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From: <airwin@us...>  20091227 19:27:19

Revision: 10730 http://plplot.svn.sourceforge.net/plplot/?rev=10730&view=rev Author: airwin Date: 20091227 19:27:12 +0000 (Sun, 27 Dec 2009) Log Message:  Implement PL_NEAR_PARALLEL crossing status. Implement fill_status to keep track of whether a given split of polygon 2 is known to have filled areas or known to not have filled areas. At the final stage where there are not crossings left between the polygons, this status helps to quickly decide whether to fill or not. Prepare calls to fill_intersection_polygon so that polygon 1 always starts outside polygon 2. That and the positive orientation requirement considerably simplify the logic of fill_intersection_polygon. Implement number_crossings to make sure that the crossings are determined in the correct order for a give segment of polygon 1. N.B. These changes build, but still produce incorrect fill results for some of the subpages of example 25. So this commit is in the nature of a code drop to keep track of the many changes that have been done with the DUSE_FILL_INTERSECTION_POLYGON=ON approach rather than a final result. Modified Paths:  trunk/src/plfill.c Modified: trunk/src/plfill.c ===================================================================  trunk/src/plfill.c 20091224 09:19:26 UTC (rev 10729) +++ trunk/src/plfill.c 20091227 19:27:12 UTC (rev 10730) @@ 36,8 +36,8 @@ /* Status codes ORed together in the return from notcrossed. * PL_NOT_CROSSED is set whenever the two line segments definitely  * (i.e., not near the ends or completely apart) do not cross each  * other. + * (i.e., intersection not near the ends or completely apart) + * do not cross each other. * * PL_NEAR_A1 is set if the intersect is near (+/ PL_NBCC) the first * end of line segment A. @@ 51,16 +51,22 @@ * PL_NEAR_B2 is set if the intersect is near (+/ PL_NBCC) the second * end of line segment B. *  * PL_PARALLEL is set if the two line segments are parallel with each other. + * PL_NEAR_PARALLEL is set if the two line segments are nearly parallel + * with each other, i.e., a change in one of the coordinates of up to + * (+/ PL_NBCC) would render them exactly parallel. + * + * PL_PARALLEL is set if the two line segments are exactly parallel + * with each other. */ enum PL_CrossedStatus {  PL_NOT_CROSSED = 0x1,  PL_NEAR_A1 = 0x2,  PL_NEAR_A2 = 0x4,  PL_NEAR_B1 = 0x8,  PL_NEAR_B2 = 0x10,  PL_PARALLEL = 0x20 + PL_NOT_CROSSED = 0x1, + PL_NEAR_A1 = 0x2, + PL_NEAR_A2 = 0x4, + PL_NEAR_B1 = 0x8, + PL_NEAR_B2 = 0x10, + PL_NEAR_PARALLEL = 0x20, + PL_PARALLEL = 0x40 }; struct point @@ 91,6 +97,7 @@ static void fill_intersection_polygon( PLINT recursion_depth, PLINT ifextrapolygon, + PLINT fill_status, void ( *fill )( short *, short *, PLINT ), const PLINT *x1, const PLINT *y1, PLINT i1start, PLINT n1, @@ 105,6 +112,12 @@ static int positive_orientation( PLINT n, const PLINT *x, const PLINT *y ); +static int +number_crossings( PLINT *xcross, PLINT *ycross, PLINT *i2cross, PLINT ncross, + PLINT i1, PLINT n1, const PLINT *x1, const PLINT *y1, + PLINT n2, const PLINT *x2, const PLINT *y2 ); + + /**\ * void plfill() * @@ 456,9 +469,9 @@ PLINT xmin, PLINT xmax, PLINT ymin, PLINT ymax, void ( *draw )( short *, short *, PLINT )) {  #ifdef USE_FILL_INTERSECTION_POLYGON  PLINT *x10, *y10, *x1, *y1, i1start = 0, i, im1, n1, n1m1; + PLINT *x10, *y10, *x1, *y1, *if1, i1start = 0, i, im1, n1, n1m1, + ifnotpointinpolygon; PLINT x2[4] = { xmin, xmax, xmax, xmin }; PLINT y2[4] = { ymin, ymin, ymax, ymax }; PLINT if2[4] = { 0, 0, 0, 0 }; @@ 528,7 +541,30 @@ free( x10 ); free( y10 ); }  fill_intersection_polygon( 0, 0, draw, x1, y1, i1start, n1, x2, y2, if2, n2 ); + + /* Insure that the first vertex of polygon 1 (starting with n1  + * 1) that is not on the border of polygon 2 is definitely outside + * polygon 2. */ + im1 = n1  1; + for ( i = 0; i < n1; i++ ) + { + if (( ifnotpointinpolygon = + notpointinpolygon( n2, x2, y2, x1[im1], y1[im1] )) != 1 ) + break; + im1 = i; + } + + if ( ifnotpointinpolygon ) + fill_intersection_polygon( 0, 0, 0, draw, x1, y1, i1start, n1, x2, y2, if2, n2 ); + else + { + if (( if1 = (PLINT *) calloc( n1, sizeof ( PLINT ))) == NULL ) + { + plexit( "plP_plfclp: Insufficient memory" ); + } + fill_intersection_polygon( 0, 0, 0, draw, x2, y2, i1start, n2, x1, y1, if1, n1 ); + free( if1 ); + } free( x1 ); free( y1 ); return; @@ 1297,15 +1333,17 @@ #define MAX_RECURSION_DEPTH 10 /* Fill intersection of two simple (not selfintersecting) polygons  * that both have a positive orientation (see +/* Fill intersection of two simple polygons that do no selfintersect, + * and which have no duplicate vertices or two consecutive edges that + * are parallel. A further requirement is that both polygons have a + * positive orientation (see * http://en.wikipedia.org/wiki/Curve_orientation). That is, as you * traverse the boundary in index order, the inside area of the  * polygon is always on the left. This requirement simplifies the  * logic of fill_instersection_polygon. N.B. it is the calling  * routine's responsibility to insure the two polygons do not have  * duplicate points, are not selfintersecting, and have positive  * orientation. + * polygon is always on the left. Finally, the first vertex of + * polygon 1 (starting with n1 1) that is not near the border of + * polygon 2 must be outside polygon 2. N.B. it is the calling + * routine's responsibility to insure all those requirements are + * satisfied. * * Two polygons that do not self intersect must have an even number of * edge crossings between them. (ignoring vertex intersections which @@ 1322,20 +1360,41 @@ * ifextrapolygon false, and the second polygon set to an additional * polygon defined by the stream (not yet implemented). */ +/* arguments to intersection_polygon: + * recursion_depth is just what it says. + * ifextrapolygon used to decide whether to use extra polygon from the stream. + *fill is the fill routine. + *x1, *y1, n1 define the polygon 1 vertices. + * i1start is the first polygon 1 index to look at (because all the previous + * ones have been completely processed). + *x2, *y2, *if2, n2 define the polygon 2 vertices plus a status indicator + * for each vertex which is 1 for a previous crossing and 2 for a polygon + * 1 vertex. + * fill_status is 1 when polygons 1 and 2 _must_ include some joint + * filled area and is 1 when polygons 1 and 2 _must_ include some + * unfilled area. fill_status of +/ 1 is determined from the + * orientations of polygon 1 and 2 from the next higher recursion + * level and how those two are combined to form the polygon 2 + * split at this recursion level. fill_status = 0 occurs (at + * recursion level 0) for polygons 1 and 2 that are independent of + * each other. */ + void fill_intersection_polygon( PLINT recursion_depth, PLINT ifextrapolygon, + PLINT fill_status, void ( *fill )( short *, short *, PLINT ), const PLINT *x1, const PLINT *y1, PLINT i1start, PLINT n1, const PLINT *x2, const PLINT *y2, const PLINT *if2, PLINT n2 ) {  PLINT i1, i1m1, i1wrap, i1wraplast,  i2, i2m1, i2wrap, i2wraplast, + PLINT i1, i1m1, i1start_new, + i2, i2m1, kk, kkstart1, kkstart21, kkstart22,  k, kstart, range1, range21, range22, ncrossed, + k, kstart, range1, range21, range22, ncrossed, ncrossed_change, nsplit1, nsplit2, nsplit2m1;  PLINT xintersect[2], yintersect[2], ifnotcrossed; + PLINT xintersect[2], yintersect[2], i1intersect[2], + i2intersect[2], ifnotcrossed; PLINT *xsplit1, *ysplit1, *ifsplit1, *xsplit2, *ysplit2, *ifsplit2; PLINT ifill, nfill = 0, @@ 1368,6 +1427,7 @@ return; } + /* Check that there are no duplicate vertices. */ i1m1 = i1start  1; if ( i1m1 < 0 ) i1m1 = n1  1; @@ 1455,268 +1515,265 @@ * split, and in that case we move on to the end phase below. */ ncrossed = 0;  i1wrap = i1start  1;  if ( i1wrap < 0 )  i1m1 = n1  1;  else  i1m1 = i1wrap; + i1m1 = i1start  1; + if ( i1m1 < 0 ) + i1m1 += n1; for ( i1 = i1start; i1 < n1; i1++ ) {  i2m1 = n2  1;  i2wrap = 1;  for ( i2 = 0; i2 < n2; i2++ ) + i2m1 = n2  1; + ncrossed_change = number_crossings( + &xintersect[ncrossed], &yintersect[ncrossed], + &i2intersect[ncrossed], 2  ncrossed, + i1, n1, x1, y1, n2, x2, y2 ); + if ( ncrossed_change > 0 ) {  if ( !( if2[i2] && if2[i2m1] )) + i1intersect[ncrossed] = i1; + if ( ncrossed_change == 2 ) ; + i1intersect[1] = i1; + + ncrossed += ncrossed_change; + if ( ncrossed == 2 ) {  ifnotcrossed = notcrossed(  &xintersect[ncrossed], &yintersect[ncrossed],  x1[i1m1], y1[i1m1], x1[i1], y1[i1],  x2[i2m1], y2[i2m1], x2[i2], y2[i2] );  /* Use only definite crossing case. */  if ( !ifnotcrossed ) + /* Have discovered the first two crossings for + * polygon 1 at i1 = i1start or above. */ + + /* Calculate polygon 2 index range in split 1 (the + * split that proceeds beyond the second intersect with + * ascending i2 values). */ + range21 = i2intersect[0]  i2intersect[1]; + if ( range21 < 0 ) + range21 += n2; + /* i2 intersect values range between 0 and n2  1 so + * the the smallest untransformed range21 value is n2 + + 1, and the largest untransformed range21 value is + * n2  1. This means the smallest transformed range21 + * value is +1. Also, for the untransformed range21 + * value of 0, go the "long way" around with + * transformed range21 = n2 so that split 1 is + * guaranteed to have the correct fill_status == +1. */ + + /* N.B. always avoid special code for range21 == 0 + * case because it is no longer necessary since there + * is a guarantee that the first vertex of polygon 1 + * (starting with n1  1) that is not near the border + * of polygon 2 will be outside polygon 2. */ + if ( 0 && range21 == 0 ) {  if ( ncrossed == 0 ) + /* For this special case the above ascii art + * does not apply, and we must use the + * following diagram instead: + * + *  1 1 ... + * + * + * + * 2???2 X X 2???2 + * + * 1 1 + * + * + * N.B. no valid split of polygon 2 is + * possible with this diagram. However, + * this diagrem can be classified the same + * as the first diagram, but with the roles + * of polygon 1 and polygon 2 swapped so + * that polygon 1 is the one that gets split + * instead of polygon 2. In fact, swapping + * those two polygons (and starting the new + * polygon 1 just at i2intersect[1] of the old + * polygon 2 to insure the present two + * intersections are immediately (at least for the + * first new polygon segment 1) found and dealt + * with to eliminate the chance of an infinite + * "swap" loop) is the only clean way to deal with + * this situation. */ + if (( xsplit2 = (PLINT *) malloc( n2 * sizeof ( PLINT ))) == NULL ) {  i1wraplast = i1wrap;  i2wraplast = i2wrap;   ncrossed++; + plexit( "fill_intersection_polygon: Insufficient memory" ); }  else + if (( ysplit2 = (PLINT *) malloc( n2 * sizeof ( PLINT ))) == NULL ) {  /* Have discovered the first two intersections for  * polygon 1 at i1 = i1start or above. */ + plexit( "fill_intersection_polygon: Insufficient memory" ); + } + if (( ifsplit1 = (PLINT *) calloc( n1, sizeof ( PLINT ))) == NULL ) + { + plexit( "fill_intersection_polygon: Insufficient memory" ); + } + kk = i2intersect[1]; + for ( i2 = 0; i2 < n2; i2++ ) + { + xsplit2[kk] = x2[i2]; + ysplit2[kk++] = y2[i2]; + if ( kk == n2 ) + kk = 0; + } + /* N.B. the positive orientation of split2 + * is preserved since the index order is + * the same as that of polygon 2, and by + * assumption that polygon and polygon 1 + * have identical positive + * orientations. fill_status does not matter + * here because a split is guaranteed at the + * next recursion level. For definiteness set + * it to zero. */ + fill_intersection_polygon( + recursion_depth + 1, ifextrapolygon, + 0, fill, + xsplit2, ysplit2, 0, n2, + x1, y1, ifsplit1, n1 ); + free( xsplit2 ); + free( ysplit2 ); + free( ifsplit1 ); + return; + } + /* New i1start is the same as the current i1 (just + * in case there are more crossings to find between + * i1m1 and i1.) */ + i1start_new = i1;  /* Calculate polygon 2 index range in split 1  * (the split that normally proceeds beyond  * the second intersect with ascending i2  * values). */  range21 = i2wraplast  i2wrap;  if ( range21 < 0 )  range21 += n2;  /* Wrap values range between 1 and n2  2 so  * the the smallest untransformed range21  * value is n2 + 1, the smallest transformed  * range21 value is 0 (only obtained if  * i2wraplast == i2wrap), and the largest  * transformed range21 value is n2  1. */  if ( range21 == 0 )  {  /* For this special case the above ascii art  * does not apply, and we must use the  * following diagram instead:  *  *  1 1 ...  *  *  *  * 2???2 X X 2???2  *  * 1 1  *  *  * N.B. no valid split of polygon 2 is  * possible with this diagram. However,  * this diagrem can be classified the same  * as the first diagram, but with the roles  * of polygon 1 and polygon 2 swapped so  * that polygon 1 is the one that gets split  * instead of polygon 2. In fact, swapping  * those two polygons (and starting the new  * polygon 1 just at i2 of the old polygon 2  * to insure the present two intersections  * are immediately (at least for the first  * new polygon segment 1) found and dealt  * with to eliminate the chance of an  * infinite "swap" loop) is the only clean  * way to deal with this situation. */  if (( xsplit2 = (PLINT *) malloc( n2 * sizeof ( PLINT ))) == NULL )  {  plexit( "fill_intersection_polygon: Insufficient memory" );  }  if (( ysplit2 = (PLINT *) malloc( n2 * sizeof ( PLINT ))) == NULL )  {  plexit( "fill_intersection_polygon: Insufficient memory" );  }  if (( ifsplit1 = (PLINT *) calloc( n1, sizeof ( PLINT ))) == NULL )  {  plexit( "fill_intersection_polygon: Insufficient memory" );  }  kk = i2;  for ( i2 = 0; i2 < n2; i2++ )  {  xsplit2[kk] = x2[i2];  ysplit2[kk++] = y2[i2];  if ( kk == n2 )  kk = 0;  }  /* N.B. the positive orientation of split2  * is preserved since the index order is  * the same as that of polygon 2, and by  * assumption that polygon and polygon 1  * have identical positive  * orientations. */  fill_intersection_polygon(  recursion_depth + 1, ifextrapolygon, fill,  xsplit2, ysplit2, 0, n2,  x1, y1, ifsplit1, n1 );  free( xsplit2 );  free( ysplit2 );  free( ifsplit1 );  return;  }  /* New i1start is the largest nonnegative polygon 1  * index below the last detected intersect. */  i1start = MAX( i1wrap, 0 ); + /* Split polygon 2 at the boundary consisting of + * first intersection, intervening (if any) range1 + * polygon 1 points and second intersection. */ + /* range1 must always be nonnegative because i1 + * range only traversed once. */ + range1 = i1intersect[1]  i1intersect[0]; + /* Polygon 2 intersects could be anywhere (since + * i2 range repeated until get an intersect). + * Divide polygon 2 into two polygons with a + * common boundary consisting of the first intersect, + * range1 points from polygon 1 starting at index + * kkstart1 of polygon 1, and the second intersect. */ + kkstart1 = i1intersect[0];  /* Split polygon 2 at the boundary consisting of  * first intersection, intervening (if any) range1  * polygon 1 points and second intersection. */  /* range1 must always be nonnegative because i1  * range only traversed once. */  range1 = i1wrap  i1wraplast;  /* Polygon 2 intersects could be anywhere (since  * i2 range repeated until get an intersect).  * Divide polygon 2 into two polygons with a  * common boundary consisting of the first intersect,  * range1 points from polygon1 starting at index  * kkstart1 of polygon 1, and the second intersect. */  kkstart1 = i1wraplast + 1; + kkstart21 = i2intersect[1];  kkstart21 = i2; + /* Split 2 of polygon 2 consists of the + * boundary + range22 (= n2  range21) points + * between kkstart22 (= i2intersect[1]1) and i2intersect[0] in + * descending order of polygon 2 indices. */ + range22 = n2  range21; + kkstart22 = i2intersect[1]  1; + if ( kkstart22 < 0 ) + kkstart22 += n2; + nsplit1 = 2 + range1 + range21; + nsplit2 = 2 + range1 + range22;  /* Split 2 of polygon 2 consists of the  * boundary + range22 (= n2  range21) points  * between kkstart22 (= i2wrap) and i2wraplast + 1 in  * descending order of polygon 2 indices. */  range22 = n2  range21;  kkstart22 = i2wrap;  if ( kkstart22 == 1 )  kkstart22 = i2m1;  nsplit1 = 2 + range1 + range21;  nsplit2 = 2 + range1 + range22; + if (( xsplit1 = (PLINT *) malloc( nsplit1 * sizeof ( PLINT ))) == NULL ) + { + plexit( "fill_intersection_polygon: Insufficient memory" ); + } + if (( ysplit1 = (PLINT *) malloc( nsplit1 * sizeof ( PLINT ))) == NULL ) + { + plexit( "fill_intersection_polygon: Insufficient memory" ); + } + if (( ifsplit1 = (PLINT *) malloc( nsplit1 * sizeof ( PLINT ))) == NULL ) + { + plexit( "fill_intersection_polygon: Insufficient memory" ); + }  if (( xsplit1 = (PLINT *) malloc( nsplit1 * sizeof ( PLINT ))) == NULL )  {  plexit( "fill_intersection_polygon: Insufficient memory" );  }  if (( ysplit1 = (PLINT *) malloc( nsplit1 * sizeof ( PLINT ))) == NULL )  {  plexit( "fill_intersection_polygon: Insufficient memory" );  }  if (( ifsplit1 = (PLINT *) malloc( nsplit1 * sizeof ( PLINT ))) == NULL )  {  plexit( "fill_intersection_polygon: Insufficient memory" );  } + if (( xsplit2 = (PLINT *) malloc( nsplit2 * sizeof ( PLINT ))) == NULL ) + { + plexit( "fill_intersection_polygon: Insufficient memory" ); + } + if (( ysplit2 = (PLINT *) malloc( nsplit2 * sizeof ( PLINT ))) == NULL ) + { + plexit( "fill_intersection_polygon: Insufficient memory" ); + } + if (( ifsplit2 = (PLINT *) malloc( nsplit2 * sizeof ( PLINT ))) == NULL ) + { + plexit( "fill_intersection_polygon: Insufficient memory" ); + } + /* Common boundary between split1 and split2. */ + /* N.B. Although basic index arithmetic for + * split 2 is done in negative orientation + * order because the index is decrementing + * relative to the index of split 2, actually + * store results in reverse order to preserve + * the positive orientation that by assumption + * both polygon 1 and 2 have. */ + k = 0; + xsplit1[k] = xintersect[0]; + ysplit1[k] = yintersect[0]; + ifsplit1[k] = 1; + nsplit2m1 = nsplit2  1; + xsplit2[nsplit2m1  k] = xintersect[0]; + ysplit2[nsplit2m1  k] = yintersect[0]; + ifsplit2[nsplit2m1  k] = 1; + kstart = k + 1; + kk = kkstart1; + /* No wrap checks on kk index below because + * it must always be in valid range (since + * polygon 1 traversed only once). */ + for ( k = kstart; k < range1 + 1; k++ ) + { + xsplit1[k] = x1[kk]; + ysplit1[k] = y1[kk]; + ifsplit1[k] = 2; + xsplit2[nsplit2m1  k] = x1[kk]; + ysplit2[nsplit2m1  k] = y1[kk++]; + ifsplit2[nsplit2m1  k] = 2; + } + xsplit1[k] = xintersect[1]; + ysplit1[k] = yintersect[1]; + ifsplit1[k] = 1; + xsplit2[nsplit2m1  k] = xintersect[1]; + ysplit2[nsplit2m1  k] = yintersect[1]; + ifsplit2[nsplit2m1  k] = 1;  if (( xsplit2 = (PLINT *) malloc( nsplit2 * sizeof ( PLINT ))) == NULL )  {  plexit( "fill_intersection_polygon: Insufficient memory" );  }  if (( ysplit2 = (PLINT *) malloc( nsplit2 * sizeof ( PLINT ))) == NULL )  {  plexit( "fill_intersection_polygon: Insufficient memory" );  }  if (( ifsplit2 = (PLINT *) malloc( nsplit2 * sizeof ( PLINT ))) == NULL )  {  plexit( "fill_intersection_polygon: Insufficient memory" );  }  /* Common boundary between split1 and split2. */  /* N.B. Although basic index arithmetic for  * split 2 is done in negative orientation  * order because the index is decrementing  * relative to the index of split 2, actually  * store results in reverse order to preserve  * the positive orientation that by assumption  * both polygon 1 and 2 have. */  k = 0;  xsplit1[k] = xintersect[0];  ysplit1[k] = yintersect[0];  ifsplit1[k] = 1;  nsplit2m1 = nsplit2  1;  xsplit2[nsplit2m1  k] = xintersect[0];  ysplit2[nsplit2m1  k] = yintersect[0];  ifsplit2[nsplit2m1  k] = 1;  kstart = k + 1;  kk = kkstart1;  /* No wrap checks on kk index below because  * it must always be in valid range (since  * polygon 1 traversed only once). */  for ( k = kstart; k < range1 + 1; k++ )  {  xsplit1[k] = x1[kk];  ysplit1[k] = y1[kk];  ifsplit1[k] = 2;  xsplit2[nsplit2m1  k] = x1[kk];  ysplit2[nsplit2m1  k] = y1[kk++];  ifsplit2[nsplit2m1  k] = 2;  }  xsplit1[k] = xintersect[1];  ysplit1[k] = yintersect[1];  ifsplit1[k] = 1;  xsplit2[nsplit2m1  k] = xintersect[1];  ysplit2[nsplit2m1  k] = yintersect[1];  ifsplit2[nsplit2m1  k] = 1; + /* Finish off collecting split1 using ascending kk + * values. */ + kstart = k + 1; + kk = kkstart21; + for ( k = kstart; k < nsplit1; k++ ) + { + xsplit1[k] = x2[kk]; + ysplit1[k] = y2[kk]; + ifsplit1[k] = if2[kk++]; + if ( kk >= n2 ) + kk = n2; + }  /* Finish off collecting split1 using ascending kk  * values. */  kstart = k + 1;  kk = kkstart21;  for ( k = kstart; k < nsplit1; k++ )  {  xsplit1[k] = x2[kk];  ysplit1[k] = y2[kk];  ifsplit1[k] = if2[kk++];  if ( kk >= n2 )  kk = n2;  } + /* N.B. the positive orientation of split1 is + * preserved since the index order is the same + * as that of polygon 2, and by assumption + * that polygon and polygon 1 have identical + * positive orientations. */ + fill_intersection_polygon( + recursion_depth + 1, ifextrapolygon, 1, fill, + x1, y1, i1start_new, n1, + xsplit1, ysplit1, ifsplit1, nsplit1 ); + free( xsplit1 ); + free( ysplit1 ); + free( ifsplit1 );  /* N.B. the positive orientation of split1 is  * preserved since the index order is the same  * as that of polygon 2, and by assumption  * that polygon and polygon 1 have identical  * positive orientations. */  fill_intersection_polygon(  recursion_depth + 1, ifextrapolygon, fill,  x1, y1, i1start, n1,  xsplit1, ysplit1, ifsplit1, nsplit1 );  free( xsplit1 );  free( ysplit1 );  free( ifsplit1 ); + /* Finish off collecting split2 using descending kk + * values. */ + kk = kkstart22; + for ( k = kstart; k < nsplit2; k++ ) + { + xsplit2[nsplit2m1  k] = x2[kk]; + ysplit2[nsplit2m1  k] = y2[kk]; + ifsplit2[nsplit2m1  k] = if2[kk]; + if ( kk < 0 ) + kk += n2; + }  /* Finish off collecting split2 using descending kk  * values. */  kk = kkstart22;  for ( k = kstart; k < nsplit2; k++ )  {  xsplit2[nsplit2m1  k] = x2[kk];  ysplit2[nsplit2m1  k] = y2[kk];  ifsplit2[nsplit2m1  k] = if2[kk];  if ( kk < 0 )  kk += n2;  }   /* N.B. the positive orientation of split2 is  * preserved since the index order is the same  * as that of polygon 2, and by assumption  * that polygon and polygon 1 have identical  * positive orientations. */  fill_intersection_polygon(  recursion_depth + 1, ifextrapolygon, fill,  x1, y1, i1start, n1,  xsplit2, ysplit2, ifsplit2, nsplit2 );  free( xsplit2 );  free( ysplit2 );  free( ifsplit2 );  return;  }  } + /* N.B. the positive orientation of split2 is + * preserved since the index order is the same + * as that of polygon 2, and by assumption + * that polygon and polygon 1 have identical + * positive orientations. */ + fill_intersection_polygon( + recursion_depth + 1, ifextrapolygon, 1, fill, + x1, y1, i1start_new, n1, + xsplit2, ysplit2, ifsplit2, nsplit2 ); + free( xsplit2 ); + free( ysplit2 ); + free( ifsplit2 ); + return; }  i2m1 = i2;  i2wrap = i2m1; }  i1m1 = i1;  i1wrap = i1m1; + i1m1 = i1; } if ( ncrossed != 0 ) @@ 1725,73 +1782,91 @@ return; }  /* This end phase is reached only if no intersections are found.  * For this case, there are 5 valid and 1 invalid combination of  * the following conditions:the intersection of polygon 2 and 1, must be  * either of them (in which case fill with the inner one), or neither  * of them (in which case don't fill at all). */ + /* This end phase is reached only if no crossings are found. */  /* Classify polygon 1 by looking for first vertex in polygon 1  * that is definitely inside or outside polygon 2. */  for ( i1 = 0; i1 < n1; i1++ ) + /* If a fill_status of +/ 1 is known, use that to fill or not since + +1 corresponds to all of polygon 2 inside polygon 1 and 1 + * corresponds to none of polygon 2 inside polygon 1. */ + if ( fill_status == 1 ) + return; + else if ( fill_status == 1 ) {  if (( ifnotpolygon1inpolygon2 =  notpointinpolygon( n2, x2, y2, x1[i1], y1[i1] )) != 1 )  break; + nfill = n2; + xfiller = x2; + yfiller = y2; }   /* Classify polygon 2 by looking for first vertex in polygon 2  * that is definitely inside or outside polygon 1. */  ifnotpolygon2inpolygon1 = 1;  for ( i2 = 0; i2 < n2; i2++ ) + else if ( fill_status == 0 ) + //else if ( 1 ) {  /* Do not bother checking vertices already known to be on the  * boundary with polygon 1. */  if ( !if2[i2] && ( ifnotpolygon2inpolygon1 =  notpointinpolygon( n1, x1, y1, x2[i2], y2[i2] )) != 1 )  break;  } + if ( recursion_depth != 0 ) + { + plwarn( "fill_intersection_polygon: Internal error; fill_status == 0 for recursion_depth > 0" ); + return; + } + /* For this case (recursion level 0) the two polygons are + * completely independent with no crossings between them or + * edges constructed from one another. + * + * The intersection of polygon 2 and 1, must be either of them (in + * which case fill with the inner one), or neither of them (in + * which case don't fill at all). */  if ( ifnotpolygon2inpolygon1 == 0 )  {  /* Polygon 2 definitely inside polygon 1. */  if ( ifnotpolygon1inpolygon2 != 0 ) + /* Classify polygon 1 by looking for first vertex in polygon 1 + * that is definitely inside or outside polygon 2. */ + for ( i1 = 0; i1 < n1; i1++ ) {  nfill = n2;  xfiller = x2;  yfiller = y2; + if (( ifnotpolygon1inpolygon2 = + notpointinpolygon( n2, x2, y2, x1[i1], y1[i1] )) != 1 ) + break; }  else + + /* Classify polygon 2 by looking for first vertex in polygon 2 + * that is definitely inside or outside polygon 1. */ + ifnotpolygon2inpolygon1 = 1; + for ( i2 = 0; i2 < n2; i2++ ) + { + /* Do not bother checking vertices already known to be on the + * boundary with polygon 1. */ + if ( !if2[i2] && ( ifnotpolygon2inpolygon1 = + notpointinpolygon( n1, x1, y1, x2[i2], y2[i2] )) != 1 ) + break; + } + + if ( ifnotpolygon2inpolygon1 == 0 && ifnotpolygon1inpolygon2 == 0 ) plwarn( "fill_intersection_polygon: Internal error; no intersections found but each polygon definitely inside the other!" );  }  else if ( ifnotpolygon2inpolygon1 == 1 )  {  /* Polygon 2 vertices near polygon 1 border. */  if ( ifnotpolygon1inpolygon2 != 0 ) + else if ( ifnotpolygon2inpolygon1 == 2 && ifnotpolygon1inpolygon2 == 2 ) + /* The polygons do not intersect each other so do not fill in this + * case. */ + return; + else if ( ifnotpolygon2inpolygon1 == 0 ) {  /* Polygon 1 vertices near polygon 2 border or definitely outside it. */ + /* Polygon 2 definitely inside polygon 1. */ nfill = n2; xfiller = x2; yfiller = y2; }  else + else if ( ifnotpolygon1inpolygon2 == 0 ) {  /* Polygon 1 vertices definitely inside polygon 2 border. */ + /* Polygon 1 definitely inside polygon 2. */ nfill = n1; xfiller = x1; yfiller = y1; }  }  else  {  /* Polygon 2 vertices definitely outside polygon 1 border. */  if ( ifnotpolygon1inpolygon2 != 2 ) + else if ( ifnotpolygon2inpolygon1 == 1 && ifnotpolygon1inpolygon2 == 1 ) {  /* Polygon 1 vertices definitely inside polygon 2 border. */  nfill = n1;  xfiller = x1;  yfiller = y1; + /* Polygon 2 vertices near polygon 1 border and vice versa which + * implies the polygons are identical. */ + nfill = n2; + xfiller = x2; + yfiller = y2; } + else + { + /* Polygon 1 inscribed in polygon 2 or vice versa. This is normally + * unlikely for two independent polygons so the implementation is + * ToDo. */ + plwarn( "fill_intersection_polygon: inscribed polygons are still ToDo" ); + } } if ( nfill > 0 ) @@ 1832,7 +1907,7 @@ PLINT xA1, PLINT yA1, PLINT xA2, PLINT yA2, PLINT xB1, PLINT yB1, PLINT xB2, PLINT yB2 ) {  PLFLT factor, fxintersect, fyintersect; + PLFLT factor, factor_NBCC, fxintersect, fyintersect; /* These variables are PLFLT not for precision, but to * avoid integer overflows if they were typed as PLINT. */ PLFLT xA2A1, yA2A1, xB2B1, yB2B1; @@ 1861,11 +1936,14 @@ xB2B1 = xB2  xB1; yB2B1 = yB2  yB1;  factor = xA2A1 * yB2B1  yA2A1 * xB2B1;  if ( fabs( factor ) == 0. ) + factor = xA2A1 * yB2B1  yA2A1 * xB2B1; + factor_NBCC = PL_NBCC * ( fabs( xA2A1 ) + fabs( yB2B1 ) + fabs( yA2A1 ) + fabs( xB2B1 )); + if ( fabs( factor ) <= factor_NBCC ) {  /* Two line segments are parallel */  status = status  PL_PARALLEL; + if ( fabs( factor ) > 0. ) + status = status  PL_NEAR_PARALLEL; + else + status = status  PL_PARALLEL; /* Choice of intersect is arbitrary in this case. Choose A1, A2, * B1, or B2 (in that order) if any of them lie inside or near * the other line segment. Otherwise, choose the average point. */ @@ 1971,3 +2049,103 @@ else return twice_area > 0.; } + +/* For the line with endpoints which are the (i11)th, and i1th + * vertices of polygon 1 with polygon 2 find all definite crossings + * with polygon 1. (The full polygon 1 information is needed only to + * help sort out (NOT IMPLEMENTED YET) ambiguous crossings near a + * vertex of polygon 1.) Sort those definite crossings in ascending + * order along the line between the (i11)th and i1th vertices of + * polygon 1, and return the first ncross (= 1 or = 2) crossings in the + * xcross, ycross, and i2cross arrays. Return a zero or positive + * status code of the actual number of crossings retained up to the + * maximum allowed value of ncross. If some error occurred, return a + * negative status code. */ + +int +number_crossings( PLINT *xcross, PLINT *ycross, PLINT *i2cross, PLINT ncross, + PLINT i1, PLINT n1, const PLINT *x1, const PLINT *y1, + PLINT n2, const PLINT *x2, const PLINT *y2 ) +{ + int i1m1, i2, i2m1, ifnotcrossed; + int ifxsort, ifascend, count_crossings = 0, status = 0; + PLINT xintersect, yintersect; + + i1m1 = i1  1; + if ( i1m1 < 0 ) + i1m1 += n1; + if ( !( ncross == 1  ncross == 2 )  + ( x1[i1m1] == x1[i1] && y1[i1m1] == y1[i1] )  n1 < 2  n2 < 2 ) + { + plwarn( "findcrossings: invalid call" ); + return 1; + } + + ifxsort = abs( x1[i1]  x1[i1m1] ) > abs( y1[i1]  y1[i1m1] ); + ifascend = ( ifxsort && x1[i1] > x1[i1m1] )  + ( !ifxsort && y1[i1] > y1[i1m1] ); + + /* Determine all crossings between the line between the (i11)th + * and i1th vertices of polygon 1 and all edges of polygon 2. + * Retain the lowest and (if ncross ==2) next lowest crossings in + * order of x (or y if ifxsort is false) along the line from i11 + * to i1. */ + + i1m1 = i1  1; + if ( i1m1 < 0 ) + i1m1 += n1; + i2m1 = n2  1; + for ( i2 = 0; i2 < n2; i2++ ) + { + if ( !( x2[i2m1] == x2[i2] && y2[i2m1] == y2[i2] )) + { + ifnotcrossed = notcrossed( &xintersect, &yintersect, + x1[i1m1], y1[i1m1], x1[i1], y1[i1], + x2[i2m1], y2[i2m1], x2[i2], y2[i2] ); + + if ( !ifnotcrossed ) + { + count_crossings++; + if ( count_crossings == 1 ) + { + xcross[0] = xintersect; + ycross[0] = yintersect; + i2cross[0] = i2; + status = 1; + } + else + { + if (( ifxsort && ifascend && xintersect < xcross[0] )  + ( !ifxsort && ifascend && yintersect < ycross[0] )  + ( ifxsort && !ifascend && xintersect >= xcross[0] )  + ( !ifxsort && !ifascend && yintersect >= ycross[0] )) + { + if ( ncross == 2 ) + { + xcross[1] = xcross[0]; + ycross[1] = ycross[0]; + i2cross[1] = i2cross[0]; + status = 2; + } + xcross[0] = xintersect; + ycross[0] = yintersect; + i2cross[0] = i2; + } + else if ( ncross == 2 && ( count_crossings == 2  ( + ( ifxsort && ifascend && xintersect < xcross[1] )  + ( !ifxsort && ifascend && yintersect < ycross[1] )  + ( ifxsort && !ifascend && xintersect >= xcross[1] )  + ( !ifxsort && !ifascend && yintersect >= ycross[1] )))) + { + xcross[1] = xintersect; + ycross[1] = yintersect; + i2cross[1] = i2; + status = 2; + } + } + } + } + i2m1 = i2; + } + return status; +} This was sent by the SourceForge.net collaborative development platform, the world's largest Open Source development site. 