@@ -814,8 +814,13 @@ int count_bboxes_overlapping_bbox(agg::rect_d &a, BBoxArray &bboxes)
814814}
815815
816816
817- inline bool isclose (double a,double b, double rtol, double atol )
817+ inline bool isclose (double a,double b)
818818{
819+ // relative and absolute tolerance values are chosen empirically
820+ // it looks the atol value matters here bacause of round-off errors
821+ const double rtol =1e-10 ;
822+ const double atol =1e-13 ;
823+
819824// as per python's math.isclose
820825return fabs (a-b) <=fmax (rtol *fmax (fabs (a),fabs (b)), atol);
821826}
@@ -830,33 +835,18 @@ inline bool segments_intersect(const double &x1,
830835const double &x4,
831836const double &y4)
832837{
833- // relative and absolute tolerance values are chosen empirically
834- // it looks the atol value matters here bacause of round-off errors
835- const double rtol =1e-10 ;
836- const double atol =1e-13 ;
837-
838- // if either segment is 0 length, they do not intersect
839- // length-squared of each segment
840- const double lensq_A = (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2);
841- const double lenqs_B = (x3 - x4) * (x3 - x4) + (y3 - y4) * (y3 - y4);
842-
843- // one of the segments is 0 length
844- if (isclose (lensq_A,0 , rtol, atol) ||isclose (lenqs_B,0 , rtol, atol)) {
845- return false ;
846- }
847-
848838// determinant
849839double den = ((y4 - y3) * (x2 - x1)) - ((x4 - x3) * (y2 - y1));
850840
851- if (isclose (den,0.0 , rtol, atol )) {// collinear segments
841+ if (isclose (den,0.0 )) {// collinear segments
852842if (x1 == x2 && x2 == x3) {// segments have infinite slope (vertical lines)
853843// and lie on the same line
854844return (fmin (y1, y2) <=fmin (y3, y4) &&fmin (y3, y4) <=fmax (y1, y2)) ||
855845 (fmin (y3, y4) <=fmin (y1, y2) &&fmin (y1, y2) <=fmax (y3, y4));
856846 }
857847else {
858848double intercept = (y1*x2 - y2*x1)*(x4 - x3) - (y3*x4 - y4*x3)*(x1 - x2);
859- if (isclose (intercept,0.0 , rtol, atol )) {// segments lie on the same line
849+ if (isclose (intercept,0.0 )) {// segments lie on the same line
860850return (fmin (x1, x2) <=fmin (x3, x4) &&fmin (x3, x4) <=fmax (x1, x2)) ||
861851 (fmin (x3, x4) <=fmin (x1, x2) &&fmin (x1, x2) <=fmax (x3, x4));
862852 }
@@ -871,10 +861,10 @@ inline bool segments_intersect(const double &x1,
871861const double u1 = n1 / den;
872862const double u2 = n2 / den;
873863
874- return ((u1 >0.0 ||isclose (u1,0.0 , rtol, atol )) &&
875- (u1 <1.0 ||isclose (u1,1.0 , rtol, atol )) &&
876- (u2 >0.0 ||isclose (u2,0.0 , rtol, atol )) &&
877- (u2 <1.0 ||isclose (u2,1.0 , rtol, atol )));
864+ return ((u1 >0.0 ||isclose (u1,0.0 )) &&
865+ (u1 <1.0 ||isclose (u1,1.0 )) &&
866+ (u2 >0.0 ||isclose (u2,0.0 )) &&
867+ (u2 <1.0 ||isclose (u2,1.0 )));
878868}
879869
880870template <class PathIterator1 ,class PathIterator2 >
@@ -898,16 +888,16 @@ bool path_intersects_path(PathIterator1 &p1, PathIterator2 &p2)
898888
899889 c1.vertex (&x11, &y11);
900890while (c1.vertex (&x12, &y12) != agg::path_cmd_stop) {
901- // if the segment in path 1 is 0 length, skip to next vertex
902- if ((x11== x12)&& ( y11== y12)) {
891+ // if the segment in path 1 is(almost) 0 length, skip to next vertex
892+ if ((isclose (( x11- x12)* (x11 - x12) + ( y11- y12) * (y11 - y12), 0 ))) {
903893continue ;
904894 }
905895 c2.rewind (0 );
906896 c2.vertex (&x21, &y21);
907897
908898while (c2.vertex (&x22, &y22) != agg::path_cmd_stop) {
909- // if the segment in path 2 is 0 length, skip to next vertex
910- if ((x21== x22)&& ( y21== y22)) {
899+ // if the segment in path 2 is(almost) 0 length, skip to next vertex
900+ if ((isclose (( x21- x22)* (x21 - x22) + ( y21- y22) * (y21 - y22), 0 ))) {
911901continue ;
912902 }
913903if (segments_intersect (x11, y11, x12, y12, x21, y21, x22, y22)) {