KiCad PCB EDA Suite
polygon_test_point_inside.cpp
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1 /*
2  * This program source code file is part of KiCad, a free EDA CAD application.
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4  * Copyright (C) 2007-2014 Jean-Pierre Charras, jp.charras at wanadoo.fr
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24 
29 #include <cmath>
30 #include <vector>
31 
33 
34 /* this algo uses the the Jordan curve theorem to find if a point is inside or outside a polygon:
35  * It run a semi-infinite line horizontally (increasing x, fixed y)
36  * out from the test point, and count how many edges it crosses.
37  * At each crossing, the ray switches between inside and outside.
38  * If odd count, the test point is inside the polygon
39  * This is called the Jordan curve theorem, or sometimes referred to as the "even-odd" test.
40  * Take care to starting and ending points of segments outlines, when the horizontal line crosses a segment outline
41  * exactly on an ending point:
42  * Because the starting point of a segment is also the ending point of the previous, only one must be used.
43  * And we do no use twice the same segment, so we do NOT use both starting and ending points of these 2 segments.
44  * So we must use only one ending point of each segment when calculating intersections
45  * but it cannot be always the starting or the ending point. This depend on relative position of 2 consectutive segments
46  * Here, the ending point above the Y reference position is used
47  * and the ending point below or equal the Y reference position is NOT used
48  * Obviously, others cases are irrelevant because there is not intersection.
49  */
50 
51 #define OUTSIDE false
52 #define INSIDE true
53 
54 
55 /* Function TestPointInsidePolygon (overlaid)
56  * same as previous, but use wxPoint and aCount corners
57  */
58 bool TestPointInsidePolygon( const wxPoint *aPolysList, int aCount, const wxPoint &aRefPoint )
59 {
60  // count intersection points to right of (refx,refy). If odd number, point (refx,refy) is inside polyline
61  int ics, ice;
62  int count = 0;
63  // find all intersection points of line with polyline sides
64  for( ics = 0, ice = aCount-1; ics < aCount; ice = ics++ )
65  {
66  int seg_startX = aPolysList[ics].x;
67  int seg_startY = aPolysList[ics].y;
68  int seg_endX = aPolysList[ice].x;
69  int seg_endY = aPolysList[ice].y;
70 
71  /* Trivial cases: skip if ref above or below the segment to test */
72  if( ( seg_startY > aRefPoint.y ) && (seg_endY > aRefPoint.y ) )
73  continue;
74 
75  // segment below ref point, or one of its ends has the same Y pos as the ref point: skip
76  // So we eliminate one end point of 2 consecutive segments.
77  // Note: also we skip horizontal segments if ref point is on this horizontal line
78  // So reference points on horizontal segments outlines always are seen as outside the polygon
79  if( ( seg_startY <= aRefPoint.y ) && (seg_endY <= aRefPoint.y ) )
80  continue;
81 
82  /* refy is between seg_startY and seg_endY.
83  * note: here: horizontal segments (seg_startY == seg_endY) are skipped,
84  * either by the first test or by the second test
85  * see if an horizontal semi infinite line from refx is intersecting the segment
86  */
87 
88  // calculate the x position of the intersection of this segment and the semi infinite line
89  // this is more easier if we move the X,Y axis origin to the segment start point:
90  seg_endX -= seg_startX;
91  seg_endY -= seg_startY;
92  double newrefx = (double) (aRefPoint.x - seg_startX);
93  double newrefy = (double) (aRefPoint.y - seg_startY);
94 
95  // Now calculate the x intersection coordinate of the line from (0,0) to (seg_endX,seg_endY)
96  // with the horizontal line at the new refy position
97  // the line slope = seg_endY/seg_endX;
98  // and the x pos relative to the new origin is intersec_x = refy/slope
99  // Note: because horizontal segments are skipped, 1/slope exists (seg_endY never == O)
100  double intersec_x = (newrefy * seg_endX) / seg_endY;
101  if( newrefx < intersec_x ) // Intersection found with the semi-infinite line from refx to infinite
102  count++;
103  }
104 
105  return count & 1 ? INSIDE : OUTSIDE;
106 }
bool TestPointInsidePolygon(const wxPoint *aPolysList, int aCount, const wxPoint &aRefPoint)
Function TestPointInsidePolygon (overlaid) same as previous, but mainly use wxPoint.
#define OUTSIDE
#define INSIDE