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/**
* @file polygon_test_point_inside.cpp
*/
#include <math.h>
#include <vector>
#include "PolyLine.h"
/* this algo uses the the Jordan curve theorem to find if a point is inside or outside a polygon:
* It run a semi-infinite line horizontally (increasing x, fixed y)
* out from the test point, and count how many edges it crosses.
* At each crossing, the ray switches between inside and outside.
* If odd count, the test point is inside the polygon
* This is called the Jordan curve theorem, or sometimes referred to as the "even-odd" test.
* Take care to starting and ending points of segments outlines, when the horizontal line crosses a segment outline
* exactly on an ending point:
* Because the starting point of a segment is also the ending point of the previous, only one must be used.
* And we do no use twice the same segment, so we do NOT use both starting and ending points of these 2 segments.
* So we must use only one ending point of each segment when calculating intersections
* but it cannot be always the starting or the ending point. This depend on relative position of 2 consectutive segments
* Here, the ending point above the Y reference position is used
* and the ending point below or equal the Y reference position is NOT used
* Obviously, others cases are irrelevant because there is not intersection.
*/
#define OUTSIDE false
#define INSIDE true
bool TestPointInsidePolygon( std::vector <CPolyPt> aPolysList,
int aIdxstart,
int aIdxend,
int aRefx,
int aRefy)
/**
* Function TestPointInsidePolygon
* test if a point is inside or outside a polygon.
* the polygon must have only lines (not arcs) for outlines.
* @param aPolysList: the list of polygons
* @param aIdxstart: the starting point of a given polygon in m_FilledPolysList.
* @param aIdxend: the ending point of this polygon in m_FilledPolysList.
* @param aRefx, aRefy: the point coordinate to test
* @return true if the point is inside, false for outside
*/
{
// count intersection points to right of (refx,refy). If odd number, point (refx,refy) is inside polyline
int ics, ice;
int count = 0;
// find all intersection points of line with polyline sides
for( ics = aIdxstart, ice = aIdxend; ics <= aIdxend; ice = ics++ )
{
int seg_startX = aPolysList[ics].x;
int seg_startY = aPolysList[ics].y;
int seg_endX = aPolysList[ice].x;
int seg_endY = aPolysList[ice].y;
/* Trivial cases: skip if ref above or below the segment to test */
if( ( seg_startY > aRefy ) && (seg_endY > aRefy ) )
continue;
// segment below ref point, or one of its ends has the same Y pos as the ref point: skip
// So we eliminate one end point of 2 consecutive segments.
// Note: also we skip horizontal segments if ref point is on this horizontal line
// So reference points on horizontal segments outlines always are seen as outside the polygon
if( ( seg_startY <= aRefy ) && (seg_endY <= aRefy ) )
continue;
/* refy is between seg_startY and seg_endY.
* note: here: horizontal segments (seg_startY == seg_endY) are skipped,
* either by the first test or by the second test
* see if an horizontal semi infinite line from refx is intersecting the segment
*/
// calculate the x position of the intersection of this segment and the semi infinite line
// this is more easier if we move the X,Y axis origin to the segment start point:
seg_endX -= seg_startX;
seg_endY -= seg_startY;
double newrefx = (double) (aRefx - seg_startX);
double newrefy = (double) (aRefy - seg_startY);
// Now calculate the x intersection coordinate of the line from (0,0) to (seg_endX,seg_endY)
// with the horizontal line at the new refy position
// the line slope = seg_endY/seg_endX;
// and the x pos relative to the new origin is intersec_x = refy/slope
// Note: because horizontal segments are skipped, 1/slope exists (seg_endY never == O)
double intersec_x = (newrefy * seg_endX) / seg_endY;
if( newrefx < intersec_x ) // Intersection found with the semi-infinite line from refx to infinite
count++;
}
return count & 1 ? INSIDE : OUTSIDE;
}
/* Function TestPointInsidePolygon (overlaid)
* same as previous, but use wxPoint and aCount corners
*/
bool TestPointInsidePolygon( wxPoint *aPolysList, int aCount,wxPoint aRefPoint )
{
// count intersection points to right of (refx,refy). If odd number, point (refx,refy) is inside polyline
int ics, ice;
int count = 0;
// find all intersection points of line with polyline sides
for( ics = 0, ice = aCount-1; ics < aCount; ice = ics++ )
{
int seg_startX = aPolysList[ics].x;
int seg_startY = aPolysList[ics].y;
int seg_endX = aPolysList[ice].x;
int seg_endY = aPolysList[ice].y;
/* Trivial cases: skip if ref above or below the segment to test */
if( ( seg_startY > aRefPoint.y ) && (seg_endY > aRefPoint.y ) )
continue;
// segment below ref point, or one of its ends has the same Y pos as the ref point: skip
// So we eliminate one end point of 2 consecutive segments.
// Note: also we skip horizontal segments if ref point is on this horizontal line
// So reference points on horizontal segments outlines always are seen as outside the polygon
if( ( seg_startY <= aRefPoint.y ) && (seg_endY <= aRefPoint.y ) )
continue;
/* refy is between seg_startY and seg_endY.
* note: here: horizontal segments (seg_startY == seg_endY) are skipped,
* either by the first test or by the second test
* see if an horizontal semi infinite line from refx is intersecting the segment
*/
// calculate the x position of the intersection of this segment and the semi infinite line
// this is more easier if we move the X,Y axis origin to the segment start point:
seg_endX -= seg_startX;
seg_endY -= seg_startY;
double newrefx = (double) (aRefPoint.x - seg_startX);
double newrefy = (double) (aRefPoint.y - seg_startY);
// Now calculate the x intersection coordinate of the line from (0,0) to (seg_endX,seg_endY)
// with the horizontal line at the new refy position
// the line slope = seg_endY/seg_endX;
// and the x pos relative to the new origin is intersec_x = refy/slope
// Note: because horizontal segments are skipped, 1/slope exists (seg_endY never == O)
double intersec_x = (newrefy * seg_endX) / seg_endY;
if( newrefx < intersec_x ) // Intersection found with the semi-infinite line from refx to infinite
count++;
}
return count & 1 ? INSIDE : OUTSIDE;
}