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      1 /* libs/graphics/sgl/SkScan_Path.cpp
      2 **
      3 ** Copyright 2006, The Android Open Source Project
      4 **
      5 ** Licensed under the Apache License, Version 2.0 (the "License");
      6 ** you may not use this file except in compliance with the License.
      7 ** You may obtain a copy of the License at
      8 **
      9 **     http://www.apache.org/licenses/LICENSE-2.0
     10 **
     11 ** Unless required by applicable law or agreed to in writing, software
     12 ** distributed under the License is distributed on an "AS IS" BASIS,
     13 ** WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
     14 ** See the License for the specific language governing permissions and
     15 ** limitations under the License.
     16 */
     17 
     18 #include "SkScanPriv.h"
     19 #include "SkBlitter.h"
     20 #include "SkEdge.h"
     21 #include "SkGeometry.h"
     22 #include "SkPath.h"
     23 #include "SkQuadClipper.h"
     24 #include "SkRegion.h"
     25 #include "SkTemplates.h"
     26 
     27 #define USE_NEW_BUILDER
     28 
     29 #define kEDGE_HEAD_Y    SK_MinS32
     30 #define kEDGE_TAIL_Y    SK_MaxS32
     31 
     32 #ifdef SK_DEBUG
     33     static void validate_sort(const SkEdge* edge)
     34     {
     35         int y = kEDGE_HEAD_Y;
     36 
     37         while (edge->fFirstY != SK_MaxS32)
     38         {
     39             edge->validate();
     40             SkASSERT(y <= edge->fFirstY);
     41 
     42             y = edge->fFirstY;
     43             edge = edge->fNext;
     44         }
     45     }
     46 #else
     47     #define validate_sort(edge)
     48 #endif
     49 
     50 static inline void remove_edge(SkEdge* edge)
     51 {
     52     edge->fPrev->fNext = edge->fNext;
     53     edge->fNext->fPrev = edge->fPrev;
     54 }
     55 
     56 static inline void swap_edges(SkEdge* prev, SkEdge* next)
     57 {
     58     SkASSERT(prev->fNext == next && next->fPrev == prev);
     59 
     60     // remove prev from the list
     61     prev->fPrev->fNext = next;
     62     next->fPrev = prev->fPrev;
     63 
     64     // insert prev after next
     65     prev->fNext = next->fNext;
     66     next->fNext->fPrev = prev;
     67     next->fNext = prev;
     68     prev->fPrev = next;
     69 }
     70 
     71 static void backward_insert_edge_based_on_x(SkEdge* edge SkDECLAREPARAM(int, curr_y))
     72 {
     73     SkFixed x = edge->fX;
     74 
     75     for (;;)
     76     {
     77         SkEdge* prev = edge->fPrev;
     78 
     79         // add 1 to curr_y since we may have added new edges (built from curves)
     80         // that start on the next scanline
     81         SkASSERT(prev && prev->fFirstY <= curr_y + 1);
     82 
     83         if (prev->fX <= x)
     84             break;
     85 
     86         swap_edges(prev, edge);
     87     }
     88 }
     89 
     90 static void insert_new_edges(SkEdge* newEdge, int curr_y)
     91 {
     92     SkASSERT(newEdge->fFirstY >= curr_y);
     93 
     94     while (newEdge->fFirstY == curr_y)
     95     {
     96         SkEdge* next = newEdge->fNext;
     97         backward_insert_edge_based_on_x(newEdge  SkPARAM(curr_y));
     98         newEdge = next;
     99     }
    100 }
    101 
    102 #ifdef SK_DEBUG
    103 static void validate_edges_for_y(const SkEdge* edge, int curr_y)
    104 {
    105     while (edge->fFirstY <= curr_y)
    106     {
    107         SkASSERT(edge->fPrev && edge->fNext);
    108         SkASSERT(edge->fPrev->fNext == edge);
    109         SkASSERT(edge->fNext->fPrev == edge);
    110         SkASSERT(edge->fFirstY <= edge->fLastY);
    111 
    112         SkASSERT(edge->fPrev->fX <= edge->fX);
    113         edge = edge->fNext;
    114     }
    115 }
    116 #else
    117     #define validate_edges_for_y(edge, curr_y)
    118 #endif
    119 
    120 #if defined _WIN32 && _MSC_VER >= 1300  // disable warning : local variable used without having been initialized
    121 #pragma warning ( push )
    122 #pragma warning ( disable : 4701 )
    123 #endif
    124 
    125 typedef void (*PrePostProc)(SkBlitter* blitter, int y, bool isStartOfScanline);
    126 #define PREPOST_START   true
    127 #define PREPOST_END     false
    128 
    129 static void walk_edges(SkEdge* prevHead, SkPath::FillType fillType,
    130                        SkBlitter* blitter, int start_y, int stop_y,
    131                        PrePostProc proc)
    132 {
    133     validate_sort(prevHead->fNext);
    134 
    135     int curr_y = start_y;
    136     // returns 1 for evenodd, -1 for winding, regardless of inverse-ness
    137     int windingMask = (fillType & 1) ? 1 : -1;
    138 
    139     for (;;)
    140     {
    141         int     w = 0;
    142         int     left SK_INIT_TO_AVOID_WARNING;
    143         bool    in_interval = false;
    144         SkEdge* currE = prevHead->fNext;
    145         SkFixed prevX = prevHead->fX;
    146 
    147         validate_edges_for_y(currE, curr_y);
    148 
    149         if (proc) {
    150             proc(blitter, curr_y, PREPOST_START);    // pre-proc
    151         }
    152 
    153         while (currE->fFirstY <= curr_y)
    154         {
    155             SkASSERT(currE->fLastY >= curr_y);
    156 
    157             int x = (currE->fX + SK_Fixed1/2) >> 16;
    158             w += currE->fWinding;
    159             if ((w & windingMask) == 0) // we finished an interval
    160             {
    161                 SkASSERT(in_interval);
    162                 int width = x - left;
    163                 SkASSERT(width >= 0);
    164                 if (width)
    165                     blitter->blitH(left, curr_y, width);
    166                 in_interval = false;
    167             }
    168             else if (!in_interval)
    169             {
    170                 left = x;
    171                 in_interval = true;
    172             }
    173 
    174             SkEdge* next = currE->fNext;
    175             SkFixed newX;
    176 
    177             if (currE->fLastY == curr_y)    // are we done with this edge?
    178             {
    179                 if (currE->fCurveCount < 0)
    180                 {
    181                     if (((SkCubicEdge*)currE)->updateCubic())
    182                     {
    183                         SkASSERT(currE->fFirstY == curr_y + 1);
    184 
    185                         newX = currE->fX;
    186                         goto NEXT_X;
    187                     }
    188                 }
    189                 else if (currE->fCurveCount > 0)
    190                 {
    191                     if (((SkQuadraticEdge*)currE)->updateQuadratic())
    192                     {
    193                         newX = currE->fX;
    194                         goto NEXT_X;
    195                     }
    196                 }
    197                 remove_edge(currE);
    198             }
    199             else
    200             {
    201                 SkASSERT(currE->fLastY > curr_y);
    202                 newX = currE->fX + currE->fDX;
    203                 currE->fX = newX;
    204             NEXT_X:
    205                 if (newX < prevX)   // ripple currE backwards until it is x-sorted
    206                     backward_insert_edge_based_on_x(currE  SkPARAM(curr_y));
    207                 else
    208                     prevX = newX;
    209             }
    210             currE = next;
    211             SkASSERT(currE);
    212         }
    213 
    214         if (proc) {
    215             proc(blitter, curr_y, PREPOST_END);    // post-proc
    216         }
    217 
    218         curr_y += 1;
    219         if (curr_y >= stop_y)
    220             break;
    221 
    222         // now currE points to the first edge with a Yint larger than curr_y
    223         insert_new_edges(currE, curr_y);
    224     }
    225 }
    226 
    227 ///////////////////////////////////////////////////////////////////////////////
    228 
    229 // this guy overrides blitH, and will call its proxy blitter with the inverse
    230 // of the spans it is given (clipped to the left/right of the cliprect)
    231 //
    232 // used to implement inverse filltypes on paths
    233 //
    234 class InverseBlitter : public SkBlitter {
    235 public:
    236     void setBlitter(SkBlitter* blitter, const SkIRect& clip, int shift) {
    237         fBlitter = blitter;
    238         fFirstX = clip.fLeft << shift;
    239         fLastX = clip.fRight << shift;
    240     }
    241     void prepost(int y, bool isStart) {
    242         if (isStart) {
    243             fPrevX = fFirstX;
    244         } else {
    245             int invWidth = fLastX - fPrevX;
    246             if (invWidth > 0) {
    247                 fBlitter->blitH(fPrevX, y, invWidth);
    248             }
    249         }
    250     }
    251 
    252     // overrides
    253     virtual void blitH(int x, int y, int width) {
    254         int invWidth = x - fPrevX;
    255         if (invWidth > 0) {
    256             fBlitter->blitH(fPrevX, y, invWidth);
    257         }
    258         fPrevX = x + width;
    259     }
    260 
    261     // we do not expect to get called with these entrypoints
    262     virtual void blitAntiH(int, int, const SkAlpha[], const int16_t runs[]) {
    263         SkASSERT(!"blitAntiH unexpected");
    264     }
    265     virtual void blitV(int x, int y, int height, SkAlpha alpha) {
    266         SkASSERT(!"blitV unexpected");
    267     }
    268     virtual void blitRect(int x, int y, int width, int height) {
    269         SkASSERT(!"blitRect unexpected");
    270     }
    271     virtual void blitMask(const SkMask&, const SkIRect& clip) {
    272         SkASSERT(!"blitMask unexpected");
    273     }
    274     virtual const SkBitmap* justAnOpaqueColor(uint32_t* value) {
    275         SkASSERT(!"justAnOpaqueColor unexpected");
    276         return NULL;
    277     }
    278 
    279 private:
    280     SkBlitter*  fBlitter;
    281     int         fFirstX, fLastX, fPrevX;
    282 };
    283 
    284 static void PrePostInverseBlitterProc(SkBlitter* blitter, int y, bool isStart) {
    285     ((InverseBlitter*)blitter)->prepost(y, isStart);
    286 }
    287 
    288 ///////////////////////////////////////////////////////////////////////////////
    289 
    290 #if defined _WIN32 && _MSC_VER >= 1300
    291 #pragma warning ( pop )
    292 #endif
    293 
    294 /*  Our line edge relies on the maximum span being <= 512, so that it can
    295     use FDot6 and keep the dx,dy in 16bits (for much faster slope divide).
    296     This function returns true if the specified line is too big.
    297 */
    298 static inline bool line_too_big(const SkPoint pts[2])
    299 {
    300     SkScalar dx = pts[1].fX - pts[0].fX;
    301     SkScalar dy = pts[1].fY - pts[0].fY;
    302 
    303     return  SkScalarAbs(dx) > SkIntToScalar(511) ||
    304             SkScalarAbs(dy) > SkIntToScalar(511);
    305 }
    306 
    307 #ifdef USE_NEW_BUILDER
    308 #include "SkEdgeBuilder.h"
    309 #else
    310 static int build_edges(SkEdge edge[], const SkPath& path,
    311                        const SkIRect* clipRect, SkEdge* list[], int shiftUp) {
    312     SkEdge**        start = list;
    313     SkPath::Iter    iter(path, true);
    314     SkPoint         pts[4];
    315     SkPath::Verb    verb;
    316 
    317     SkQuadClipper qclipper;
    318     if (clipRect) {
    319         SkIRect r;
    320         r.set(clipRect->fLeft >> shiftUp, clipRect->fTop >> shiftUp,
    321               clipRect->fRight >> shiftUp, clipRect->fBottom >> shiftUp);
    322         qclipper.setClip(r);
    323     }
    324 
    325     while ((verb = iter.next(pts)) != SkPath::kDone_Verb) {
    326         switch (verb) {
    327             case SkPath::kLine_Verb:
    328                 if (edge->setLine(pts[0], pts[1], clipRect, shiftUp)) {
    329                     *list++ = edge;
    330                     edge = (SkEdge*)((char*)edge + sizeof(SkEdge));
    331                 }
    332                 break;
    333             case SkPath::kQuad_Verb: {
    334                 SkPoint tmp[5], clippedPts[3];
    335                 SkPoint* p = tmp;
    336                 int     count = SkChopQuadAtYExtrema(pts, tmp);
    337 
    338                 do {
    339                     const SkPoint* qpts = p;
    340                     if (clipRect) {
    341                         if (!qclipper.clipQuad(p, clippedPts)) {
    342                             goto NEXT_CHOPPED_QUAD;
    343                         }
    344                         qpts = clippedPts;
    345                     }
    346                     if (((SkQuadraticEdge*)edge)->setQuadratic(qpts, shiftUp)) {
    347                         *list++ = edge;
    348                         edge = (SkEdge*)((char*)edge + sizeof(SkQuadraticEdge));
    349                     }
    350                 NEXT_CHOPPED_QUAD:
    351                     p += 2;
    352                 } while (--count >= 0);
    353                 break;
    354             }
    355             case SkPath::kCubic_Verb: {
    356                 SkPoint tmp[10];
    357                 SkPoint* p = tmp;
    358                 int     count = SkChopCubicAtYExtrema(pts, tmp);
    359                 SkASSERT(count >= 0 && count <= 2);
    360 
    361                 do {
    362                     if (((SkCubicEdge*)edge)->setCubic(p, clipRect, shiftUp))
    363                     {
    364                         *list++ = edge;
    365                         edge = (SkEdge*)((char*)edge + sizeof(SkCubicEdge));
    366                     }
    367                     p += 3;
    368                 } while (--count >= 0);
    369                 break;
    370             }
    371         default:
    372             break;
    373         }
    374     }
    375     return (int)(list - start);
    376 }
    377 
    378 #ifdef SK_DEBUG
    379 /* 'quick' computation of the max sized needed to allocated for
    380     our edgelist.
    381 */
    382 static int worst_case_edge_count(const SkPath& path, size_t* storage)
    383 {
    384     size_t  size = 0;
    385     int     edgeCount = 0;
    386 
    387     SkPath::Iter    iter(path, true);
    388     SkPath::Verb    verb;
    389 
    390     while ((verb = iter.next(NULL)) != SkPath::kDone_Verb)
    391     {
    392         switch (verb) {
    393         case SkPath::kLine_Verb:
    394             edgeCount += 1;
    395             size += sizeof(SkQuadraticEdge);    // treat line like Quad (in case its > 512)
    396             break;
    397         case SkPath::kQuad_Verb:
    398             edgeCount += 2;                     // might need 2 edges when we chop on Y extrema
    399             size += 2 * sizeof(SkQuadraticEdge);
    400             break;
    401         case SkPath::kCubic_Verb:
    402             edgeCount += 3;                     // might need 3 edges when we chop on Y extrema
    403             size += 3 * sizeof(SkCubicEdge);
    404             break;
    405         default:
    406             break;
    407         }
    408     }
    409 
    410     SkASSERT(storage);
    411     *storage = size;
    412     return edgeCount;
    413 }
    414 #endif
    415 
    416 /* Much faster than worst_case_edge_count, but over estimates even more
    417 */
    418 static int cheap_worst_case_edge_count(const SkPath& path, size_t* storage) {
    419     int ptCount = path.getPoints(NULL, 0);
    420     // worst case is curve, close, curve, close, as that is
    421     //     2 lines per pt, or             : pts * 2
    422     //     2 quads + 1 line per 2 pts, or : pts * 3 / 2
    423     //     3 cubics + 1 line per 3 pts    : pts * 4 / 3
    424     int edgeCount = ptCount << 1;
    425     // worst storage, due to relative size of different edge types, is
    426     // quads * 3 / 2
    427     size_t quadSize = (ptCount * 3 >> 1) * sizeof(SkQuadraticEdge);
    428 #if 0
    429     size_t lineSize = (ptCount << 1) * sizeof(SkEdge);
    430     size_t cubicSize = (ptCount * 3 / 4) * sizeof(SkCubicEdge);
    431     SkASSERT(lineSize <= quadSize);
    432     SkASSERT(cubicSize <= quadSize);
    433 #endif
    434     *storage = quadSize;
    435     return edgeCount;
    436 }
    437 #endif
    438 
    439 ///////////////////////////////////////////////////////////////////////////////
    440 
    441 extern "C" {
    442     static int edge_compare(const void* a, const void* b) {
    443         const SkEdge* edgea = *(const SkEdge**)a;
    444         const SkEdge* edgeb = *(const SkEdge**)b;
    445 
    446         int valuea = edgea->fFirstY;
    447         int valueb = edgeb->fFirstY;
    448 
    449         if (valuea == valueb) {
    450             valuea = edgea->fX;
    451             valueb = edgeb->fX;
    452         }
    453 
    454         // this overflows if valuea >>> valueb or vice-versa
    455         //     return valuea - valueb;
    456         // do perform the slower but safe compares
    457         return (valuea < valueb) ? -1 : (valuea > valueb);
    458     }
    459 }
    460 
    461 static SkEdge* sort_edges(SkEdge* list[], int count, SkEdge** last) {
    462     qsort(list, count, sizeof(SkEdge*), edge_compare);
    463 
    464     // now make the edges linked in sorted order
    465     for (int i = 1; i < count; i++) {
    466         list[i - 1]->fNext = list[i];
    467         list[i]->fPrev = list[i - 1];
    468     }
    469 
    470     *last = list[count - 1];
    471     return list[0];
    472 }
    473 
    474 // clipRect may be null, even though we always have a clip. This indicates that
    475 // the path is contained in the clip, and so we can ignore it during the blit
    476 //
    477 // clipRect (if no null) has already been shifted up
    478 //
    479 void sk_fill_path(const SkPath& path, const SkIRect* clipRect, SkBlitter* blitter,
    480                   int start_y, int stop_y, int shiftEdgesUp, const SkRegion& clipRgn)
    481 {
    482     SkASSERT(&path && blitter);
    483 
    484 #ifdef USE_NEW_BUILDER
    485     SkEdgeBuilder   builder;
    486 
    487     int count = builder.build(path, clipRect, shiftEdgesUp);
    488     SkEdge**    list = builder.edgeList();
    489 #else
    490     size_t  size;
    491     int     maxCount = cheap_worst_case_edge_count(path, &size);
    492 
    493 #ifdef SK_DEBUG
    494     {
    495         size_t  size2;
    496         int     maxCount2 = worst_case_edge_count(path, &size2);
    497 
    498         SkASSERT(maxCount >= maxCount2 && size >= size2);
    499     }
    500 #endif
    501 
    502     SkAutoMalloc    memory(maxCount * sizeof(SkEdge*) + size);
    503     SkEdge**        list = (SkEdge**)memory.get();
    504     SkEdge*         initialEdge = (SkEdge*)(list + maxCount);
    505     int             count = build_edges(initialEdge, path, clipRect, list,
    506                                         shiftEdgesUp);
    507     SkASSERT(count <= maxCount);
    508 #endif
    509 
    510     if (count < 2) {
    511         return;
    512     }
    513 
    514     SkEdge headEdge, tailEdge, *last;
    515     // this returns the first and last edge after they're sorted into a dlink list
    516     SkEdge* edge = sort_edges(list, count, &last);
    517 
    518     headEdge.fPrev = NULL;
    519     headEdge.fNext = edge;
    520     headEdge.fFirstY = kEDGE_HEAD_Y;
    521     headEdge.fX = SK_MinS32;
    522     edge->fPrev = &headEdge;
    523 
    524     tailEdge.fPrev = last;
    525     tailEdge.fNext = NULL;
    526     tailEdge.fFirstY = kEDGE_TAIL_Y;
    527     last->fNext = &tailEdge;
    528 
    529     // now edge is the head of the sorted linklist
    530 
    531     start_y <<= shiftEdgesUp;
    532     stop_y <<= shiftEdgesUp;
    533     if (clipRect && start_y < clipRect->fTop) {
    534         start_y = clipRect->fTop;
    535     }
    536     if (clipRect && stop_y > clipRect->fBottom) {
    537         stop_y = clipRect->fBottom;
    538     }
    539 
    540     InverseBlitter  ib;
    541     PrePostProc     proc = NULL;
    542 
    543     if (path.isInverseFillType()) {
    544         ib.setBlitter(blitter, clipRgn.getBounds(), shiftEdgesUp);
    545         blitter = &ib;
    546         proc = PrePostInverseBlitterProc;
    547     }
    548 
    549     walk_edges(&headEdge, path.getFillType(), blitter, start_y, stop_y, proc);
    550 }
    551 
    552 void sk_blit_above_and_below(SkBlitter* blitter, const SkIRect& ir,
    553                              const SkRegion& clip) {
    554     const SkIRect& cr = clip.getBounds();
    555     SkIRect tmp;
    556 
    557     tmp.fLeft = cr.fLeft;
    558     tmp.fRight = cr.fRight;
    559 
    560     tmp.fTop = cr.fTop;
    561     tmp.fBottom = ir.fTop;
    562     if (!tmp.isEmpty()) {
    563         blitter->blitRectRegion(tmp, clip);
    564     }
    565 
    566     tmp.fTop = ir.fBottom;
    567     tmp.fBottom = cr.fBottom;
    568     if (!tmp.isEmpty()) {
    569         blitter->blitRectRegion(tmp, clip);
    570     }
    571 }
    572 
    573 /////////////////////////////////////////////////////////////////////////////////////
    574 
    575 SkScanClipper::SkScanClipper(SkBlitter* blitter, const SkRegion* clip, const SkIRect& ir)
    576 {
    577     fBlitter = NULL;     // null means blit nothing
    578     fClipRect = NULL;
    579 
    580     if (clip)
    581     {
    582         fClipRect = &clip->getBounds();
    583         if (!SkIRect::Intersects(*fClipRect, ir))  // completely clipped out
    584             return;
    585 
    586         if (clip->isRect())
    587         {
    588             if (fClipRect->contains(ir))
    589                 fClipRect = NULL;
    590             else
    591             {
    592                 // only need a wrapper blitter if we're horizontally clipped
    593                 if (fClipRect->fLeft > ir.fLeft || fClipRect->fRight < ir.fRight)
    594                 {
    595                     fRectBlitter.init(blitter, *fClipRect);
    596                     blitter = &fRectBlitter;
    597                 }
    598             }
    599         }
    600         else
    601         {
    602             fRgnBlitter.init(blitter, clip);
    603             blitter = &fRgnBlitter;
    604         }
    605     }
    606     fBlitter = blitter;
    607 }
    608 
    609 ///////////////////////////////////////////////////////////////////////////////
    610 
    611 void SkScan::FillPath(const SkPath& path, const SkRegion& clip,
    612                       SkBlitter* blitter) {
    613     if (clip.isEmpty()) {
    614         return;
    615     }
    616 
    617     SkIRect ir;
    618     path.getBounds().round(&ir);
    619     if (ir.isEmpty()) {
    620         if (path.isInverseFillType()) {
    621             blitter->blitRegion(clip);
    622         }
    623         return;
    624     }
    625 
    626     SkScanClipper   clipper(blitter, &clip, ir);
    627 
    628     blitter = clipper.getBlitter();
    629     if (blitter) {
    630         if (path.isInverseFillType()) {
    631             sk_blit_above_and_below(blitter, ir, clip);
    632         }
    633         sk_fill_path(path, clipper.getClipRect(), blitter, ir.fTop, ir.fBottom, 0, clip);
    634     } else {
    635         // what does it mean to not have a blitter if path.isInverseFillType???
    636     }
    637 }
    638 
    639 ///////////////////////////////////////////////////////////////////////////////
    640 
    641 static int build_tri_edges(SkEdge edge[], const SkPoint pts[],
    642                            const SkIRect* clipRect, SkEdge* list[]) {
    643     SkEdge** start = list;
    644 
    645     if (edge->setLine(pts[0], pts[1], clipRect, 0)) {
    646         *list++ = edge;
    647         edge = (SkEdge*)((char*)edge + sizeof(SkEdge));
    648     }
    649     if (edge->setLine(pts[1], pts[2], clipRect, 0)) {
    650         *list++ = edge;
    651         edge = (SkEdge*)((char*)edge + sizeof(SkEdge));
    652     }
    653     if (edge->setLine(pts[2], pts[0], clipRect, 0)) {
    654         *list++ = edge;
    655     }
    656     return (int)(list - start);
    657 }
    658 
    659 
    660 static void sk_fill_triangle(const SkPoint pts[], const SkIRect* clipRect,
    661                              SkBlitter* blitter, const SkIRect& ir) {
    662     SkASSERT(pts && blitter);
    663 
    664     SkEdge edgeStorage[3];
    665     SkEdge* list[3];
    666 
    667     int count = build_tri_edges(edgeStorage, pts, clipRect, list);
    668     if (count < 2) {
    669         return;
    670     }
    671 
    672     SkEdge headEdge, tailEdge, *last;
    673 
    674     // this returns the first and last edge after they're sorted into a dlink list
    675     SkEdge* edge = sort_edges(list, count, &last);
    676 
    677     headEdge.fPrev = NULL;
    678     headEdge.fNext = edge;
    679     headEdge.fFirstY = kEDGE_HEAD_Y;
    680     headEdge.fX = SK_MinS32;
    681     edge->fPrev = &headEdge;
    682 
    683     tailEdge.fPrev = last;
    684     tailEdge.fNext = NULL;
    685     tailEdge.fFirstY = kEDGE_TAIL_Y;
    686     last->fNext = &tailEdge;
    687 
    688     // now edge is the head of the sorted linklist
    689     int stop_y = ir.fBottom;
    690     if (clipRect && stop_y > clipRect->fBottom) {
    691         stop_y = clipRect->fBottom;
    692     }
    693     int start_y = ir.fTop;
    694     if (clipRect && start_y < clipRect->fTop) {
    695         start_y = clipRect->fTop;
    696     }
    697     walk_edges(&headEdge, SkPath::kEvenOdd_FillType, blitter, start_y, stop_y, NULL);
    698 }
    699 
    700 void SkScan::FillTriangle(const SkPoint pts[], const SkRegion* clip,
    701                           SkBlitter* blitter) {
    702     if (clip && clip->isEmpty()) {
    703         return;
    704     }
    705 
    706     SkRect  r;
    707     SkIRect ir;
    708     r.set(pts, 3);
    709     r.round(&ir);
    710     if (ir.isEmpty()) {
    711         return;
    712     }
    713 
    714     SkScanClipper   clipper(blitter, clip, ir);
    715 
    716     blitter = clipper.getBlitter();
    717     if (NULL != blitter) {
    718         sk_fill_triangle(pts, clipper.getClipRect(), blitter, ir);
    719     }
    720 }
    721 
    722