pcb 4.1.1
An interactive printed circuit board layout editor.

trackball.c

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00001 /*
00002  * (c) Copyright 1993, 1994, Silicon Graphics, Inc.
00003  * ALL RIGHTS RESERVED
00004  * Permission to use, copy, modify, and distribute this software for
00005  * any purpose and without fee is hereby granted, provided that the above
00006  * copyright notice appear in all copies and that both the copyright notice
00007  * and this permission notice appear in supporting documentation, and that
00008  * the name of Silicon Graphics, Inc. not be used in advertising
00009  * or publicity pertaining to distribution of the software without specific,
00010  * written prior permission.
00011  *
00012  * THE MATERIAL EMBODIED ON THIS SOFTWARE IS PROVIDED TO YOU "AS-IS"
00013  * AND WITHOUT WARRANTY OF ANY KIND, EXPRESS, IMPLIED OR OTHERWISE,
00014  * INCLUDING WITHOUT LIMITATION, ANY WARRANTY OF MERCHANTABILITY OR
00015  * FITNESS FOR A PARTICULAR PURPOSE.  IN NO EVENT SHALL SILICON
00016  * GRAPHICS, INC.  BE LIABLE TO YOU OR ANYONE ELSE FOR ANY DIRECT,
00017  * SPECIAL, INCIDENTAL, INDIRECT OR CONSEQUENTIAL DAMAGES OF ANY
00018  * KIND, OR ANY DAMAGES WHATSOEVER, INCLUDING WITHOUT LIMITATION,
00019  * LOSS OF PROFIT, LOSS OF USE, SAVINGS OR REVENUE, OR THE CLAIMS OF
00020  * THIRD PARTIES, WHETHER OR NOT SILICON GRAPHICS, INC.  HAS BEEN
00021  * ADVISED OF THE POSSIBILITY OF SUCH LOSS, HOWEVER CAUSED AND ON
00022  * ANY THEORY OF LIABILITY, ARISING OUT OF OR IN PAD_CONNECTION WITH THE
00023  * POSSESSION, USE OR PERFORMANCE OF THIS SOFTWARE.
00024  *
00025  * US Government Users Restricted Rights
00026  * Use, duplication, or disclosure by the Government is subject to
00027  * restrictions set forth in FAR 52.227.19(c)(2) or subparagraph
00028  * (c)(1)(ii) of the Rights in Technical Data and Computer Software
00029  * clause at DFARS 252.227-7013 and/or in similar or successor
00030  * clauses in the FAR or the DOD or NASA FAR Supplement.
00031  * Unpublished-- rights reserved under the copyright laws of the
00032  * United States.  Contractor/manufacturer is Silicon Graphics,
00033  * Inc., 2011 N.  Shoreline Blvd., Mountain View, CA 94039-7311.
00034  *
00035  * OpenGL(TM) is a trademark of Silicon Graphics, Inc.
00036  */
00037 /*
00038  * Trackball code:
00039  *
00040  * Implementation of a virtual trackball.
00041  * Implemented by Gavin Bell, lots of ideas from Thant Tessman and
00042  *   the August '88 issue of Siggraph's "Computer Graphics," pp. 121-129.
00043  *
00044  * Vector manip code:
00045  *
00046  * Original code from:
00047  * David M. Ciemiewicz, Mark Grossman, Henry Moreton, and Paul Haeberli
00048  *
00049  * Much mucking with by:
00050  * Gavin Bell
00051  */
00052 #include <math.h>
00053 #include "trackball.h"
00054 
00055 /*
00056  * This size should really be based on the distance from the center of
00057  * rotation to the point on the object underneath the mouse.  That
00058  * point would then track the mouse as closely as possible.  This is a
00059  * simple example, though, so that is left as an Exercise for the
00060  * Programmer.
00061  */
00062 #define TRACKBALLSIZE  (0.8f)
00063 
00064 /*
00065  * Local function prototypes (not defined in trackball.h)
00066  */
00067 static float tb_project_to_sphere(float, float, float);
00068 static void normalize_quat(float [4]);
00069 
00070 void
00071 vzero(float *v)
00072 {
00073     v[0] = 0.0;
00074     v[1] = 0.0;
00075     v[2] = 0.0;
00076 }
00077 
00078 void
00079 vset(float *v, float x, float y, float z)
00080 {
00081     v[0] = x;
00082     v[1] = y;
00083     v[2] = z;
00084 }
00085 
00086 void
00087 vsub(const float *src1, const float *src2, float *dst)
00088 {
00089     dst[0] = src1[0] - src2[0];
00090     dst[1] = src1[1] - src2[1];
00091     dst[2] = src1[2] - src2[2];
00092 }
00093 
00094 void
00095 vcopy(const float *v1, float *v2)
00096 {
00097     register int i;
00098     for (i = 0 ; i < 3 ; i++)
00099         v2[i] = v1[i];
00100 }
00101 
00102 void
00103 vcross(const float *v1, const float *v2, float *cross)
00104 {
00105     float temp[3];
00106 
00107     temp[0] = (v1[1] * v2[2]) - (v1[2] * v2[1]);
00108     temp[1] = (v1[2] * v2[0]) - (v1[0] * v2[2]);
00109     temp[2] = (v1[0] * v2[1]) - (v1[1] * v2[0]);
00110     vcopy(temp, cross);
00111 }
00112 
00113 float
00114 vlength(const float *v)
00115 {
00116     return (float) sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]);
00117 }
00118 
00119 void
00120 vscale(float *v, float div)
00121 {
00122     v[0] *= div;
00123     v[1] *= div;
00124     v[2] *= div;
00125 }
00126 
00127 void
00128 vnormal(float *v)
00129 {
00130     vscale(v, 1.0f/vlength(v));
00131 }
00132 
00133 float
00134 vdot(const float *v1, const float *v2)
00135 {
00136     return v1[0]*v2[0] + v1[1]*v2[1] + v1[2]*v2[2];
00137 }
00138 
00139 void
00140 vadd(const float *src1, const float *src2, float *dst)
00141 {
00142     dst[0] = src1[0] + src2[0];
00143     dst[1] = src1[1] + src2[1];
00144     dst[2] = src1[2] + src2[2];
00145 }
00146 
00147 /*
00148  * Ok, simulate a track-ball.  Project the points onto the virtual
00149  * trackball, then figure out the axis of rotation, which is the cross
00150  * product of P1 P2 and O P1 (O is the center of the ball, 0,0,0)
00151  * Note:  This is a deformed trackball-- is a trackball in the center,
00152  * but is deformed into a hyperbolic sheet of rotation away from the
00153  * center.  This particular function was chosen after trying out
00154  * several variations.
00155  *
00156  * It is assumed that the arguments to this routine are in the range
00157  * (-1.0 ... 1.0)
00158  */
00159 void
00160 trackball(float q[4], float p1x, float p1y, float p2x, float p2y)
00161 {
00162     float a[3]; /* Axis of rotation */
00163     float phi;  /* how much to rotate about axis */
00164     float p1[3], p2[3], d[3];
00165     float t;
00166 
00167     if (p1x == p2x && p1y == p2y) {
00168         /* Zero rotation */
00169         vzero(q);
00170         q[3] = 1.0;
00171         return;
00172     }
00173 
00174     /*
00175      * First, figure out z-coordinates for projection of P1 and P2 to
00176      * deformed sphere
00177      */
00178     vset(p1, p1x, p1y, tb_project_to_sphere(TRACKBALLSIZE, p1x, p1y));
00179     vset(p2, p2x, p2y, tb_project_to_sphere(TRACKBALLSIZE, p2x, p2y));
00180 
00181     /*
00182      *  Now, we want the cross product of P1 and P2
00183      */
00184     vcross(p2,p1,a);
00185 
00186     /*
00187      *  Figure out how much to rotate around that axis.
00188      */
00189     vsub(p1, p2, d);
00190     t = vlength(d) / (2.0f*TRACKBALLSIZE);
00191 
00192     /*
00193      * Avoid problems with out-of-control values...
00194      */
00195     if (t > 1.0) t = 1.0;
00196     if (t < -1.0) t = -1.0;
00197     phi = 2.0f * (float) asin(t);
00198 
00199     axis_to_quat(a,phi,q);
00200 }
00201 
00202 /*
00203  *  Given an axis and angle, compute quaternion.
00204  */
00205 void
00206 axis_to_quat(float a[3], float phi, float q[4])
00207 {
00208     vnormal(a);
00209     vcopy(a, q);
00210     vscale(q, (float) sin(phi/2.0));
00211     q[3] = (float) cos(phi/2.0);
00212 }
00213 
00214 /*
00215  * Project an x,y pair onto a sphere of radius r OR a hyperbolic sheet
00216  * if we are away from the center of the sphere.
00217  */
00218 static float
00219 tb_project_to_sphere(float r, float x, float y)
00220 {
00221     float d, t, z;
00222 
00223     d = hypotf(x, y);
00224     if (d < r * 0.70710678118654752440) {    /* Inside sphere */
00225         z = (float) sqrt(r*r - d*d);
00226     } else {           /* On hyperbola */
00227         t = r / 1.41421356237309504880f;
00228         z = t*t / d;
00229     }
00230     return z;
00231 }
00232 
00233 /*
00234  * Given two rotations, e1 and e2, expressed as quaternion rotations,
00235  * figure out the equivalent single rotation and stuff it into dest.
00236  *
00237  * This routine also normalizes the result every RENORMCOUNT times it is
00238  * called, to keep error from creeping in.
00239  *
00240  * NOTE: This routine is written so that q1 or q2 may be the same
00241  * as dest (or each other).
00242  */
00243 
00244 #define RENORMCOUNT 97
00245 
00246 void
00247 add_quats(float q1[4], float q2[4], float dest[4])
00248 {
00249     static int count=0;
00250     float t1[4], t2[4], t3[4];
00251     float tf[4];
00252 
00253     vcopy(q1,t1);
00254     vscale(t1,q2[3]);
00255 
00256     vcopy(q2,t2);
00257     vscale(t2,q1[3]);
00258 
00259     vcross(q2,q1,t3);
00260     vadd(t1,t2,tf);
00261     vadd(t3,tf,tf);
00262     tf[3] = q1[3] * q2[3] - vdot(q1,q2);
00263 
00264     dest[0] = tf[0];
00265     dest[1] = tf[1];
00266     dest[2] = tf[2];
00267     dest[3] = tf[3];
00268 
00269     if (++count > RENORMCOUNT) {
00270         count = 0;
00271         normalize_quat(dest);
00272     }
00273 }
00274 
00275 /*
00276  * Quaternions always obey:  a^2 + b^2 + c^2 + d^2 = 1.0
00277  * If they don't add up to 1.0, dividing by their magnitued will
00278  * renormalize them.
00279  *
00280  * Note: See the following for more information on quaternions:
00281  *
00282  * - Shoemake, K., Animating rotation with quaternion curves, Computer
00283  *   Graphics 19, No 3 (Proc. SIGGRAPH'85), 245-254, 1985.
00284  * - Pletinckx, D., Quaternion calculus as a basic tool in computer
00285  *   graphics, The Visual Computer 5, 2-13, 1989.
00286  */
00287 static void
00288 normalize_quat(float q[4])
00289 {
00290     int i;
00291     float mag;
00292 
00293     mag = (q[0]*q[0] + q[1]*q[1] + q[2]*q[2] + q[3]*q[3]);
00294     for (i = 0; i < 4; i++) q[i] /= mag;
00295 }
00296 
00297 /*
00298  * Build a rotation matrix, given a quaternion rotation.
00299  *
00300  */
00301 void
00302 build_rotmatrix(float m[4][4], float q[4])
00303 {
00304     m[0][0] = 1.0f - 2.0f * (q[1] * q[1] + q[2] * q[2]);
00305     m[0][1] = 2.0f * (q[0] * q[1] - q[2] * q[3]);
00306     m[0][2] = 2.0f * (q[2] * q[0] + q[1] * q[3]);
00307     m[0][3] = 0.0f;
00308 
00309     m[1][0] = 2.0f * (q[0] * q[1] + q[2] * q[3]);
00310     m[1][1]= 1.0f - 2.0f * (q[2] * q[2] + q[0] * q[0]);
00311     m[1][2] = 2.0f * (q[1] * q[2] - q[0] * q[3]);
00312     m[1][3] = 0.0f;
00313 
00314     m[2][0] = 2.0f * (q[2] * q[0] - q[1] * q[3]);
00315     m[2][1] = 2.0f * (q[1] * q[2] + q[0] * q[3]);
00316     m[2][2] = 1.0f - 2.0f * (q[1] * q[1] + q[0] * q[0]);
00317     m[2][3] = 0.0f;
00318 
00319     m[3][0] = 0.0f;
00320     m[3][1] = 0.0f;
00321     m[3][2] = 0.0f;
00322     m[3][3] = 1.0f;
00323 }
00324