KiCad PCB EDA Suite
trigo.cpp
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1 /*
2  * This program source code file is part of KiCad, a free EDA CAD application.
3  *
4  * Copyright (C) 2014 Jean-Pierre Charras, jp.charras at wanadoo.fr
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24 
30 #include <limits> // for numeric_limits
31 #include <stdlib.h> // for abs
32 #include <type_traits> // for swap
33 
34 #include <geometry/seg.h>
35 #include <math/util.h>
36 #include <math/vector2d.h> // for VECTOR2I
37 #include <trigo.h>
38 
39 // Returns true if the point P is on the segment S.
40 // faster than TestSegmentHit() because P should be exactly on S
41 // therefore works fine only for H, V and 45 deg segm (suitable for wires in eeschema)
42 bool IsPointOnSegment( const wxPoint& aSegStart, const wxPoint& aSegEnd,
43  const wxPoint& aTestPoint )
44 {
45  wxPoint vectSeg = aSegEnd - aSegStart; // Vector from S1 to S2
46  wxPoint vectPoint = aTestPoint - aSegStart; // Vector from S1 to P
47 
48  // Use long long here to avoid overflow in calculations
49  if( (long long) vectSeg.x * vectPoint.y - (long long) vectSeg.y * vectPoint.x )
50  return false; /* Cross product non-zero, vectors not parallel */
51 
52  if( ( (long long) vectSeg.x * vectPoint.x + (long long) vectSeg.y * vectPoint.y ) <
53  ( (long long) vectPoint.x * vectPoint.x + (long long) vectPoint.y * vectPoint.y ) )
54  return false; /* Point not on segment */
55 
56  return true;
57 }
58 
59 
60 // Returns true if the segment 1 intersected the segment 2.
61 bool SegmentIntersectsSegment( const wxPoint& a_p1_l1, const wxPoint& a_p2_l1,
62  const wxPoint& a_p1_l2, const wxPoint& a_p2_l2,
63  wxPoint* aIntersectionPoint )
64 {
65 
66  //We are forced to use 64bit ints because the internal units can overflow 32bit ints when
67  // multiplied with each other, the alternative would be to scale the units down (i.e. divide
68  // by a fixed number).
69  int64_t dX_a, dY_a, dX_b, dY_b, dX_ab, dY_ab;
70  int64_t num_a, num_b, den;
71 
72  //Test for intersection within the bounds of both line segments using line equations of the
73  // form:
74  // x_k(u_k) = u_k * dX_k + x_k(0)
75  // y_k(u_k) = u_k * dY_k + y_k(0)
76  // with 0 <= u_k <= 1 and k = [ a, b ]
77 
78  dX_a = int64_t{ a_p2_l1.x } - a_p1_l1.x;
79  dY_a = int64_t{ a_p2_l1.y } - a_p1_l1.y;
80  dX_b = int64_t{ a_p2_l2.x } - a_p1_l2.x;
81  dY_b = int64_t{ a_p2_l2.y } - a_p1_l2.y;
82  dX_ab = int64_t{ a_p1_l2.x } - a_p1_l1.x;
83  dY_ab = int64_t{ a_p1_l2.y } - a_p1_l1.y;
84 
85  den = dY_a * dX_b - dY_b * dX_a ;
86 
87  //Check if lines are parallel
88  if( den == 0 )
89  return false;
90 
91  num_a = dY_ab * dX_b - dY_b * dX_ab;
92  num_b = dY_ab * dX_a - dY_a * dX_ab;
93 
94  // Only compute the intersection point if requested
95  if( aIntersectionPoint )
96  {
97  *aIntersectionPoint = a_p1_l1;
98  aIntersectionPoint->x += KiROUND( dX_a * ( double )num_a / ( double )den );
99  aIntersectionPoint->y += KiROUND( dY_a * ( double )num_b / ( double )den );
100  }
101 
102  if( den < 0 )
103  {
104  den = -den;
105  num_a = -num_a;
106  num_b = -num_b;
107  }
108 
109  //Test sign( u_a ) and return false if negative
110  if( num_a < 0 )
111  return false;
112 
113  //Test sign( u_b ) and return false if negative
114  if( num_b < 0 )
115  return false;
116 
117  //Test to ensure (u_a <= 1)
118  if( num_a > den )
119  return false;
120 
121  //Test to ensure (u_b <= 1)
122  if( num_b > den )
123  return false;
124 
125  return true;
126 }
127 
128 
129 bool TestSegmentHit( const wxPoint& aRefPoint, const wxPoint& aStart, const wxPoint& aEnd,
130  int aDist )
131 {
132  int xmin = aStart.x;
133  int xmax = aEnd.x;
134  int ymin = aStart.y;
135  int ymax = aEnd.y;
136  wxPoint delta = aStart - aRefPoint;
137 
138  if( xmax < xmin )
139  std::swap( xmax, xmin );
140 
141  if( ymax < ymin )
142  std::swap( ymax, ymin );
143 
144  // First, check if we are outside of the bounding box
145  if( ( ymin - aRefPoint.y > aDist ) || ( aRefPoint.y - ymax > aDist ) )
146  return false;
147 
148  if( ( xmin - aRefPoint.x > aDist ) || ( aRefPoint.x - xmax > aDist ) )
149  return false;
150 
151  // Next, eliminate easy cases
152  if( aStart.x == aEnd.x && aRefPoint.y > ymin && aRefPoint.y < ymax )
153  return std::abs( delta.x ) <= aDist;
154 
155  if( aStart.y == aEnd.y && aRefPoint.x > xmin && aRefPoint.x < xmax )
156  return std::abs( delta.y ) <= aDist;
157 
158  SEG segment( aStart, aEnd );
159  return segment.SquaredDistance( aRefPoint ) < SEG::Square( aDist + 1 );
160 }
161 
162 
163 const VECTOR2I GetArcMid( const VECTOR2I& aStart, const VECTOR2I& aEnd, const VECTOR2I& aCenter,
164  bool aMinArcAngle )
165 {
166  VECTOR2I startVector = aStart - aCenter;
167  VECTOR2I endVector = aEnd - aCenter;
168 
169  double startAngle = ArcTangente( startVector.y, startVector.x );
170  double endAngle = ArcTangente( endVector.y, endVector.x );
171  double midPointRotAngleDeciDeg = NormalizeAngle180( startAngle - endAngle ) / 2;
172 
173  if( !aMinArcAngle )
174  midPointRotAngleDeciDeg += 1800.0;
175 
176  VECTOR2I newMid = aStart;
177  RotatePoint( newMid, aCenter, midPointRotAngleDeciDeg );
178 
179  return newMid;
180 }
181 
182 
183 double ArcTangente( int dy, int dx )
184 {
185 
186  /* gcc is surprisingly smart in optimizing these conditions in
187  a tree! */
188 
189  if( dx == 0 && dy == 0 )
190  return 0;
191 
192  if( dy == 0 )
193  {
194  if( dx >= 0 )
195  return 0;
196  else
197  return -1800;
198  }
199 
200  if( dx == 0 )
201  {
202  if( dy >= 0 )
203  return 900;
204  else
205  return -900;
206  }
207 
208  if( dx == dy )
209  {
210  if( dx >= 0 )
211  return 450;
212  else
213  return -1800 + 450;
214  }
215 
216  if( dx == -dy )
217  {
218  if( dx >= 0 )
219  return -450;
220  else
221  return 1800 - 450;
222  }
223 
224  // Of course dy and dx are treated as double
225  return RAD2DECIDEG( std::atan2( (double) dy, (double) dx ) );
226 }
227 
228 
229 void RotatePoint( int* pX, int* pY, double angle )
230 {
231  int tmp;
232 
234 
235  // Cheap and dirty optimizations for 0, 90, 180, and 270 degrees.
236  if( angle == 0 )
237  return;
238 
239  if( angle == 900 ) /* sin = 1, cos = 0 */
240  {
241  tmp = *pX;
242  *pX = *pY;
243  *pY = -tmp;
244  }
245  else if( angle == 1800 ) /* sin = 0, cos = -1 */
246  {
247  *pX = -*pX;
248  *pY = -*pY;
249  }
250  else if( angle == 2700 ) /* sin = -1, cos = 0 */
251  {
252  tmp = *pX;
253  *pX = -*pY;
254  *pY = tmp;
255  }
256  else
257  {
258  double fangle = DECIDEG2RAD( angle );
259  double sinus = sin( fangle );
260  double cosinus = cos( fangle );
261  double fpx = (*pY * sinus ) + (*pX * cosinus );
262  double fpy = (*pY * cosinus ) - (*pX * sinus );
263  *pX = KiROUND( fpx );
264  *pY = KiROUND( fpy );
265  }
266 }
267 
268 
269 void RotatePoint( int* pX, int* pY, int cx, int cy, double angle )
270 {
271  int ox, oy;
272 
273  ox = *pX - cx;
274  oy = *pY - cy;
275 
276  RotatePoint( &ox, &oy, angle );
277 
278  *pX = ox + cx;
279  *pY = oy + cy;
280 }
281 
282 
283 void RotatePoint( wxPoint* point, const wxPoint& centre, double angle )
284 {
285  int ox, oy;
286 
287  ox = point->x - centre.x;
288  oy = point->y - centre.y;
289 
290  RotatePoint( &ox, &oy, angle );
291  point->x = ox + centre.x;
292  point->y = oy + centre.y;
293 }
294 
295 void RotatePoint( VECTOR2I& point, const VECTOR2I& centre, double angle )
296 {
297  wxPoint c( centre.x, centre.y );
298  wxPoint p( point.x, point.y );
299 
300  RotatePoint(&p, c, angle);
301 
302  point.x = p.x;
303  point.y = p.y;
304 }
305 
306 
307 void RotatePoint( double* pX, double* pY, double cx, double cy, double angle )
308 {
309  double ox, oy;
310 
311  ox = *pX - cx;
312  oy = *pY - cy;
313 
314  RotatePoint( &ox, &oy, angle );
315 
316  *pX = ox + cx;
317  *pY = oy + cy;
318 }
319 
320 
321 void RotatePoint( double* pX, double* pY, double angle )
322 {
323  double tmp;
324 
326 
327  // Cheap and dirty optimizations for 0, 90, 180, and 270 degrees.
328  if( angle == 0 )
329  return;
330 
331  if( angle == 900 ) /* sin = 1, cos = 0 */
332  {
333  tmp = *pX;
334  *pX = *pY;
335  *pY = -tmp;
336  }
337  else if( angle == 1800 ) /* sin = 0, cos = -1 */
338  {
339  *pX = -*pX;
340  *pY = -*pY;
341  }
342  else if( angle == 2700 ) /* sin = -1, cos = 0 */
343  {
344  tmp = *pX;
345  *pX = -*pY;
346  *pY = tmp;
347  }
348  else
349  {
350  double fangle = DECIDEG2RAD( angle );
351  double sinus = sin( fangle );
352  double cosinus = cos( fangle );
353 
354  double fpx = (*pY * sinus ) + (*pX * cosinus );
355  double fpy = (*pY * cosinus ) - (*pX * sinus );
356  *pX = fpx;
357  *pY = fpy;
358  }
359 }
360 
361 
362 const wxPoint GetArcCenter( const VECTOR2I& aStart, const VECTOR2I& aEnd, double aAngle )
363 {
364  VECTOR2I start = aStart;
365  VECTOR2I end = aEnd;
366 
367  if( aAngle < 0 )
368  {
369  std::swap( start, end );
370  aAngle = abs( aAngle );
371  }
372 
373  if( aAngle > 180 )
374  {
375  std::swap( start, end );
376  aAngle = 360 - aAngle;
377  }
378 
379  int chord = ( start - end ).EuclideanNorm();
380  int r = ( chord / 2 ) / sin( aAngle * M_PI / 360.0 );
381 
382  VECTOR2I vec = end - start;
383  vec = vec.Resize( r );
384  vec = vec.Rotate( ( 180.0 - aAngle ) * M_PI / 360.0 );
385 
386  return (wxPoint) ( start + vec );
387 }
388 
389 
390 const VECTOR2D GetArcCenter( const VECTOR2D& aStart, const VECTOR2D& aMid, const VECTOR2D& aEnd )
391 {
392  VECTOR2D center;
393  double yDelta_21 = aMid.y - aStart.y;
394  double xDelta_21 = aMid.x - aStart.x;
395  double yDelta_32 = aEnd.y - aMid.y;
396  double xDelta_32 = aEnd.x - aMid.x;
397 
398  // This is a special case for aMid as the half-way point when aSlope = 0 and bSlope = inf
399  // or the other way around. In that case, the center lies in a straight line between
400  // aStart and aEnd
401  if( ( ( xDelta_21 == 0.0 ) && ( yDelta_32 == 0.0 ) ) ||
402  ( ( yDelta_21 == 0.0 ) && ( xDelta_32 == 0.0 ) ) )
403  {
404  center.x = ( aStart.x + aEnd.x ) / 2.0;
405  center.y = ( aStart.y + aEnd.y ) / 2.0 ;
406  return center;
407  }
408 
409  // Prevent div=0 errors
410  if( xDelta_21 == 0.0 )
411  xDelta_21 = std::numeric_limits<double>::epsilon();
412 
413  if( xDelta_32 == 0.0 )
414  xDelta_32 = -std::numeric_limits<double>::epsilon();
415 
416  double aSlope = yDelta_21 / xDelta_21;
417  double bSlope = yDelta_32 / xDelta_32;
418 
419  if( aSlope == bSlope )
420  {
421  if( aStart == aEnd )
422  {
423  // This is a special case for a 360 degrees arc. In this case, the center is halfway between
424  // the midpoint and either end point
425  center.x = ( aStart.x + aMid.x ) / 2.0;
426  center.y = ( aStart.y + aMid.y ) / 2.0 ;
427  return center;
428  }
429  else
430  {
431  // If the points are colinear, the center is at infinity, so offset
432  // the slope by a minimal amount
433  // Warning: This will induce a small error in the center location
434  aSlope += std::numeric_limits<double>::epsilon();
435  bSlope -= std::numeric_limits<double>::epsilon();
436  }
437  }
438 
439  // Prevent divide by zero error
440  if( aSlope == 0.0 )
441  aSlope = std::numeric_limits<double>::epsilon();
442 
443  center.x = ( aSlope * bSlope * ( aStart.y - aEnd.y ) +
444  bSlope * ( aStart.x + aMid.x ) -
445  aSlope * ( aMid.x + aEnd.x ) ) / ( 2 * ( bSlope - aSlope ) );
446 
447  center.y = ( ( ( aStart.x + aMid.x ) / 2.0 - center.x ) / aSlope +
448  ( aStart.y + aMid.y ) / 2.0 );
449 
450  return center;
451 }
452 
453 
454 const VECTOR2I GetArcCenter( const VECTOR2I& aStart, const VECTOR2I& aMid, const VECTOR2I& aEnd )
455 {
456  VECTOR2D dStart( static_cast<double>( aStart.x ), static_cast<double>( aStart.y ) );
457  VECTOR2D dMid( static_cast<double>( aMid.x ), static_cast<double>( aMid.y ) );
458  VECTOR2D dEnd( static_cast<double>( aEnd.x ), static_cast<double>( aEnd.y ) );
459  VECTOR2D dCenter = GetArcCenter( dStart, dMid, dEnd );
460 
461  VECTOR2I iCenter;
462 
463  iCenter.x = KiROUND( Clamp<double>( double( std::numeric_limits<int>::min() / 2.0 ),
464  dCenter.x,
465  double( std::numeric_limits<int>::max() / 2.0 ) ) );
466 
467  iCenter.y = KiROUND( Clamp<double>( double( std::numeric_limits<int>::min() / 2.0 ),
468  dCenter.y,
469  double( std::numeric_limits<int>::max() / 2.0 ) ) );
470 
471  return iCenter;
472 }
473 
474 
475 const wxPoint GetArcCenter( const wxPoint& aStart, const wxPoint& aMid, const wxPoint& aEnd )
476 {
477  VECTOR2D dStart( static_cast<double>( aStart.x ), static_cast<double>( aStart.y ) );
478  VECTOR2D dMid( static_cast<double>( aMid.x ), static_cast<double>( aMid.y ) );
479  VECTOR2D dEnd( static_cast<double>( aEnd.x ), static_cast<double>( aEnd.y ) );
480  VECTOR2D dCenter = GetArcCenter( dStart, dMid, dEnd );
481 
482  wxPoint iCenter;
483 
484  iCenter.x = KiROUND( Clamp<double>( double( std::numeric_limits<int>::min() / 2.0 ),
485  dCenter.x,
486  double( std::numeric_limits<int>::max() / 2.0 ) ) );
487 
488  iCenter.y = KiROUND( Clamp<double>( double( std::numeric_limits<int>::min() / 2.0 ),
489  dCenter.y,
490  double( std::numeric_limits<int>::max() / 2.0 ) ) );
491 
492  return iCenter;
493 }
494 
495 
496 double GetArcAngle( const VECTOR2I& aStart, const VECTOR2I& aMid, const VECTOR2I& aEnd )
497 {
498  VECTOR2I center = GetArcCenter( aStart, aMid, aEnd );
499 
500  // Check if the new arc is CW or CCW
501  VECTOR2D startLine = aStart - center;
502  VECTOR2D endLine = aEnd - center;
503  double angle = RAD2DECIDEG( endLine.Angle() - startLine.Angle() );
504 
505  VECTOR2D v1, v2;
506  v1 = aStart - aMid;
507  v2 = aEnd - aMid;
508  double theta = RAD2DECIDEG( v1.Angle() );
509 
510  RotatePoint( &( v1.x ), &( v1.y ), theta );
511  RotatePoint( &( v2.x ), &( v2.y ), theta );
512 
513  bool clockwise = ( ( v1.Angle() - v2.Angle() ) > 0 );
514 
515  // Normalize the angle
516  if( clockwise && angle < 0.0 )
517  angle += 3600.0;
518  else if( !clockwise && angle > 0.0 )
519  angle -= 3600.0;
520 
521  return angle;
522 }
double EuclideanNorm(const wxPoint &vector)
Euclidean norm of a 2D vector.
Definition: trigo.h:146
bool IsPointOnSegment(const wxPoint &aSegStart, const wxPoint &aSegEnd, const wxPoint &aTestPoint)
Test if aTestPoint is on line defined by aSegStart and aSegEnd.
Definition: trigo.cpp:42
VECTOR2I v2(1, 0)
Test suite for KiCad math code.
const wxPoint GetArcCenter(const VECTOR2I &aStart, const VECTOR2I &aEnd, double aAngle)
Definition: trigo.cpp:362
const VECTOR2I GetArcMid(const VECTOR2I &aStart, const VECTOR2I &aEnd, const VECTOR2I &aCenter, bool aMinArcAngle)
Return the middle point of an arc, half-way between aStart and aEnd.
Definition: trigo.cpp:163
double GetArcAngle(const VECTOR2I &aStart, const VECTOR2I &aMid, const VECTOR2I &aEnd)
Return the subtended angle for a given arc.
Definition: trigo.cpp:496
Define a general 2D-vector/point.
Definition: vector2d.h:61
double RAD2DECIDEG(double rad)
Definition: trigo.h:234
ecoord SquaredDistance(const SEG &aSeg) const
Definition: seg.cpp:39
void RotatePoint(int *pX, int *pY, double angle)
Definition: trigo.cpp:229
void NORMALIZE_ANGLE_POS(T &Angle)
Definition: trigo.h:290
static SEG::ecoord Square(int a)
Definition: seg.h:122
T NormalizeAngle180(T Angle)
Normalize angle to be in the -180.0 .. 180.0 range.
Definition: trigo.h:387
double ArcTangente(int dy, int dx)
Definition: trigo.cpp:183
double Angle() const
Compute the angle of the vector.
Definition: vector2d.h:307
Definition: seg.h:40
VECTOR2< T > Resize(T aNewLength) const
Return a vector of the same direction, but length specified in aNewLength.
Definition: vector2d.h:404
VECTOR2< T > Rotate(double aAngle) const
Rotate the vector by a given angle.
Definition: vector2d.h:371
static DIRECTION_45::AngleType angle(const VECTOR2I &a, const VECTOR2I &b)
double DECIDEG2RAD(double deg)
Definition: trigo.h:233
bool SegmentIntersectsSegment(const wxPoint &a_p1_l1, const wxPoint &a_p2_l1, const wxPoint &a_p1_l2, const wxPoint &a_p2_l2, wxPoint *aIntersectionPoint)
Test if two lines intersect.
Definition: trigo.cpp:61
constexpr ret_type KiROUND(fp_type v)
Round a floating point number to an integer using "round halfway cases away from zero".
Definition: util.h:73
bool TestSegmentHit(const wxPoint &aRefPoint, const wxPoint &aStart, const wxPoint &aEnd, int aDist)
Test if aRefPoint is with aDistance on the line defined by aStart and aEnd.
Definition: trigo.cpp:129
constexpr int delta