KiCad PCB EDA Suite
trackball.cpp
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37  * ====================================================================
38  * Code in this file has been modified by the KiCad project.
39  * For modifications:
40  * Copyright (C) 2016 KiCad Developers, see AUTHORS.txt for contributors.
41  */
42 /*
43  * Trackball code:
44  *
45  * Implementation of a virtual trackball.
46  * Implemented by Gavin Bell, lots of ideas from Thant Tessman and
47  * the August '88 issue of Siggraph's "Computer Graphics," pp. 121-129.
48  *
49  * Vector manip code:
50  *
51  * Original code from:
52  * David M. Ciemiewicz, Mark Grossman, Henry Moreton, and Paul Haeberli
53  *
54  * Much mucking with by:
55  * Gavin Bell
56  */
57 #include <cmath>
58 #include <trackball.h>
59 
60 /*
61  * This size should really be based on the distance from the center of
62  * rotation to the point on the object underneath the mouse. That
63  * point would then track the mouse as closely as possible. This is a
64  * simple example, though, so that is left as an Exercise for the
65  * Programmer.
66  */
67 #define TRACKBALLSIZE (0.8f)
68 
69 /*
70  * Local function prototypes (not defined in trackball.h)
71  */
72 static double tb_project_to_sphere( double, double, double );
73 static void normalize_quat( double [4] );
74 
75 void vzero( double *v )
76 {
77  v[0] = 0.0;
78  v[1] = 0.0;
79  v[2] = 0.0;
80 }
81 
82 void vset( double *v, double x, double y, double z )
83 {
84  v[0] = x;
85  v[1] = y;
86  v[2] = z;
87 }
88 
89 void vsub( const double *src1, const double *src2, double *dst )
90 {
91  dst[0] = src1[0] - src2[0];
92  dst[1] = src1[1] - src2[1];
93  dst[2] = src1[2] - src2[2];
94 }
95 
96 void vcopy( const double *v1, double *v2 )
97 {
98  int i;
99 
100  for( i = 0 ; i < 3 ; i++ )
101  v2[i] = v1[i];
102 }
103 
104 void vcross( const double *v1, const double *v2, double *cross )
105 {
106  double temp[3];
107 
108  temp[0] = (v1[1] * v2[2]) - (v1[2] * v2[1]);
109  temp[1] = (v1[2] * v2[0]) - (v1[0] * v2[2]);
110  temp[2] = (v1[0] * v2[1]) - (v1[1] * v2[0]);
111  vcopy(temp, cross);
112 }
113 
114 double vlength( const double *v )
115 {
116  return (double) sqrt( v[0] * v[0] + v[1] * v[1] + v[2] * v[2] );
117 }
118 
119 void vscale( double *v, double div )
120 {
121  v[0] *= div;
122  v[1] *= div;
123  v[2] *= div;
124 }
125 
126 void vnormal( double *v )
127 {
128  vscale( v, 1.0f / vlength( v ) );
129 }
130 
131 double vdot( const double *v1, const double *v2 )
132 {
133  return v1[0]*v2[0] + v1[1]*v2[1] + v1[2]*v2[2];
134 }
135 
136 void vadd( const double *src1, const double *src2, double *dst )
137 {
138  dst[0] = src1[0] + src2[0];
139  dst[1] = src1[1] + src2[1];
140  dst[2] = src1[2] + src2[2];
141 }
142 
143 /*
144  * Ok, simulate a track-ball. Project the points onto the virtual
145  * trackball, then figure out the axis of rotation, which is the cross
146  * product of P1 P2 and O P1 (O is the center of the ball, 0,0,0)
147  * Note: This is a deformed trackball-- is a trackball in the center,
148  * but is deformed into a hyperbolic sheet of rotation away from the
149  * center. This particular function was chosen after trying out
150  * several variations.
151  *
152  * It is assumed that the arguments to this routine are in the range
153  * (-1.0 ... 1.0)
154  */
155 void trackball( double q[4], double p1x, double p1y, double p2x, double p2y )
156 {
157  double a[3]; /* Axis of rotation */
158  double phi; /* how much to rotate about axis */
159  double p1[3], p2[3], d[3];
160  double t;
161 
162  if( p1x == p2x && p1y == p2y )
163  {
164  /* Zero rotation */
165  vzero( q );
166  q[3] = 1.0;
167  return;
168  }
169 
170  /*
171  * First, figure out z-coordinates for projection of P1 and P2 to
172  * deformed sphere
173  */
174  vset( p1, p1x, p1y, tb_project_to_sphere( TRACKBALLSIZE, p1x, p1y ) );
175  vset( p2, p2x, p2y, tb_project_to_sphere( TRACKBALLSIZE, p2x, p2y ) );
176 
177  /*
178  * Now, we want the cross product of P1 and P2
179  */
180  vcross(p2,p1,a);
181 
182  /*
183  * Figure out how much to rotate around that axis.
184  */
185  vsub( p1, p2, d );
186  t = vlength( d ) / (2.0f * TRACKBALLSIZE);
187 
188  /*
189  * Avoid problems with out-of-control values...
190  */
191  if( t > 1.0 )
192  t = 1.0;
193 
194  if( t < -1.0 )
195  t = -1.0;
196 
197  phi = 2.0f * (double) asin( t );
198 
199  axis_to_quat( a, phi, q );
200 }
201 
202 /*
203  * Given an axis and angle, compute quaternion.
204  */
205 void axis_to_quat( double a[3], double phi, double q[4] )
206 {
207  vnormal( a );
208  vcopy( a, q );
209  vscale( q, (double) sin( phi / 2.0) );
210  q[3] = (double) cos( phi / 2.0 );
211 }
212 
213 /*
214  * Project an x,y pair onto a sphere of radius r OR a hyperbolic sheet
215  * if we are away from the center of the sphere.
216  */
217 static double tb_project_to_sphere( double r, double x, double y )
218 {
219  double d, z;
220 
221  d = (double) sqrt( x*x + y*y );
222 
223  if( d < r * 0.70710678118654752440 )
224  { /* Inside sphere */
225  z = (double) sqrt( r*r - d*d );
226  }
227  else
228  { /* On hyperbola */
229  const double t = r / 1.41421356237309504880f;
230  z = t*t / d;
231  }
232 
233  return z;
234 }
235 
236 /*
237  * Given two rotations, e1 and e2, expressed as quaternion rotations,
238  * figure out the equivalent single rotation and stuff it into dest.
239  *
240  * This routine also normalizes the result every RENORMCOUNT times it is
241  * called, to keep error from creeping in.
242  *
243  * NOTE: This routine is written so that q1 or q2 may be the same
244  * as dest (or each other).
245  */
246 
247 #define RENORMCOUNT 97
248 
249 void add_quats( double q1[4], double q2[4], double dest[4] )
250 {
251  static int count=0;
252  double t1[4], t2[4], t3[4];
253  double tf[4];
254 
255  vcopy( q1, t1 );
256  vscale( t1, q2[3] );
257 
258  vcopy( q2, t2 );
259  vscale( t2, q1[3] );
260 
261  vcross( q2, q1, t3 );
262  vadd( t1, t2, tf );
263  vadd( t3, tf, tf );
264 
265  tf[3] = q1[3] * q2[3] - vdot( q1, q2 );
266 
267  dest[0] = tf[0];
268  dest[1] = tf[1];
269  dest[2] = tf[2];
270  dest[3] = tf[3];
271 
272  if( ++count > RENORMCOUNT )
273  {
274  count = 0;
275  normalize_quat( dest );
276  }
277 }
278 
279 /*
280  * Quaternions always obey: a^2 + b^2 + c^2 + d^2 = 1.0
281  * If they don't add up to 1.0, dividing by their magnitued will
282  * renormalize them.
283  *
284  * Note: See the following for more information on quaternions:
285  *
286  * - Shoemake, K., Animating rotation with quaternion curves, Computer
287  * Graphics 19, No 3 (Proc. SIGGRAPH'85), 245-254, 1985.
288  * - Pletinckx, D., Quaternion calculus as a basic tool in computer
289  * graphics, The Visual Computer 5, 2-13, 1989.
290  */
291 static void normalize_quat( double q[4] )
292 {
293  int i;
294  double mag;
295 
296  mag = (q[0]*q[0] + q[1]*q[1] + q[2]*q[2] + q[3]*q[3]);
297 
298  for( i = 0; i < 4; i++ )
299  q[i] /= mag;
300 }
301 
302 /*
303  * Build a rotation matrix, given a quaternion rotation.
304  *
305  */
306 void build_rotmatrix( float m[4][4], double q[4] )
307 {
308  m[0][0] = (float)(1.0 - 2.0 * (q[1] * q[1] + q[2] * q[2]));
309  m[0][1] = (float)(2.0 * (q[0] * q[1] - q[2] * q[3]));
310  m[0][2] = (float)(2.0 * (q[2] * q[0] + q[1] * q[3]));
311  m[0][3] = 0.0f;
312 
313  m[1][0] = (float)(2.0 * (q[0] * q[1] + q[2] * q[3]));
314  m[1][1] = (float)(1.0 - 2.0f * (q[2] * q[2] + q[0] * q[0]));
315  m[1][2] = (float)(2.0 * (q[1] * q[2] - q[0] * q[3]));
316  m[1][3] = 0.0f;
317 
318  m[2][0] = (float)(2.0 * (q[2] * q[0] - q[1] * q[3]));
319  m[2][1] = (float)(2.0 * (q[1] * q[2] + q[0] * q[3]));
320  m[2][2] = (float)(1.0 - 2.0 * (q[1] * q[1] + q[0] * q[0]));
321  m[2][3] = 0.0f;
322 
323  m[3][0] = 0.0f;
324  m[3][1] = 0.0f;
325  m[3][2] = 0.0f;
326  m[3][3] = 1.0f;
327 }
328 
static double tb_project_to_sphere(double, double, double)
Definition: trackball.cpp:217
void build_rotmatrix(float m[4][4], double q[4])
Definition: trackball.cpp:306
void axis_to_quat(double a[3], double phi, double q[4])
Definition: trackball.cpp:205
void trackball(double q[4], double p1x, double p1y, double p2x, double p2y)
Definition: trackball.cpp:155
void vscale(double *v, double div)
Definition: trackball.cpp:119
void vset(double *v, double x, double y, double z)
Definition: trackball.cpp:82
void vcross(const double *v1, const double *v2, double *cross)
Definition: trackball.cpp:104
double vlength(const double *v)
Definition: trackball.cpp:114
double vdot(const double *v1, const double *v2)
Definition: trackball.cpp:131
void vcopy(const double *v1, double *v2)
Definition: trackball.cpp:96
void add_quats(double q1[4], double q2[4], double dest[4])
Definition: trackball.cpp:249
void vadd(const double *src1, const double *src2, double *dst)
Definition: trackball.cpp:136
#define TRACKBALLSIZE
Definition: trackball.cpp:67
void vnormal(double *v)
Definition: trackball.cpp:126
double t
Definition: trace.cpp:1108
void vsub(const double *src1, const double *src2, double *dst)
Definition: trackball.cpp:89
void vzero(double *v)
Definition: trackball.cpp:75
static void normalize_quat(double[4])
Definition: trackball.cpp:291
#define RENORMCOUNT
Definition: trackball.cpp:247