyperbolic sheet
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* if we are away from the center of the sphere.
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tb_project_to_sphere(float r, float x, float y)
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if (d < r * 0.70710678118654752440) { /* Inside sphere */
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} else { /* On hyperbola */
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t = r / 1.41421356237309504880;
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* Given two rotations, e1 and e2, expressed as quaternion rotations,
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* figure out the equivalent single rotation and stuff it into dest.
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* This routine also normalizes the result every RENORMCOUNT times it is
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* called, to keep error from creeping in.
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* NOTE: This routine is written so that q1 or q2 may be the same
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* as dest (or each other).
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#define RENORMCOUNT 97
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add_quats(const float q1[4], const float q2[4], float dest[4])
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float t1[4], t2[4], t3[4];
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printf("q1 = %f %f %f %f\n", q1[0], q1[1], q1[2], q1[3]);
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printf("q2 = %f %f %f %f\n", q2[0], q2[1], q2[2], q2[3]);
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tf[3] = q1[3] * q2[3] - vdot(q1,q2);
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printf("tf = %f %f %f %f\n", tf[0], tf[1], tf[2], tf[3]);
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if (++count > RENORMCOUNT) {
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normalize_quat(dest);
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* Quaternions always obey: a^2 + b^2 + c^2 + d^2 = 1.0
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* If they don't add up to 1.0, dividing by their magnitued will
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* Note: See the following for more information on quaternions:
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* - Shoemake, K., Animating rotation with quaternion curves, Computer
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* Graphics 19, No 3 (Proc. SIGGRAPH'85), 245-254, 1985.
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* - Pletinckx, D., Quaternion calculus as a basic tool in computer
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* graphics, The Visual Computer 5, 2-13, 1989.
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normalize_quat(float q[4])
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mag = sqrt(q[0]*q[0] + q[1]*q[1] + q[2]*q[2] + q[3]*q[3]);
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for (i = 0; i < 4; i++)
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* Build a rotation matrix, given a quaternion rotation.
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build_rotmatrix(float m[4][4], const float q[4])
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m[0][0] = 1.0 - 2.0 * (q[1] * q[1] + q[2] * q[2]);
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m[0][1] = 2.0 * (q[0] * q[1] - q[2] * q[3]);
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m[0][2] = 2.0 * (q[2] * q[0] + q[1] * q[3]);
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m[1][0] = 2.0 * (q[0] * q[1] + q[2] * q[3]);
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m[1][1]= 1.0 - 2.0 * (q[2] * q[2] + q[0] * q[0]);
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m[1][2] = 2.0 * (q[1] * q[2] - q[0] * q[3]);
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m[2][0] = 2.0 * (q[2] * q[0] - q[1] * q[3]);
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m[2][1] = 2.0 * (q[1] * q[2] + q[0] * q[3]);
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m[2][2] = 1.0 - 2.0 * (q[1] * q[1] + q[0] * q[0]);
added
removed
progs/demos/trackball.c
