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      1 /*
      2  * Copyright 2011 Google Inc.
      3  *
      4  * Use of this source code is governed by a BSD-style license that can be
      5  * found in the LICENSE file.
      6  */
      7 
      8 #include "GrAAHairLinePathRenderer.h"
      9 
     10 #include "GrContext.h"
     11 #include "GrDrawState.h"
     12 #include "GrDrawTargetCaps.h"
     13 #include "GrEffect.h"
     14 #include "GrGpu.h"
     15 #include "GrIndexBuffer.h"
     16 #include "GrPathUtils.h"
     17 #include "GrTBackendEffectFactory.h"
     18 #include "SkGeometry.h"
     19 #include "SkStroke.h"
     20 #include "SkTemplates.h"
     21 
     22 #include "effects/GrBezierEffect.h"
     23 
     24 namespace {
     25 // quadratics are rendered as 5-sided polys in order to bound the
     26 // AA stroke around the center-curve. See comments in push_quad_index_buffer and
     27 // bloat_quad. Quadratics and conics share an index buffer
     28 static const int kVertsPerQuad = 5;
     29 static const int kIdxsPerQuad = 9;
     30 
     31 // lines are rendered as:
     32 //      *______________*
     33 //      |\ -_______   /|
     34 //      | \        \ / |
     35 //      |  *--------*  |
     36 //      | /  ______/ \ |
     37 //      */_-__________\*
     38 // For: 6 vertices and 18 indices (for 6 triangles)
     39 static const int kVertsPerLineSeg = 6;
     40 static const int kIdxsPerLineSeg = 18;
     41 
     42 static const int kNumQuadsInIdxBuffer = 256;
     43 static const size_t kQuadIdxSBufize = kIdxsPerQuad *
     44                                       sizeof(uint16_t) *
     45                                       kNumQuadsInIdxBuffer;
     46 
     47 static const int kNumLineSegsInIdxBuffer = 256;
     48 static const size_t kLineSegIdxSBufize = kIdxsPerLineSeg *
     49                                          sizeof(uint16_t) *
     50                                          kNumLineSegsInIdxBuffer;
     51 
     52 static bool push_quad_index_data(GrIndexBuffer* qIdxBuffer) {
     53     uint16_t* data = (uint16_t*) qIdxBuffer->map();
     54     bool tempData = NULL == data;
     55     if (tempData) {
     56         data = SkNEW_ARRAY(uint16_t, kNumQuadsInIdxBuffer * kIdxsPerQuad);
     57     }
     58     for (int i = 0; i < kNumQuadsInIdxBuffer; ++i) {
     59 
     60         // Each quadratic is rendered as a five sided polygon. This poly bounds
     61         // the quadratic's bounding triangle but has been expanded so that the
     62         // 1-pixel wide area around the curve is inside the poly.
     63         // If a,b,c are the original control points then the poly a0,b0,c0,c1,a1
     64         // that is rendered would look like this:
     65         //              b0
     66         //              b
     67         //
     68         //     a0              c0
     69         //      a            c
     70         //       a1       c1
     71         // Each is drawn as three triangles specified by these 9 indices:
     72         int baseIdx = i * kIdxsPerQuad;
     73         uint16_t baseVert = (uint16_t)(i * kVertsPerQuad);
     74         data[0 + baseIdx] = baseVert + 0; // a0
     75         data[1 + baseIdx] = baseVert + 1; // a1
     76         data[2 + baseIdx] = baseVert + 2; // b0
     77         data[3 + baseIdx] = baseVert + 2; // b0
     78         data[4 + baseIdx] = baseVert + 4; // c1
     79         data[5 + baseIdx] = baseVert + 3; // c0
     80         data[6 + baseIdx] = baseVert + 1; // a1
     81         data[7 + baseIdx] = baseVert + 4; // c1
     82         data[8 + baseIdx] = baseVert + 2; // b0
     83     }
     84     if (tempData) {
     85         bool ret = qIdxBuffer->updateData(data, kQuadIdxSBufize);
     86         delete[] data;
     87         return ret;
     88     } else {
     89         qIdxBuffer->unmap();
     90         return true;
     91     }
     92 }
     93 
     94 static bool push_line_index_data(GrIndexBuffer* lIdxBuffer) {
     95     uint16_t* data = (uint16_t*) lIdxBuffer->map();
     96     bool tempData = NULL == data;
     97     if (tempData) {
     98         data = SkNEW_ARRAY(uint16_t, kNumLineSegsInIdxBuffer * kIdxsPerLineSeg);
     99     }
    100     for (int i = 0; i < kNumLineSegsInIdxBuffer; ++i) {
    101         // Each line segment is rendered as two quads and two triangles.
    102         // p0 and p1 have alpha = 1 while all other points have alpha = 0.
    103         // The four external points are offset 1 pixel perpendicular to the
    104         // line and half a pixel parallel to the line.
    105         //
    106         // p4                  p5
    107         //      p0         p1
    108         // p2                  p3
    109         //
    110         // Each is drawn as six triangles specified by these 18 indices:
    111         int baseIdx = i * kIdxsPerLineSeg;
    112         uint16_t baseVert = (uint16_t)(i * kVertsPerLineSeg);
    113         data[0 + baseIdx] = baseVert + 0;
    114         data[1 + baseIdx] = baseVert + 1;
    115         data[2 + baseIdx] = baseVert + 3;
    116 
    117         data[3 + baseIdx] = baseVert + 0;
    118         data[4 + baseIdx] = baseVert + 3;
    119         data[5 + baseIdx] = baseVert + 2;
    120 
    121         data[6 + baseIdx] = baseVert + 0;
    122         data[7 + baseIdx] = baseVert + 4;
    123         data[8 + baseIdx] = baseVert + 5;
    124 
    125         data[9 + baseIdx] = baseVert + 0;
    126         data[10+ baseIdx] = baseVert + 5;
    127         data[11+ baseIdx] = baseVert + 1;
    128 
    129         data[12 + baseIdx] = baseVert + 0;
    130         data[13 + baseIdx] = baseVert + 2;
    131         data[14 + baseIdx] = baseVert + 4;
    132 
    133         data[15 + baseIdx] = baseVert + 1;
    134         data[16 + baseIdx] = baseVert + 5;
    135         data[17 + baseIdx] = baseVert + 3;
    136     }
    137     if (tempData) {
    138         bool ret = lIdxBuffer->updateData(data, kLineSegIdxSBufize);
    139         delete[] data;
    140         return ret;
    141     } else {
    142         lIdxBuffer->unmap();
    143         return true;
    144     }
    145 }
    146 }
    147 
    148 GrPathRenderer* GrAAHairLinePathRenderer::Create(GrContext* context) {
    149     GrGpu* gpu = context->getGpu();
    150     GrIndexBuffer* qIdxBuf = gpu->createIndexBuffer(kQuadIdxSBufize, false);
    151     SkAutoTUnref<GrIndexBuffer> qIdxBuffer(qIdxBuf);
    152     if (NULL == qIdxBuf || !push_quad_index_data(qIdxBuf)) {
    153         return NULL;
    154     }
    155     GrIndexBuffer* lIdxBuf = gpu->createIndexBuffer(kLineSegIdxSBufize, false);
    156     SkAutoTUnref<GrIndexBuffer> lIdxBuffer(lIdxBuf);
    157     if (NULL == lIdxBuf || !push_line_index_data(lIdxBuf)) {
    158         return NULL;
    159     }
    160     return SkNEW_ARGS(GrAAHairLinePathRenderer,
    161                       (context, lIdxBuf, qIdxBuf));
    162 }
    163 
    164 GrAAHairLinePathRenderer::GrAAHairLinePathRenderer(
    165                                         const GrContext* context,
    166                                         const GrIndexBuffer* linesIndexBuffer,
    167                                         const GrIndexBuffer* quadsIndexBuffer) {
    168     fLinesIndexBuffer = linesIndexBuffer;
    169     linesIndexBuffer->ref();
    170     fQuadsIndexBuffer = quadsIndexBuffer;
    171     quadsIndexBuffer->ref();
    172 }
    173 
    174 GrAAHairLinePathRenderer::~GrAAHairLinePathRenderer() {
    175     fLinesIndexBuffer->unref();
    176     fQuadsIndexBuffer->unref();
    177 }
    178 
    179 namespace {
    180 
    181 #define PREALLOC_PTARRAY(N) SkSTArray<(N),SkPoint, true>
    182 
    183 // Takes 178th time of logf on Z600 / VC2010
    184 int get_float_exp(float x) {
    185     GR_STATIC_ASSERT(sizeof(int) == sizeof(float));
    186 #ifdef SK_DEBUG
    187     static bool tested;
    188     if (!tested) {
    189         tested = true;
    190         SkASSERT(get_float_exp(0.25f) == -2);
    191         SkASSERT(get_float_exp(0.3f) == -2);
    192         SkASSERT(get_float_exp(0.5f) == -1);
    193         SkASSERT(get_float_exp(1.f) == 0);
    194         SkASSERT(get_float_exp(2.f) == 1);
    195         SkASSERT(get_float_exp(2.5f) == 1);
    196         SkASSERT(get_float_exp(8.f) == 3);
    197         SkASSERT(get_float_exp(100.f) == 6);
    198         SkASSERT(get_float_exp(1000.f) == 9);
    199         SkASSERT(get_float_exp(1024.f) == 10);
    200         SkASSERT(get_float_exp(3000000.f) == 21);
    201     }
    202 #endif
    203     const int* iptr = (const int*)&x;
    204     return (((*iptr) & 0x7f800000) >> 23) - 127;
    205 }
    206 
    207 // Uses the max curvature function for quads to estimate
    208 // where to chop the conic. If the max curvature is not
    209 // found along the curve segment it will return 1 and
    210 // dst[0] is the original conic. If it returns 2 the dst[0]
    211 // and dst[1] are the two new conics.
    212 int split_conic(const SkPoint src[3], SkConic dst[2], const SkScalar weight) {
    213     SkScalar t = SkFindQuadMaxCurvature(src);
    214     if (t == 0) {
    215         if (dst) {
    216             dst[0].set(src, weight);
    217         }
    218         return 1;
    219     } else {
    220         if (dst) {
    221             SkConic conic;
    222             conic.set(src, weight);
    223             conic.chopAt(t, dst);
    224         }
    225         return 2;
    226     }
    227 }
    228 
    229 // Calls split_conic on the entire conic and then once more on each subsection.
    230 // Most cases will result in either 1 conic (chop point is not within t range)
    231 // or 3 points (split once and then one subsection is split again).
    232 int chop_conic(const SkPoint src[3], SkConic dst[4], const SkScalar weight) {
    233     SkConic dstTemp[2];
    234     int conicCnt = split_conic(src, dstTemp, weight);
    235     if (2 == conicCnt) {
    236         int conicCnt2 = split_conic(dstTemp[0].fPts, dst, dstTemp[0].fW);
    237         conicCnt = conicCnt2 + split_conic(dstTemp[1].fPts, &dst[conicCnt2], dstTemp[1].fW);
    238     } else {
    239         dst[0] = dstTemp[0];
    240     }
    241     return conicCnt;
    242 }
    243 
    244 // returns 0 if quad/conic is degen or close to it
    245 // in this case approx the path with lines
    246 // otherwise returns 1
    247 int is_degen_quad_or_conic(const SkPoint p[3]) {
    248     static const SkScalar gDegenerateToLineTol = SK_Scalar1;
    249     static const SkScalar gDegenerateToLineTolSqd =
    250         SkScalarMul(gDegenerateToLineTol, gDegenerateToLineTol);
    251 
    252     if (p[0].distanceToSqd(p[1]) < gDegenerateToLineTolSqd ||
    253         p[1].distanceToSqd(p[2]) < gDegenerateToLineTolSqd) {
    254         return 1;
    255     }
    256 
    257     SkScalar dsqd = p[1].distanceToLineBetweenSqd(p[0], p[2]);
    258     if (dsqd < gDegenerateToLineTolSqd) {
    259         return 1;
    260     }
    261 
    262     if (p[2].distanceToLineBetweenSqd(p[1], p[0]) < gDegenerateToLineTolSqd) {
    263         return 1;
    264     }
    265     return 0;
    266 }
    267 
    268 // we subdivide the quads to avoid huge overfill
    269 // if it returns -1 then should be drawn as lines
    270 int num_quad_subdivs(const SkPoint p[3]) {
    271     static const SkScalar gDegenerateToLineTol = SK_Scalar1;
    272     static const SkScalar gDegenerateToLineTolSqd =
    273         SkScalarMul(gDegenerateToLineTol, gDegenerateToLineTol);
    274 
    275     if (p[0].distanceToSqd(p[1]) < gDegenerateToLineTolSqd ||
    276         p[1].distanceToSqd(p[2]) < gDegenerateToLineTolSqd) {
    277         return -1;
    278     }
    279 
    280     SkScalar dsqd = p[1].distanceToLineBetweenSqd(p[0], p[2]);
    281     if (dsqd < gDegenerateToLineTolSqd) {
    282         return -1;
    283     }
    284 
    285     if (p[2].distanceToLineBetweenSqd(p[1], p[0]) < gDegenerateToLineTolSqd) {
    286         return -1;
    287     }
    288 
    289     // tolerance of triangle height in pixels
    290     // tuned on windows  Quadro FX 380 / Z600
    291     // trade off of fill vs cpu time on verts
    292     // maybe different when do this using gpu (geo or tess shaders)
    293     static const SkScalar gSubdivTol = 175 * SK_Scalar1;
    294 
    295     if (dsqd <= SkScalarMul(gSubdivTol, gSubdivTol)) {
    296         return 0;
    297     } else {
    298         static const int kMaxSub = 4;
    299         // subdividing the quad reduces d by 4. so we want x = log4(d/tol)
    300         // = log4(d*d/tol*tol)/2
    301         // = log2(d*d/tol*tol)
    302 
    303         // +1 since we're ignoring the mantissa contribution.
    304         int log = get_float_exp(dsqd/(gSubdivTol*gSubdivTol)) + 1;
    305         log = SkTMin(SkTMax(0, log), kMaxSub);
    306         return log;
    307     }
    308 }
    309 
    310 /**
    311  * Generates the lines and quads to be rendered. Lines are always recorded in
    312  * device space. We will do a device space bloat to account for the 1pixel
    313  * thickness.
    314  * Quads are recorded in device space unless m contains
    315  * perspective, then in they are in src space. We do this because we will
    316  * subdivide large quads to reduce over-fill. This subdivision has to be
    317  * performed before applying the perspective matrix.
    318  */
    319 int generate_lines_and_quads(const SkPath& path,
    320                              const SkMatrix& m,
    321                              const SkIRect& devClipBounds,
    322                              GrAAHairLinePathRenderer::PtArray* lines,
    323                              GrAAHairLinePathRenderer::PtArray* quads,
    324                              GrAAHairLinePathRenderer::PtArray* conics,
    325                              GrAAHairLinePathRenderer::IntArray* quadSubdivCnts,
    326                              GrAAHairLinePathRenderer::FloatArray* conicWeights) {
    327     SkPath::Iter iter(path, false);
    328 
    329     int totalQuadCount = 0;
    330     SkRect bounds;
    331     SkIRect ibounds;
    332 
    333     bool persp = m.hasPerspective();
    334 
    335     for (;;) {
    336         SkPoint pathPts[4];
    337         SkPoint devPts[4];
    338         SkPath::Verb verb = iter.next(pathPts);
    339         switch (verb) {
    340             case SkPath::kConic_Verb: {
    341                 SkConic dst[4];
    342                 // We chop the conics to create tighter clipping to hide error
    343                 // that appears near max curvature of very thin conics. Thin
    344                 // hyperbolas with high weight still show error.
    345                 int conicCnt = chop_conic(pathPts, dst, iter.conicWeight());
    346                 for (int i = 0; i < conicCnt; ++i) {
    347                     SkPoint* chopPnts = dst[i].fPts;
    348                     m.mapPoints(devPts, chopPnts, 3);
    349                     bounds.setBounds(devPts, 3);
    350                     bounds.outset(SK_Scalar1, SK_Scalar1);
    351                     bounds.roundOut(&ibounds);
    352                     if (SkIRect::Intersects(devClipBounds, ibounds)) {
    353                         if (is_degen_quad_or_conic(devPts)) {
    354                             SkPoint* pts = lines->push_back_n(4);
    355                             pts[0] = devPts[0];
    356                             pts[1] = devPts[1];
    357                             pts[2] = devPts[1];
    358                             pts[3] = devPts[2];
    359                         } else {
    360                             // when in perspective keep conics in src space
    361                             SkPoint* cPts = persp ? chopPnts : devPts;
    362                             SkPoint* pts = conics->push_back_n(3);
    363                             pts[0] = cPts[0];
    364                             pts[1] = cPts[1];
    365                             pts[2] = cPts[2];
    366                             conicWeights->push_back() = dst[i].fW;
    367                         }
    368                     }
    369                 }
    370                 break;
    371             }
    372             case SkPath::kMove_Verb:
    373                 break;
    374             case SkPath::kLine_Verb:
    375                 m.mapPoints(devPts, pathPts, 2);
    376                 bounds.setBounds(devPts, 2);
    377                 bounds.outset(SK_Scalar1, SK_Scalar1);
    378                 bounds.roundOut(&ibounds);
    379                 if (SkIRect::Intersects(devClipBounds, ibounds)) {
    380                     SkPoint* pts = lines->push_back_n(2);
    381                     pts[0] = devPts[0];
    382                     pts[1] = devPts[1];
    383                 }
    384                 break;
    385             case SkPath::kQuad_Verb: {
    386                 SkPoint choppedPts[5];
    387                 // Chopping the quad helps when the quad is either degenerate or nearly degenerate.
    388                 // When it is degenerate it allows the approximation with lines to work since the
    389                 // chop point (if there is one) will be at the parabola's vertex. In the nearly
    390                 // degenerate the QuadUVMatrix computed for the points is almost singular which
    391                 // can cause rendering artifacts.
    392                 int n = SkChopQuadAtMaxCurvature(pathPts, choppedPts);
    393                 for (int i = 0; i < n; ++i) {
    394                     SkPoint* quadPts = choppedPts + i * 2;
    395                     m.mapPoints(devPts, quadPts, 3);
    396                     bounds.setBounds(devPts, 3);
    397                     bounds.outset(SK_Scalar1, SK_Scalar1);
    398                     bounds.roundOut(&ibounds);
    399 
    400                     if (SkIRect::Intersects(devClipBounds, ibounds)) {
    401                         int subdiv = num_quad_subdivs(devPts);
    402                         SkASSERT(subdiv >= -1);
    403                         if (-1 == subdiv) {
    404                             SkPoint* pts = lines->push_back_n(4);
    405                             pts[0] = devPts[0];
    406                             pts[1] = devPts[1];
    407                             pts[2] = devPts[1];
    408                             pts[3] = devPts[2];
    409                         } else {
    410                             // when in perspective keep quads in src space
    411                             SkPoint* qPts = persp ? quadPts : devPts;
    412                             SkPoint* pts = quads->push_back_n(3);
    413                             pts[0] = qPts[0];
    414                             pts[1] = qPts[1];
    415                             pts[2] = qPts[2];
    416                             quadSubdivCnts->push_back() = subdiv;
    417                             totalQuadCount += 1 << subdiv;
    418                         }
    419                     }
    420                 }
    421                 break;
    422             }
    423             case SkPath::kCubic_Verb:
    424                 m.mapPoints(devPts, pathPts, 4);
    425                 bounds.setBounds(devPts, 4);
    426                 bounds.outset(SK_Scalar1, SK_Scalar1);
    427                 bounds.roundOut(&ibounds);
    428                 if (SkIRect::Intersects(devClipBounds, ibounds)) {
    429                     PREALLOC_PTARRAY(32) q;
    430                     // we don't need a direction if we aren't constraining the subdivision
    431                     static const SkPath::Direction kDummyDir = SkPath::kCCW_Direction;
    432                     // We convert cubics to quadratics (for now).
    433                     // In perspective have to do conversion in src space.
    434                     if (persp) {
    435                         SkScalar tolScale =
    436                             GrPathUtils::scaleToleranceToSrc(SK_Scalar1, m,
    437                                                              path.getBounds());
    438                         GrPathUtils::convertCubicToQuads(pathPts, tolScale, false, kDummyDir, &q);
    439                     } else {
    440                         GrPathUtils::convertCubicToQuads(devPts, SK_Scalar1, false, kDummyDir, &q);
    441                     }
    442                     for (int i = 0; i < q.count(); i += 3) {
    443                         SkPoint* qInDevSpace;
    444                         // bounds has to be calculated in device space, but q is
    445                         // in src space when there is perspective.
    446                         if (persp) {
    447                             m.mapPoints(devPts, &q[i], 3);
    448                             bounds.setBounds(devPts, 3);
    449                             qInDevSpace = devPts;
    450                         } else {
    451                             bounds.setBounds(&q[i], 3);
    452                             qInDevSpace = &q[i];
    453                         }
    454                         bounds.outset(SK_Scalar1, SK_Scalar1);
    455                         bounds.roundOut(&ibounds);
    456                         if (SkIRect::Intersects(devClipBounds, ibounds)) {
    457                             int subdiv = num_quad_subdivs(qInDevSpace);
    458                             SkASSERT(subdiv >= -1);
    459                             if (-1 == subdiv) {
    460                                 SkPoint* pts = lines->push_back_n(4);
    461                                 // lines should always be in device coords
    462                                 pts[0] = qInDevSpace[0];
    463                                 pts[1] = qInDevSpace[1];
    464                                 pts[2] = qInDevSpace[1];
    465                                 pts[3] = qInDevSpace[2];
    466                             } else {
    467                                 SkPoint* pts = quads->push_back_n(3);
    468                                 // q is already in src space when there is no
    469                                 // perspective and dev coords otherwise.
    470                                 pts[0] = q[0 + i];
    471                                 pts[1] = q[1 + i];
    472                                 pts[2] = q[2 + i];
    473                                 quadSubdivCnts->push_back() = subdiv;
    474                                 totalQuadCount += 1 << subdiv;
    475                             }
    476                         }
    477                     }
    478                 }
    479                 break;
    480             case SkPath::kClose_Verb:
    481                 break;
    482             case SkPath::kDone_Verb:
    483                 return totalQuadCount;
    484         }
    485     }
    486 }
    487 
    488 struct LineVertex {
    489     SkPoint fPos;
    490     GrColor fCoverage;
    491 };
    492 
    493 struct BezierVertex {
    494     SkPoint fPos;
    495     union {
    496         struct {
    497             SkScalar fK;
    498             SkScalar fL;
    499             SkScalar fM;
    500         } fConic;
    501         SkVector   fQuadCoord;
    502         struct {
    503             SkScalar fBogus[4];
    504         };
    505     };
    506 };
    507 
    508 GR_STATIC_ASSERT(sizeof(BezierVertex) == 3 * sizeof(SkPoint));
    509 
    510 void intersect_lines(const SkPoint& ptA, const SkVector& normA,
    511                      const SkPoint& ptB, const SkVector& normB,
    512                      SkPoint* result) {
    513 
    514     SkScalar lineAW = -normA.dot(ptA);
    515     SkScalar lineBW = -normB.dot(ptB);
    516 
    517     SkScalar wInv = SkScalarMul(normA.fX, normB.fY) -
    518         SkScalarMul(normA.fY, normB.fX);
    519     wInv = SkScalarInvert(wInv);
    520 
    521     result->fX = SkScalarMul(normA.fY, lineBW) - SkScalarMul(lineAW, normB.fY);
    522     result->fX = SkScalarMul(result->fX, wInv);
    523 
    524     result->fY = SkScalarMul(lineAW, normB.fX) - SkScalarMul(normA.fX, lineBW);
    525     result->fY = SkScalarMul(result->fY, wInv);
    526 }
    527 
    528 void set_uv_quad(const SkPoint qpts[3], BezierVertex verts[kVertsPerQuad]) {
    529     // this should be in the src space, not dev coords, when we have perspective
    530     GrPathUtils::QuadUVMatrix DevToUV(qpts);
    531     DevToUV.apply<kVertsPerQuad, sizeof(BezierVertex), sizeof(SkPoint)>(verts);
    532 }
    533 
    534 void bloat_quad(const SkPoint qpts[3], const SkMatrix* toDevice,
    535                 const SkMatrix* toSrc, BezierVertex verts[kVertsPerQuad],
    536                 SkRect* devBounds) {
    537     SkASSERT(!toDevice == !toSrc);
    538     // original quad is specified by tri a,b,c
    539     SkPoint a = qpts[0];
    540     SkPoint b = qpts[1];
    541     SkPoint c = qpts[2];
    542 
    543     if (toDevice) {
    544         toDevice->mapPoints(&a, 1);
    545         toDevice->mapPoints(&b, 1);
    546         toDevice->mapPoints(&c, 1);
    547     }
    548     // make a new poly where we replace a and c by a 1-pixel wide edges orthog
    549     // to edges ab and bc:
    550     //
    551     //   before       |        after
    552     //                |              b0
    553     //         b      |
    554     //                |
    555     //                |     a0            c0
    556     // a         c    |        a1       c1
    557     //
    558     // edges a0->b0 and b0->c0 are parallel to original edges a->b and b->c,
    559     // respectively.
    560     BezierVertex& a0 = verts[0];
    561     BezierVertex& a1 = verts[1];
    562     BezierVertex& b0 = verts[2];
    563     BezierVertex& c0 = verts[3];
    564     BezierVertex& c1 = verts[4];
    565 
    566     SkVector ab = b;
    567     ab -= a;
    568     SkVector ac = c;
    569     ac -= a;
    570     SkVector cb = b;
    571     cb -= c;
    572 
    573     // We should have already handled degenerates
    574     SkASSERT(ab.length() > 0 && cb.length() > 0);
    575 
    576     ab.normalize();
    577     SkVector abN;
    578     abN.setOrthog(ab, SkVector::kLeft_Side);
    579     if (abN.dot(ac) > 0) {
    580         abN.negate();
    581     }
    582 
    583     cb.normalize();
    584     SkVector cbN;
    585     cbN.setOrthog(cb, SkVector::kLeft_Side);
    586     if (cbN.dot(ac) < 0) {
    587         cbN.negate();
    588     }
    589 
    590     a0.fPos = a;
    591     a0.fPos += abN;
    592     a1.fPos = a;
    593     a1.fPos -= abN;
    594 
    595     c0.fPos = c;
    596     c0.fPos += cbN;
    597     c1.fPos = c;
    598     c1.fPos -= cbN;
    599 
    600     intersect_lines(a0.fPos, abN, c0.fPos, cbN, &b0.fPos);
    601     devBounds->growToInclude(&verts[0].fPos, sizeof(BezierVertex), kVertsPerQuad);
    602 
    603     if (toSrc) {
    604         toSrc->mapPointsWithStride(&verts[0].fPos, sizeof(BezierVertex), kVertsPerQuad);
    605     }
    606 }
    607 
    608 // Equations based off of Loop-Blinn Quadratic GPU Rendering
    609 // Input Parametric:
    610 // P(t) = (P0*(1-t)^2 + 2*w*P1*t*(1-t) + P2*t^2) / (1-t)^2 + 2*w*t*(1-t) + t^2)
    611 // Output Implicit:
    612 // f(x, y, w) = f(P) = K^2 - LM
    613 // K = dot(k, P), L = dot(l, P), M = dot(m, P)
    614 // k, l, m are calculated in function GrPathUtils::getConicKLM
    615 void set_conic_coeffs(const SkPoint p[3], BezierVertex verts[kVertsPerQuad],
    616                       const SkScalar weight) {
    617     SkScalar klm[9];
    618 
    619     GrPathUtils::getConicKLM(p, weight, klm);
    620 
    621     for (int i = 0; i < kVertsPerQuad; ++i) {
    622         const SkPoint pnt = verts[i].fPos;
    623         verts[i].fConic.fK = pnt.fX * klm[0] + pnt.fY * klm[1] + klm[2];
    624         verts[i].fConic.fL = pnt.fX * klm[3] + pnt.fY * klm[4] + klm[5];
    625         verts[i].fConic.fM = pnt.fX * klm[6] + pnt.fY * klm[7] + klm[8];
    626     }
    627 }
    628 
    629 void add_conics(const SkPoint p[3],
    630                 const SkScalar weight,
    631                 const SkMatrix* toDevice,
    632                 const SkMatrix* toSrc,
    633                 BezierVertex** vert,
    634                 SkRect* devBounds) {
    635     bloat_quad(p, toDevice, toSrc, *vert, devBounds);
    636     set_conic_coeffs(p, *vert, weight);
    637     *vert += kVertsPerQuad;
    638 }
    639 
    640 void add_quads(const SkPoint p[3],
    641                int subdiv,
    642                const SkMatrix* toDevice,
    643                const SkMatrix* toSrc,
    644                BezierVertex** vert,
    645                SkRect* devBounds) {
    646     SkASSERT(subdiv >= 0);
    647     if (subdiv) {
    648         SkPoint newP[5];
    649         SkChopQuadAtHalf(p, newP);
    650         add_quads(newP + 0, subdiv-1, toDevice, toSrc, vert, devBounds);
    651         add_quads(newP + 2, subdiv-1, toDevice, toSrc, vert, devBounds);
    652     } else {
    653         bloat_quad(p, toDevice, toSrc, *vert, devBounds);
    654         set_uv_quad(p, *vert);
    655         *vert += kVertsPerQuad;
    656     }
    657 }
    658 
    659 void add_line(const SkPoint p[2],
    660               const SkMatrix* toSrc,
    661               GrColor coverage,
    662               LineVertex** vert) {
    663     const SkPoint& a = p[0];
    664     const SkPoint& b = p[1];
    665 
    666     SkVector ortho, vec = b;
    667     vec -= a;
    668 
    669     if (vec.setLength(SK_ScalarHalf)) {
    670         // Create a vector orthogonal to 'vec' and of unit length
    671         ortho.fX = 2.0f * vec.fY;
    672         ortho.fY = -2.0f * vec.fX;
    673 
    674         (*vert)[0].fPos = a;
    675         (*vert)[0].fCoverage = coverage;
    676         (*vert)[1].fPos = b;
    677         (*vert)[1].fCoverage = coverage;
    678         (*vert)[2].fPos = a - vec + ortho;
    679         (*vert)[2].fCoverage = 0;
    680         (*vert)[3].fPos = b + vec + ortho;
    681         (*vert)[3].fCoverage = 0;
    682         (*vert)[4].fPos = a - vec - ortho;
    683         (*vert)[4].fCoverage = 0;
    684         (*vert)[5].fPos = b + vec - ortho;
    685         (*vert)[5].fCoverage = 0;
    686 
    687         if (NULL != toSrc) {
    688             toSrc->mapPointsWithStride(&(*vert)->fPos,
    689                                        sizeof(LineVertex),
    690                                        kVertsPerLineSeg);
    691         }
    692     } else {
    693         // just make it degenerate and likely offscreen
    694         for (int i = 0; i < kVertsPerLineSeg; ++i) {
    695             (*vert)[i].fPos.set(SK_ScalarMax, SK_ScalarMax);
    696         }
    697     }
    698 
    699     *vert += kVertsPerLineSeg;
    700 }
    701 
    702 }
    703 
    704 ///////////////////////////////////////////////////////////////////////////////
    705 
    706 namespace {
    707 
    708 // position + edge
    709 extern const GrVertexAttrib gHairlineBezierAttribs[] = {
    710     {kVec2f_GrVertexAttribType, 0,                  kPosition_GrVertexAttribBinding},
    711     {kVec4f_GrVertexAttribType, sizeof(SkPoint),    kEffect_GrVertexAttribBinding}
    712 };
    713 
    714 // position + coverage
    715 extern const GrVertexAttrib gHairlineLineAttribs[] = {
    716     {kVec2f_GrVertexAttribType,  0,               kPosition_GrVertexAttribBinding},
    717     {kVec4ub_GrVertexAttribType, sizeof(SkPoint), kCoverage_GrVertexAttribBinding},
    718 };
    719 
    720 };
    721 
    722 bool GrAAHairLinePathRenderer::createLineGeom(const SkPath& path,
    723                                               GrDrawTarget* target,
    724                                               const PtArray& lines,
    725                                               int lineCnt,
    726                                               GrDrawTarget::AutoReleaseGeometry* arg,
    727                                               SkRect* devBounds) {
    728     GrDrawState* drawState = target->drawState();
    729 
    730     const SkMatrix& viewM = drawState->getViewMatrix();
    731 
    732     int vertCnt = kVertsPerLineSeg * lineCnt;
    733 
    734     drawState->setVertexAttribs<gHairlineLineAttribs>(SK_ARRAY_COUNT(gHairlineLineAttribs));
    735     SkASSERT(sizeof(LineVertex) == drawState->getVertexSize());
    736 
    737     if (!arg->set(target, vertCnt, 0)) {
    738         return false;
    739     }
    740 
    741     LineVertex* verts = reinterpret_cast<LineVertex*>(arg->vertices());
    742 
    743     const SkMatrix* toSrc = NULL;
    744     SkMatrix ivm;
    745 
    746     if (viewM.hasPerspective()) {
    747         if (viewM.invert(&ivm)) {
    748             toSrc = &ivm;
    749         }
    750     }
    751     devBounds->set(lines.begin(), lines.count());
    752     for (int i = 0; i < lineCnt; ++i) {
    753         add_line(&lines[2*i], toSrc, drawState->getCoverageColor(), &verts);
    754     }
    755     // All the verts computed by add_line are within sqrt(1^2 + 0.5^2) of the end points.
    756     static const SkScalar kSqrtOfOneAndAQuarter = 1.118f;
    757     // Add a little extra to account for vector normalization precision.
    758     static const SkScalar kOutset = kSqrtOfOneAndAQuarter + SK_Scalar1 / 20;
    759     devBounds->outset(kOutset, kOutset);
    760 
    761     return true;
    762 }
    763 
    764 bool GrAAHairLinePathRenderer::createBezierGeom(
    765                                           const SkPath& path,
    766                                           GrDrawTarget* target,
    767                                           const PtArray& quads,
    768                                           int quadCnt,
    769                                           const PtArray& conics,
    770                                           int conicCnt,
    771                                           const IntArray& qSubdivs,
    772                                           const FloatArray& cWeights,
    773                                           GrDrawTarget::AutoReleaseGeometry* arg,
    774                                           SkRect* devBounds) {
    775     GrDrawState* drawState = target->drawState();
    776 
    777     const SkMatrix& viewM = drawState->getViewMatrix();
    778 
    779     int vertCnt = kVertsPerQuad * quadCnt + kVertsPerQuad * conicCnt;
    780 
    781     target->drawState()->setVertexAttribs<gHairlineBezierAttribs>(SK_ARRAY_COUNT(gHairlineBezierAttribs));
    782     SkASSERT(sizeof(BezierVertex) == target->getDrawState().getVertexSize());
    783 
    784     if (!arg->set(target, vertCnt, 0)) {
    785         return false;
    786     }
    787 
    788     BezierVertex* verts = reinterpret_cast<BezierVertex*>(arg->vertices());
    789 
    790     const SkMatrix* toDevice = NULL;
    791     const SkMatrix* toSrc = NULL;
    792     SkMatrix ivm;
    793 
    794     if (viewM.hasPerspective()) {
    795         if (viewM.invert(&ivm)) {
    796             toDevice = &viewM;
    797             toSrc = &ivm;
    798         }
    799     }
    800 
    801     // Seed the dev bounds with some pts known to be inside. Each quad and conic grows the bounding
    802     // box to include its vertices.
    803     SkPoint seedPts[2];
    804     if (quadCnt) {
    805         seedPts[0] = quads[0];
    806         seedPts[1] = quads[2];
    807     } else if (conicCnt) {
    808         seedPts[0] = conics[0];
    809         seedPts[1] = conics[2];
    810     }
    811     if (NULL != toDevice) {
    812         toDevice->mapPoints(seedPts, 2);
    813     }
    814     devBounds->set(seedPts[0], seedPts[1]);
    815 
    816     int unsubdivQuadCnt = quads.count() / 3;
    817     for (int i = 0; i < unsubdivQuadCnt; ++i) {
    818         SkASSERT(qSubdivs[i] >= 0);
    819         add_quads(&quads[3*i], qSubdivs[i], toDevice, toSrc, &verts, devBounds);
    820     }
    821 
    822     // Start Conics
    823     for (int i = 0; i < conicCnt; ++i) {
    824         add_conics(&conics[3*i], cWeights[i], toDevice, toSrc, &verts, devBounds);
    825     }
    826     return true;
    827 }
    828 
    829 bool GrAAHairLinePathRenderer::canDrawPath(const SkPath& path,
    830                                            const SkStrokeRec& stroke,
    831                                            const GrDrawTarget* target,
    832                                            bool antiAlias) const {
    833     if (!antiAlias) {
    834         return false;
    835     }
    836 
    837     if (!IsStrokeHairlineOrEquivalent(stroke,
    838                                       target->getDrawState().getViewMatrix(),
    839                                       NULL)) {
    840         return false;
    841     }
    842 
    843     if (SkPath::kLine_SegmentMask == path.getSegmentMasks() ||
    844         target->caps()->shaderDerivativeSupport()) {
    845         return true;
    846     }
    847     return false;
    848 }
    849 
    850 template <class VertexType>
    851 bool check_bounds(GrDrawState* drawState, const SkRect& devBounds, void* vertices, int vCount)
    852 {
    853     SkRect tolDevBounds = devBounds;
    854     // The bounds ought to be tight, but in perspective the below code runs the verts
    855     // through the view matrix to get back to dev coords, which can introduce imprecision.
    856     if (drawState->getViewMatrix().hasPerspective()) {
    857         tolDevBounds.outset(SK_Scalar1 / 1000, SK_Scalar1 / 1000);
    858     } else {
    859         // Non-persp matrices cause this path renderer to draw in device space.
    860         SkASSERT(drawState->getViewMatrix().isIdentity());
    861     }
    862     SkRect actualBounds;
    863 
    864     VertexType* verts = reinterpret_cast<VertexType*>(vertices);
    865     bool first = true;
    866     for (int i = 0; i < vCount; ++i) {
    867         SkPoint pos = verts[i].fPos;
    868         // This is a hack to workaround the fact that we move some degenerate segments offscreen.
    869         if (SK_ScalarMax == pos.fX) {
    870             continue;
    871         }
    872         drawState->getViewMatrix().mapPoints(&pos, 1);
    873         if (first) {
    874             actualBounds.set(pos.fX, pos.fY, pos.fX, pos.fY);
    875             first = false;
    876         } else {
    877             actualBounds.growToInclude(pos.fX, pos.fY);
    878         }
    879     }
    880     if (!first) {
    881         return tolDevBounds.contains(actualBounds);
    882     }
    883 
    884     return true;
    885 }
    886 
    887 bool GrAAHairLinePathRenderer::onDrawPath(const SkPath& path,
    888                                           const SkStrokeRec& stroke,
    889                                           GrDrawTarget* target,
    890                                           bool antiAlias) {
    891     GrDrawState* drawState = target->drawState();
    892 
    893     SkScalar hairlineCoverage;
    894     if (IsStrokeHairlineOrEquivalent(stroke,
    895                                      target->getDrawState().getViewMatrix(),
    896                                      &hairlineCoverage)) {
    897         uint8_t newCoverage = SkScalarRoundToInt(hairlineCoverage *
    898                                                  target->getDrawState().getCoverage());
    899         target->drawState()->setCoverage(newCoverage);
    900     }
    901 
    902     SkIRect devClipBounds;
    903     target->getClip()->getConservativeBounds(drawState->getRenderTarget(), &devClipBounds);
    904 
    905     int lineCnt;
    906     int quadCnt;
    907     int conicCnt;
    908     PREALLOC_PTARRAY(128) lines;
    909     PREALLOC_PTARRAY(128) quads;
    910     PREALLOC_PTARRAY(128) conics;
    911     IntArray qSubdivs;
    912     FloatArray cWeights;
    913     quadCnt = generate_lines_and_quads(path, drawState->getViewMatrix(), devClipBounds,
    914                                        &lines, &quads, &conics, &qSubdivs, &cWeights);
    915     lineCnt = lines.count() / 2;
    916     conicCnt = conics.count() / 3;
    917 
    918     // do lines first
    919     if (lineCnt) {
    920         GrDrawTarget::AutoReleaseGeometry arg;
    921         SkRect devBounds;
    922 
    923         if (!this->createLineGeom(path,
    924                                   target,
    925                                   lines,
    926                                   lineCnt,
    927                                   &arg,
    928                                   &devBounds)) {
    929             return false;
    930         }
    931 
    932         GrDrawTarget::AutoStateRestore asr;
    933 
    934         // createLineGeom transforms the geometry to device space when the matrix does not have
    935         // perspective.
    936         if (target->getDrawState().getViewMatrix().hasPerspective()) {
    937             asr.set(target, GrDrawTarget::kPreserve_ASRInit);
    938         } else if (!asr.setIdentity(target, GrDrawTarget::kPreserve_ASRInit)) {
    939             return false;
    940         }
    941         GrDrawState* drawState = target->drawState();
    942 
    943         // Check devBounds
    944         SkASSERT(check_bounds<LineVertex>(drawState, devBounds, arg.vertices(),
    945                                           kVertsPerLineSeg * lineCnt));
    946 
    947         {
    948             GrDrawState::AutoRestoreEffects are(drawState);
    949             target->setIndexSourceToBuffer(fLinesIndexBuffer);
    950             int lines = 0;
    951             while (lines < lineCnt) {
    952                 int n = SkTMin(lineCnt - lines, kNumLineSegsInIdxBuffer);
    953                 target->drawIndexed(kTriangles_GrPrimitiveType,
    954                                     kVertsPerLineSeg*lines,     // startV
    955                                     0,                          // startI
    956                                     kVertsPerLineSeg*n,         // vCount
    957                                     kIdxsPerLineSeg*n,          // iCount
    958                                     &devBounds);
    959                 lines += n;
    960             }
    961         }
    962     }
    963 
    964     // then quadratics/conics
    965     if (quadCnt || conicCnt) {
    966         GrDrawTarget::AutoReleaseGeometry arg;
    967         SkRect devBounds;
    968 
    969         if (!this->createBezierGeom(path,
    970                                     target,
    971                                     quads,
    972                                     quadCnt,
    973                                     conics,
    974                                     conicCnt,
    975                                     qSubdivs,
    976                                     cWeights,
    977                                     &arg,
    978                                     &devBounds)) {
    979             return false;
    980         }
    981 
    982         GrDrawTarget::AutoStateRestore asr;
    983 
    984         // createGeom transforms the geometry to device space when the matrix does not have
    985         // perspective.
    986         if (target->getDrawState().getViewMatrix().hasPerspective()) {
    987             asr.set(target, GrDrawTarget::kPreserve_ASRInit);
    988         } else if (!asr.setIdentity(target, GrDrawTarget::kPreserve_ASRInit)) {
    989             return false;
    990         }
    991         GrDrawState* drawState = target->drawState();
    992 
    993         static const int kEdgeAttrIndex = 1;
    994 
    995         // Check devBounds
    996         SkASSERT(check_bounds<BezierVertex>(drawState, devBounds, arg.vertices(),
    997                                             kVertsPerQuad * quadCnt + kVertsPerQuad * conicCnt));
    998 
    999         if (quadCnt > 0) {
   1000             GrEffectRef* hairQuadEffect = GrQuadEffect::Create(kHairlineAA_GrEffectEdgeType,
   1001                                                                *target->caps());
   1002             SkASSERT(NULL != hairQuadEffect);
   1003             GrDrawState::AutoRestoreEffects are(drawState);
   1004             target->setIndexSourceToBuffer(fQuadsIndexBuffer);
   1005             drawState->addCoverageEffect(hairQuadEffect, kEdgeAttrIndex)->unref();
   1006             int quads = 0;
   1007             while (quads < quadCnt) {
   1008                 int n = SkTMin(quadCnt - quads, kNumQuadsInIdxBuffer);
   1009                 target->drawIndexed(kTriangles_GrPrimitiveType,
   1010                                     kVertsPerQuad*quads,               // startV
   1011                                     0,                                 // startI
   1012                                     kVertsPerQuad*n,                   // vCount
   1013                                     kIdxsPerQuad*n,                    // iCount
   1014                                     &devBounds);
   1015                 quads += n;
   1016             }
   1017         }
   1018 
   1019         if (conicCnt > 0) {
   1020             GrDrawState::AutoRestoreEffects are(drawState);
   1021             GrEffectRef* hairConicEffect = GrConicEffect::Create(kHairlineAA_GrEffectEdgeType,
   1022                                                                  *target->caps());
   1023             SkASSERT(NULL != hairConicEffect);
   1024             drawState->addCoverageEffect(hairConicEffect, 1, 2)->unref();
   1025             int conics = 0;
   1026             while (conics < conicCnt) {
   1027                 int n = SkTMin(conicCnt - conics, kNumQuadsInIdxBuffer);
   1028                 target->drawIndexed(kTriangles_GrPrimitiveType,
   1029                                     kVertsPerQuad*(quadCnt + conics),  // startV
   1030                                     0,                                 // startI
   1031                                     kVertsPerQuad*n,                   // vCount
   1032                                     kIdxsPerQuad*n,                    // iCount
   1033                                     &devBounds);
   1034                 conics += n;
   1035             }
   1036         }
   1037     }
   1038 
   1039     target->resetIndexSource();
   1040 
   1041     return true;
   1042 }
   1043