KiCad PCB EDA Suite
shape_arc.cpp
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6  * @author Tomasz Wlostowski <tomasz.wlostowski@cern.ch>
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25 
27 #include <geometry/seg.h> // for SEG
28 #include <geometry/shape_arc.h>
30 #include <trigo.h>
31 
32 
33 SHAPE_ARC::SHAPE_ARC( const VECTOR2I& aArcCenter, const VECTOR2I& aArcStartPoint,
34  double aCenterAngle, int aWidth ) :
35  SHAPE( SH_ARC ), m_width( aWidth )
36 {
37  m_start = aArcStartPoint;
38  m_mid = aArcStartPoint;
39  m_end = aArcStartPoint;
40 
41  RotatePoint( m_mid, aArcCenter, -aCenterAngle * 10.0 / 2.0 );
42  RotatePoint( m_end, aArcCenter, -aCenterAngle * 10.0 );
43 
44  update_bbox();
45 }
46 
47 
48 SHAPE_ARC::SHAPE_ARC( const VECTOR2I& aArcStart, const VECTOR2I& aArcMid,
49  const VECTOR2I& aArcEnd, int aWidth ) :
50  SHAPE( SH_ARC ), m_start( aArcStart ), m_mid( aArcMid ), m_end( aArcEnd ),
51  m_width( aWidth )
52 {
53  update_bbox();
54 }
55 
56 
57 SHAPE_ARC::SHAPE_ARC( const SEG& aSegmentA, const SEG& aSegmentB, int aRadius, int aWidth )
58  : SHAPE( SH_ARC )
59 {
60  m_width = aWidth;
61 
62  /*
63  * Construct an arc that is tangent to two segments with a given radius.
64  *
65  * p
66  * A
67  * A \
68  * / \
69  * / . . \ segB
70  * /. .\
71  * segA / c \
72  * / B
73  * /
74  * /
75  * B
76  *
77  *
78  * segA is the fist segment (with its points A and B)
79  * segB is the second segment (with its points A and B)
80  * p is the point at which segA and segB would intersect if they were projected
81  * c is the centre of the arc to be constructed
82  * rad is the radius of the arc to be constructed
83  *
84  * We can create two vectors, betweeen point p and segA /segB
85  * pToA = p - segA.B //< note that segA.A would also be valid as it is colinear
86  * pToB = p - segB.B //< note that segB.A would also be valid as it is colinear
87  *
88  * Let the angle formed by segA and segB be called 'alpha':
89  * alpha = angle( pToA ) - angle( pToB )
90  *
91  * The distance PC can be computed as
92  * distPC = rad / abs( sin( alpha / 2 ) )
93  *
94  * The polar angle of the vector PC can be computed as:
95  * anglePC = angle( pToA ) + alpha / 2
96  *
97  * Therefore:
98  * C.x = P.x + distPC*cos( anglePC )
99  * C.y = P.y + distPC*sin( anglePC )
100  */
101 
102  OPT_VECTOR2I p = aSegmentA.Intersect( aSegmentB, true, true );
103 
104  if( !p || aSegmentA.Length() == 0 || aSegmentB.Length() == 0 )
105  {
106  // Catch bugs in debug
107  wxASSERT_MSG( false, "The input segments do not intersect or one is zero length." );
108 
109  // Make a 180 degree arc around aSegmentA in case we end up here in release
110  m_start = aSegmentA.A;
111  m_end = aSegmentA.B;
112  m_mid = m_start;
113 
114  VECTOR2I arcCenter = aSegmentA.Center();
115  RotatePoint( m_mid, arcCenter, 900.0 ); // mid point at 90 degrees
116  }
117  else
118  {
119  VECTOR2I pToA = aSegmentA.B - p.get();
120  VECTOR2I pToB = aSegmentB.B - p.get();
121 
122  if( pToA.EuclideanNorm() == 0 )
123  pToA = aSegmentA.A - p.get();
124 
125  if( pToB.EuclideanNorm() == 0 )
126  pToB = aSegmentB.A - p.get();
127 
128  double pToAangle = ArcTangente( pToA.y, pToA.x );
129  double pToBangle = ArcTangente( pToB.y, pToB.x );
130 
131  double alpha = NormalizeAngle180( pToAangle - pToBangle );
132 
133  double distPC = (double) aRadius / abs( sin( DECIDEG2RAD( alpha / 2 ) ) );
134  double angPC = pToAangle - alpha / 2;
135 
136  VECTOR2I arcCenter;
137 
138  arcCenter.x = p.get().x + KiROUND( distPC * cos( DECIDEG2RAD( angPC ) ) );
139  arcCenter.y = p.get().y + KiROUND( distPC * sin( DECIDEG2RAD( angPC ) ) );
140 
141  // The end points of the arc are the orthogonal projected lines from the line segments
142  // to the center of the arc
143  m_start = aSegmentA.LineProject( arcCenter );
144  m_end = aSegmentB.LineProject( arcCenter );
145 
146  //The mid point is rotated start point around center, half the angle of the arc.
147  VECTOR2I startVector = m_start - arcCenter;
148  VECTOR2I endVector = m_end - arcCenter;
149 
150  double startAngle = ArcTangente( startVector.y, startVector.x );
151  double endAngle = ArcTangente( endVector.y, endVector.x );
152 
153  double midPointRotAngle = NormalizeAngle180( startAngle - endAngle ) / 2;
154  m_mid = m_start;
155  RotatePoint( m_mid, arcCenter, midPointRotAngle );
156  }
157 
158  update_bbox();
159 }
160 
161 
163  : SHAPE( SH_ARC )
164 {
165  m_start = aOther.m_start;
166  m_end = aOther.m_end;
167  m_mid = aOther.m_mid;
168  m_width = aOther.m_width;
169  m_bbox = aOther.m_bbox;
170 }
171 
172 
174  double aAngle, double aWidth )
175 {
176  m_start = aStart;
177  m_mid = aStart;
178  m_end = aEnd;
179  m_width = aWidth;
180 
181  VECTOR2I center( GetArcCenter( aStart, aEnd, aAngle ) );
182 
183  RotatePoint( m_mid, center, -aAngle * 10.0 / 2.0 );
184 
185  update_bbox();
186 
187  return *this;
188 }
189 
190 
191 bool SHAPE_ARC::Collide( const SEG& aSeg, int aClearance, int* aActual, VECTOR2I* aLocation ) const
192 {
193  int minDist = aClearance + m_width / 2;
194  VECTOR2I center = GetCenter();
195  ecoord dist_sq;
196  ecoord closest_dist_sq = VECTOR2I::ECOORD_MAX;
197  VECTOR2I nearest;
198 
199  VECTOR2I ab = ( aSeg.B - aSeg.A );
200  VECTOR2I ac = ( center - aSeg.A );
201 
202  ecoord lenAbSq = ab.SquaredEuclideanNorm();
203  double lambda = (double) ac.Dot( ab ) / (double) lenAbSq;
204 
205  if( lambda >= 0.0 && lambda <= 1.0 )
206  {
207  VECTOR2I p;
208 
209  p.x = (double) aSeg.A.x * lambda + (double) aSeg.B.x * (1.0 - lambda);
210  p.y = (double) aSeg.A.y * lambda + (double) aSeg.B.y * (1.0 - lambda);
211 
212  dist_sq = ( m_start - p ).SquaredEuclideanNorm();
213 
214  if( dist_sq < closest_dist_sq )
215  {
216  closest_dist_sq = dist_sq;
217  nearest = p;
218  }
219 
220  dist_sq = ( m_end - p ).SquaredEuclideanNorm();
221 
222  if( dist_sq < closest_dist_sq )
223  {
224  closest_dist_sq = dist_sq;
225  nearest = p;
226  }
227  }
228 
229  dist_sq = aSeg.SquaredDistance( m_start );
230 
231  if( dist_sq < closest_dist_sq )
232  {
233  closest_dist_sq = dist_sq;
234  nearest = m_start;
235  }
236 
237  dist_sq = aSeg.SquaredDistance( m_end );
238 
239  if( dist_sq < closest_dist_sq )
240  {
241  closest_dist_sq = dist_sq;
242  nearest = m_end;
243  }
244 
245  if( closest_dist_sq == 0 || closest_dist_sq < SEG::Square( minDist ) )
246  {
247  if( aLocation )
248  *aLocation = nearest;
249 
250  if( aActual )
251  *aActual = std::max( 0, (int) sqrt( closest_dist_sq ) - m_width / 2 );
252 
253  return true;
254  }
255 
256  return false;
257 }
258 
259 
261 {
262  std::vector<VECTOR2I> points;
263  // Put start and end points in the point list
264  points.push_back( m_start );
265  points.push_back( m_end );
266 
267  double start_angle = GetStartAngle();
268  double end_angle = start_angle + GetCentralAngle();
269 
270  // we always count quadrants clockwise (increasing angle)
271  if( start_angle > end_angle )
272  std::swap( start_angle, end_angle );
273 
274  int quad_angle_start = std::ceil( start_angle / 90.0 );
275  int quad_angle_end = std::floor( end_angle / 90.0 );
276 
277  // count through quadrants included in arc
278  for( int quad_angle = quad_angle_start; quad_angle <= quad_angle_end; ++quad_angle )
279  {
280  const int radius = KiROUND( GetRadius() );
281  VECTOR2I quad_pt = GetCenter();
282 
283  switch( quad_angle % 4 )
284  {
285  case 0: quad_pt += { radius, 0 }; break;
286  case 1:
287  case -3: quad_pt += { 0, radius }; break;
288  case 2:
289  case -2: quad_pt += { -radius, 0 }; break;
290  case 3:
291  case -1: quad_pt += { 0, -radius }; break;
292  default: assert( false );
293  }
294 
295  points.push_back( quad_pt );
296  }
297 
298  m_bbox.Compute( points );
299 }
300 
301 
302 const BOX2I SHAPE_ARC::BBox( int aClearance ) const
303 {
304  BOX2I bbox( m_bbox );
305 
306  if( aClearance != 0 )
307  bbox.Inflate( aClearance );
308 
309  return bbox;
310 }
311 
312 
313 bool SHAPE_ARC::Collide( const VECTOR2I& aP, int aClearance, int* aActual,
314  VECTOR2I* aLocation ) const
315 {
316  int minDist = aClearance + m_width / 2;
317  auto bbox = BBox( minDist );
318 
319  if( !bbox.Contains( aP ) )
320  return false;
321 
322  ecoord min_dist_sq = SEG::Square( minDist );
323  ecoord r_sq = SEG::Square( GetRadius() );
324 
325  ecoord dist_sq = ( aP - GetCenter() ).SquaredEuclideanNorm();
326  ecoord dist_to_edge_sq = abs( dist_sq - r_sq );
327 
328  if( dist_to_edge_sq == 0 || dist_to_edge_sq < min_dist_sq )
329  {
330  if( aLocation )
331  *aLocation = ( aP + GetCenter() ) / 2;
332 
333  if( aActual )
334  *aActual = std::max( 0, (int) sqrt( dist_to_edge_sq ) - m_width / 2 );
335 
336  return true;
337  }
338 
339  return false;
340 }
341 
342 
344 {
345  VECTOR2D d( m_start - GetCenter() );
346 
347  auto ang = 180.0 / M_PI * atan2( d.y, d.x );
348 
349  return NormalizeAngleDegrees( ang, 0.0, 360.0 );
350 }
351 
352 
354 {
355  VECTOR2D d( m_end - GetCenter() );
356 
357  auto ang = 180.0 / M_PI * atan2( d.y, d.x );
358 
359  return NormalizeAngleDegrees( ang, 0.0, 360.0 );
360 }
361 
362 
364 {
365  return GetArcCenter( m_start, m_mid, m_end );
366 }
367 
368 
370 {
371  VECTOR2I center = GetCenter();
372  VECTOR2I p0 = m_start - center;
373  VECTOR2I p1 = m_mid - center;
374  VECTOR2I p2 = m_end - center;
375  double angle1 = ArcTangente( p1.y, p1.x ) - ArcTangente( p0.y, p0.x );
376  double angle2 = ArcTangente( p2.y, p2.x ) - ArcTangente( p1.y, p1.x );
377 
378  return ( NormalizeAngle180( angle1 ) + NormalizeAngle180( angle2 ) ) / 10.0;
379 }
380 
381 
382 double SHAPE_ARC::GetRadius() const
383 {
384  return ( m_start - GetCenter() ).EuclideanNorm();
385 }
386 
387 
388 const SHAPE_LINE_CHAIN SHAPE_ARC::ConvertToPolyline( double aAccuracy ) const
389 {
390  SHAPE_LINE_CHAIN rv;
391  double r = GetRadius();
392  double sa = GetStartAngle();
393  auto c = GetCenter();
394  double ca = GetCentralAngle();
395 
396  int n;
397 
398  if( r < aAccuracy )
399  n = 0;
400  else
401  n = GetArcToSegmentCount( r, aAccuracy, ca );
402 
403  // Split the error on either side of the arc. Since we want the start and end points
404  // to be exactly on the arc, the first and last segments need to be shorter to stay within
405  // the error band (since segments normally start 1/2 the error band outside the arc).
406  r += aAccuracy / 2;
407  n = n * 2;
408 
409  rv.Append( m_start );
410 
411  for( int i = 1; i < n ; i += 2 )
412  {
413  double a = sa;
414 
415  if( n != 0 )
416  a += ( ca * i ) / n;
417 
418  double x = c.x + r * cos( a * M_PI / 180.0 );
419  double y = c.y + r * sin( a * M_PI / 180.0 );
420 
421  rv.Append( KiROUND( x ), KiROUND( y ) );
422  }
423 
424  rv.Append( m_end );
425 
426  return rv;
427 }
428 
429 
430 void SHAPE_ARC::Move( const VECTOR2I& aVector )
431 {
432  m_start += aVector;
433  m_end += aVector;
434  m_mid += aVector;
435  update_bbox();
436 }
437 
438 
439 void SHAPE_ARC::Rotate( double aAngle, const VECTOR2I& aCenter )
440 {
441  m_start -= aCenter;
442  m_end -= aCenter;
443  m_mid -= aCenter;
444 
445  m_start = m_start.Rotate( aAngle );
446  m_end = m_end.Rotate( aAngle );
447  m_mid = m_mid.Rotate( aAngle );
448 
449  m_start += aCenter;
450  m_end += aCenter;
451  m_mid += aCenter;
452 
453  update_bbox();
454 }
455 
456 
457 void SHAPE_ARC::Mirror( bool aX, bool aY, const VECTOR2I& aVector )
458 {
459  if( aX )
460  {
461  m_start.x = -m_start.x + 2 * aVector.x;
462  m_end.x = -m_end.x + 2 * aVector.x;
463  m_mid.x = -m_mid.x + 2 * aVector.x;
464  }
465 
466  if( aY )
467  {
468  m_start.y = -m_start.y + 2 * aVector.y;
469  m_end.y = -m_end.y + 2 * aVector.y;
470  m_mid.y = -m_mid.y + 2 * aVector.y;
471  }
472 
473  update_bbox();
474 }
475 
476 
478 {
479  std::swap( m_start, m_end );
480 }
481 
482 
484 {
485  return SHAPE_ARC( m_end, m_mid, m_start, m_width );
486 }
int Length() const
Return the length (this).
Definition: seg.h:340
void Mirror(bool aX=true, bool aY=false, const VECTOR2I &aVector={ 0, 0 })
Definition: shape_arc.cpp:457
void Rotate(double aAngle, const VECTOR2I &aCenter) override
Function Rotate rotates the arc by a given angle about a point.
Definition: shape_arc.cpp:439
bool Collide(const SEG &aSeg, int aClearance=0, int *aActual=nullptr, VECTOR2I *aLocation=nullptr) const override
Check if the boundary of shape (this) lies closer to the segment aSeg than aClearance,...
Definition: shape_arc.cpp:191
OPT_VECTOR2I Intersect(const SEG &aSeg, bool aIgnoreEndpoints=false, bool aLines=false) const
Compute intersection point of segment (this) with segment aSeg.
Definition: seg.cpp:105
double GetRadius() const
Definition: shape_arc.cpp:382
VECTOR2I m_end
Definition: shape_arc.h:173
SHAPE_ARC & ConstructFromStartEndAngle(const VECTOR2I &aStart, const VECTOR2I &aEnd, double aAngle, double aWidth=0)
Constructs this arc from the given start, end and angle.
Definition: shape_arc.cpp:173
void Compute(const Container &aPointList)
Compute the bounding box from a given list of points.
Definition: box2.h:91
extended_type SquaredEuclideanNorm() const
Compute the squared euclidean norm of the vector, which is defined as (x ** 2 + y ** 2).
Definition: vector2d.h:300
ecoord SquaredDistance(const SEG &aSeg) const
Definition: seg.cpp:38
double GetStartAngle() const
Definition: shape_arc.cpp:343
VECTOR2I Center() const
Definition: seg.h:376
void RotatePoint(int *pX, int *pY, double angle)
Definition: trigo.cpp:228
static SEG::ecoord Square(int a)
Definition: seg.h:123
void Append(int aX, int aY, bool aAllowDuplication=false)
Function Append()
T NormalizeAngle180(T Angle)
Normalize angle to be in the -180.0 .. 180.0 range.
Definition: trigo.h:376
VECTOR2I m_mid
Definition: shape_arc.h:172
static constexpr extended_type ECOORD_MAX
Definition: vector2d.h:79
VECTOR2I LineProject(const VECTOR2I &aP) const
Compute the perpendicular projection point of aP on a line passing through ends of the segment.
Definition: seg.h:389
const SHAPE_LINE_CHAIN ConvertToPolyline(double aAccuracy=0.005 *PCB_IU_PER_MM) const
Constructs a SHAPE_LINE_CHAIN of segments from a given arc.
Definition: shape_arc.cpp:388
OPT< VECTOR2I > OPT_VECTOR2I
Definition: seg.h:39
circular arc
Definition: shape.h:50
a few functions useful in geometry calculations.
An abstract shape on 2D plane.
Definition: shape.h:116
double GetEndAngle() const
Definition: shape_arc.cpp:353
void update_bbox()
Definition: shape_arc.cpp:260
void Reverse()
Definition: shape_arc.cpp:477
Definition: seg.h:41
void Move(const VECTOR2I &aVector) override
Definition: shape_arc.cpp:430
BOX2< Vec > & Inflate(coord_type dx, coord_type dy)
Function Inflate inflates the rectangle horizontally by dx and vertically by dy.
Definition: box2.h:302
VECTOR2< T > Rotate(double aAngle) const
Rotate the vector by a given angle.
Definition: vector2d.h:371
extended_type Dot(const VECTOR2< T > &aVector) const
Compute dot product of self with aVector.
Definition: vector2d.h:521
VECTOR2I::extended_type ecoord
Definition: shape.h:236
SHAPE_LINE_CHAIN.
VECTOR2I m_start
Definition: shape_arc.h:171
VECTOR2I A
Definition: seg.h:49
double GetCentralAngle() const
Definition: shape_arc.cpp:369
double DECIDEG2RAD(double deg)
Definition: trigo.h:235
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:68
SHAPE_ARC()
Definition: shape_arc.h:39
double NormalizeAngleDegrees(double Angle, double aMin, double aMax)
Normalize angle to be aMin < angle <= aMax angle is in degrees.
Definition: trigo.h:323
const BOX2I BBox(int aClearance=0) const override
Compute a bounding box of the shape, with a margin of aClearance a collision.
Definition: shape_arc.cpp:302
SHAPE_ARC Reversed() const
Definition: shape_arc.cpp:483
T EuclideanNorm() const
Compute the Euclidean norm of the vector, which is defined as sqrt(x ** 2 + y ** 2).
Definition: vector2d.h:293
double ArcTangente(int dy, int dx)
Definition: trigo.cpp:182
const VECTOR2I GetArcCenter(const VECTOR2I &aStart, const VECTOR2I &aMid, const VECTOR2I &aEnd)
Determine the center of an arc or circle given three points on its circumference.
Definition: trigo.cpp:450
int m_width
Definition: shape_arc.h:175
int GetArcToSegmentCount(int aRadius, int aErrorMax, double aArcAngleDegree)
BOX2I m_bbox
Definition: shape_arc.h:176
VECTOR2I GetCenter() const
Definition: shape_arc.cpp:363
VECTOR2I B
Definition: seg.h:50