| /* |
| * Copyright 2011 Google Inc. |
| * |
| * Use of this source code is governed by a BSD-style license that can be |
| * found in the LICENSE file. |
| */ |
| |
| #include "GrPathUtils.h" |
| |
| #include "GrPoint.h" |
| #include "SkGeometry.h" |
| |
| SkScalar GrPathUtils::scaleToleranceToSrc(SkScalar devTol, |
| const SkMatrix& viewM, |
| const SkRect& pathBounds) { |
| // In order to tesselate the path we get a bound on how much the matrix can |
| // stretch when mapping to screen coordinates. |
| SkScalar stretch = viewM.getMaxStretch(); |
| SkScalar srcTol = devTol; |
| |
| if (stretch < 0) { |
| // take worst case mapRadius amoung four corners. |
| // (less than perfect) |
| for (int i = 0; i < 4; ++i) { |
| SkMatrix mat; |
| mat.setTranslate((i % 2) ? pathBounds.fLeft : pathBounds.fRight, |
| (i < 2) ? pathBounds.fTop : pathBounds.fBottom); |
| mat.postConcat(viewM); |
| stretch = SkMaxScalar(stretch, mat.mapRadius(SK_Scalar1)); |
| } |
| } |
| srcTol = SkScalarDiv(srcTol, stretch); |
| return srcTol; |
| } |
| |
| static const int MAX_POINTS_PER_CURVE = 1 << 10; |
| static const SkScalar gMinCurveTol = SkFloatToScalar(0.0001f); |
| |
| uint32_t GrPathUtils::quadraticPointCount(const GrPoint points[], |
| SkScalar tol) { |
| if (tol < gMinCurveTol) { |
| tol = gMinCurveTol; |
| } |
| SkASSERT(tol > 0); |
| |
| SkScalar d = points[1].distanceToLineSegmentBetween(points[0], points[2]); |
| if (d <= tol) { |
| return 1; |
| } else { |
| // Each time we subdivide, d should be cut in 4. So we need to |
| // subdivide x = log4(d/tol) times. x subdivisions creates 2^(x) |
| // points. |
| // 2^(log4(x)) = sqrt(x); |
| int temp = SkScalarCeil(SkScalarSqrt(SkScalarDiv(d, tol))); |
| int pow2 = GrNextPow2(temp); |
| // Because of NaNs & INFs we can wind up with a degenerate temp |
| // such that pow2 comes out negative. Also, our point generator |
| // will always output at least one pt. |
| if (pow2 < 1) { |
| pow2 = 1; |
| } |
| return GrMin(pow2, MAX_POINTS_PER_CURVE); |
| } |
| } |
| |
| uint32_t GrPathUtils::generateQuadraticPoints(const GrPoint& p0, |
| const GrPoint& p1, |
| const GrPoint& p2, |
| SkScalar tolSqd, |
| GrPoint** points, |
| uint32_t pointsLeft) { |
| if (pointsLeft < 2 || |
| (p1.distanceToLineSegmentBetweenSqd(p0, p2)) < tolSqd) { |
| (*points)[0] = p2; |
| *points += 1; |
| return 1; |
| } |
| |
| GrPoint q[] = { |
| { SkScalarAve(p0.fX, p1.fX), SkScalarAve(p0.fY, p1.fY) }, |
| { SkScalarAve(p1.fX, p2.fX), SkScalarAve(p1.fY, p2.fY) }, |
| }; |
| GrPoint r = { SkScalarAve(q[0].fX, q[1].fX), SkScalarAve(q[0].fY, q[1].fY) }; |
| |
| pointsLeft >>= 1; |
| uint32_t a = generateQuadraticPoints(p0, q[0], r, tolSqd, points, pointsLeft); |
| uint32_t b = generateQuadraticPoints(r, q[1], p2, tolSqd, points, pointsLeft); |
| return a + b; |
| } |
| |
| uint32_t GrPathUtils::cubicPointCount(const GrPoint points[], |
| SkScalar tol) { |
| if (tol < gMinCurveTol) { |
| tol = gMinCurveTol; |
| } |
| SkASSERT(tol > 0); |
| |
| SkScalar d = GrMax( |
| points[1].distanceToLineSegmentBetweenSqd(points[0], points[3]), |
| points[2].distanceToLineSegmentBetweenSqd(points[0], points[3])); |
| d = SkScalarSqrt(d); |
| if (d <= tol) { |
| return 1; |
| } else { |
| int temp = SkScalarCeil(SkScalarSqrt(SkScalarDiv(d, tol))); |
| int pow2 = GrNextPow2(temp); |
| // Because of NaNs & INFs we can wind up with a degenerate temp |
| // such that pow2 comes out negative. Also, our point generator |
| // will always output at least one pt. |
| if (pow2 < 1) { |
| pow2 = 1; |
| } |
| return GrMin(pow2, MAX_POINTS_PER_CURVE); |
| } |
| } |
| |
| uint32_t GrPathUtils::generateCubicPoints(const GrPoint& p0, |
| const GrPoint& p1, |
| const GrPoint& p2, |
| const GrPoint& p3, |
| SkScalar tolSqd, |
| GrPoint** points, |
| uint32_t pointsLeft) { |
| if (pointsLeft < 2 || |
| (p1.distanceToLineSegmentBetweenSqd(p0, p3) < tolSqd && |
| p2.distanceToLineSegmentBetweenSqd(p0, p3) < tolSqd)) { |
| (*points)[0] = p3; |
| *points += 1; |
| return 1; |
| } |
| GrPoint q[] = { |
| { SkScalarAve(p0.fX, p1.fX), SkScalarAve(p0.fY, p1.fY) }, |
| { SkScalarAve(p1.fX, p2.fX), SkScalarAve(p1.fY, p2.fY) }, |
| { SkScalarAve(p2.fX, p3.fX), SkScalarAve(p2.fY, p3.fY) } |
| }; |
| GrPoint r[] = { |
| { SkScalarAve(q[0].fX, q[1].fX), SkScalarAve(q[0].fY, q[1].fY) }, |
| { SkScalarAve(q[1].fX, q[2].fX), SkScalarAve(q[1].fY, q[2].fY) } |
| }; |
| GrPoint s = { SkScalarAve(r[0].fX, r[1].fX), SkScalarAve(r[0].fY, r[1].fY) }; |
| pointsLeft >>= 1; |
| uint32_t a = generateCubicPoints(p0, q[0], r[0], s, tolSqd, points, pointsLeft); |
| uint32_t b = generateCubicPoints(s, r[1], q[2], p3, tolSqd, points, pointsLeft); |
| return a + b; |
| } |
| |
| int GrPathUtils::worstCasePointCount(const SkPath& path, int* subpaths, |
| SkScalar tol) { |
| if (tol < gMinCurveTol) { |
| tol = gMinCurveTol; |
| } |
| SkASSERT(tol > 0); |
| |
| int pointCount = 0; |
| *subpaths = 1; |
| |
| bool first = true; |
| |
| SkPath::Iter iter(path, false); |
| SkPath::Verb verb; |
| |
| GrPoint pts[4]; |
| while ((verb = iter.next(pts)) != SkPath::kDone_Verb) { |
| |
| switch (verb) { |
| case SkPath::kLine_Verb: |
| pointCount += 1; |
| break; |
| case SkPath::kQuad_Verb: |
| pointCount += quadraticPointCount(pts, tol); |
| break; |
| case SkPath::kCubic_Verb: |
| pointCount += cubicPointCount(pts, tol); |
| break; |
| case SkPath::kMove_Verb: |
| pointCount += 1; |
| if (!first) { |
| ++(*subpaths); |
| } |
| break; |
| default: |
| break; |
| } |
| first = false; |
| } |
| return pointCount; |
| } |
| |
| void GrPathUtils::QuadUVMatrix::set(const GrPoint qPts[3]) { |
| // can't make this static, no cons :( |
| SkMatrix UVpts; |
| #ifndef SK_SCALAR_IS_FLOAT |
| GrCrash("Expected scalar is float."); |
| #endif |
| SkMatrix m; |
| // We want M such that M * xy_pt = uv_pt |
| // We know M * control_pts = [0 1/2 1] |
| // [0 0 1] |
| // [1 1 1] |
| // We invert the control pt matrix and post concat to both sides to get M. |
| UVpts.setAll(0, SK_ScalarHalf, SK_Scalar1, |
| 0, 0, SK_Scalar1, |
| SkScalarToPersp(SK_Scalar1), |
| SkScalarToPersp(SK_Scalar1), |
| SkScalarToPersp(SK_Scalar1)); |
| m.setAll(qPts[0].fX, qPts[1].fX, qPts[2].fX, |
| qPts[0].fY, qPts[1].fY, qPts[2].fY, |
| SkScalarToPersp(SK_Scalar1), |
| SkScalarToPersp(SK_Scalar1), |
| SkScalarToPersp(SK_Scalar1)); |
| if (!m.invert(&m)) { |
| // The quad is degenerate. Hopefully this is rare. Find the pts that are |
| // farthest apart to compute a line (unless it is really a pt). |
| SkScalar maxD = qPts[0].distanceToSqd(qPts[1]); |
| int maxEdge = 0; |
| SkScalar d = qPts[1].distanceToSqd(qPts[2]); |
| if (d > maxD) { |
| maxD = d; |
| maxEdge = 1; |
| } |
| d = qPts[2].distanceToSqd(qPts[0]); |
| if (d > maxD) { |
| maxD = d; |
| maxEdge = 2; |
| } |
| // We could have a tolerance here, not sure if it would improve anything |
| if (maxD > 0) { |
| // Set the matrix to give (u = 0, v = distance_to_line) |
| GrVec lineVec = qPts[(maxEdge + 1)%3] - qPts[maxEdge]; |
| // when looking from the point 0 down the line we want positive |
| // distances to be to the left. This matches the non-degenerate |
| // case. |
| lineVec.setOrthog(lineVec, GrPoint::kLeft_Side); |
| lineVec.dot(qPts[0]); |
| // first row |
| fM[0] = 0; |
| fM[1] = 0; |
| fM[2] = 0; |
| // second row |
| fM[3] = lineVec.fX; |
| fM[4] = lineVec.fY; |
| fM[5] = -lineVec.dot(qPts[maxEdge]); |
| } else { |
| // It's a point. It should cover zero area. Just set the matrix such |
| // that (u, v) will always be far away from the quad. |
| fM[0] = 0; fM[1] = 0; fM[2] = 100.f; |
| fM[3] = 0; fM[4] = 0; fM[5] = 100.f; |
| } |
| } else { |
| m.postConcat(UVpts); |
| |
| // The matrix should not have perspective. |
| SkDEBUGCODE(static const SkScalar gTOL = SkFloatToScalar(1.f / 100.f)); |
| SkASSERT(SkScalarAbs(m.get(SkMatrix::kMPersp0)) < gTOL); |
| SkASSERT(SkScalarAbs(m.get(SkMatrix::kMPersp1)) < gTOL); |
| |
| // It may not be normalized to have 1.0 in the bottom right |
| float m33 = m.get(SkMatrix::kMPersp2); |
| if (1.f != m33) { |
| m33 = 1.f / m33; |
| fM[0] = m33 * m.get(SkMatrix::kMScaleX); |
| fM[1] = m33 * m.get(SkMatrix::kMSkewX); |
| fM[2] = m33 * m.get(SkMatrix::kMTransX); |
| fM[3] = m33 * m.get(SkMatrix::kMSkewY); |
| fM[4] = m33 * m.get(SkMatrix::kMScaleY); |
| fM[5] = m33 * m.get(SkMatrix::kMTransY); |
| } else { |
| fM[0] = m.get(SkMatrix::kMScaleX); |
| fM[1] = m.get(SkMatrix::kMSkewX); |
| fM[2] = m.get(SkMatrix::kMTransX); |
| fM[3] = m.get(SkMatrix::kMSkewY); |
| fM[4] = m.get(SkMatrix::kMScaleY); |
| fM[5] = m.get(SkMatrix::kMTransY); |
| } |
| } |
| } |
| |
| namespace { |
| |
| // a is the first control point of the cubic. |
| // ab is the vector from a to the second control point. |
| // dc is the vector from the fourth to the third control point. |
| // d is the fourth control point. |
| // p is the candidate quadratic control point. |
| // this assumes that the cubic doesn't inflect and is simple |
| bool is_point_within_cubic_tangents(const SkPoint& a, |
| const SkVector& ab, |
| const SkVector& dc, |
| const SkPoint& d, |
| SkPath::Direction dir, |
| const SkPoint p) { |
| SkVector ap = p - a; |
| SkScalar apXab = ap.cross(ab); |
| if (SkPath::kCW_Direction == dir) { |
| if (apXab > 0) { |
| return false; |
| } |
| } else { |
| SkASSERT(SkPath::kCCW_Direction == dir); |
| if (apXab < 0) { |
| return false; |
| } |
| } |
| |
| SkVector dp = p - d; |
| SkScalar dpXdc = dp.cross(dc); |
| if (SkPath::kCW_Direction == dir) { |
| if (dpXdc < 0) { |
| return false; |
| } |
| } else { |
| SkASSERT(SkPath::kCCW_Direction == dir); |
| if (dpXdc > 0) { |
| return false; |
| } |
| } |
| return true; |
| } |
| |
| void convert_noninflect_cubic_to_quads(const SkPoint p[4], |
| SkScalar toleranceSqd, |
| bool constrainWithinTangents, |
| SkPath::Direction dir, |
| SkTArray<SkPoint, true>* quads, |
| int sublevel = 0) { |
| |
| // Notation: Point a is always p[0]. Point b is p[1] unless p[1] == p[0], in which case it is |
| // p[2]. Point d is always p[3]. Point c is p[2] unless p[2] == p[3], in which case it is p[1]. |
| |
| SkVector ab = p[1] - p[0]; |
| SkVector dc = p[2] - p[3]; |
| |
| if (ab.isZero()) { |
| if (dc.isZero()) { |
| SkPoint* degQuad = quads->push_back_n(3); |
| degQuad[0] = p[0]; |
| degQuad[1] = p[0]; |
| degQuad[2] = p[3]; |
| return; |
| } |
| ab = p[2] - p[0]; |
| } |
| if (dc.isZero()) { |
| dc = p[1] - p[3]; |
| } |
| |
| // When the ab and cd tangents are nearly parallel with vector from d to a the constraint that |
| // the quad point falls between the tangents becomes hard to enforce and we are likely to hit |
| // the max subdivision count. However, in this case the cubic is approaching a line and the |
| // accuracy of the quad point isn't so important. We check if the two middle cubic control |
| // points are very close to the baseline vector. If so then we just pick quadratic points on the |
| // control polygon. |
| |
| if (constrainWithinTangents) { |
| SkVector da = p[0] - p[3]; |
| SkScalar invDALengthSqd = da.lengthSqd(); |
| if (invDALengthSqd > SK_ScalarNearlyZero) { |
| invDALengthSqd = SkScalarInvert(invDALengthSqd); |
| // cross(ab, da)^2/length(da)^2 == sqd distance from b to line from d to a. |
| // same goed for point c using vector cd. |
| SkScalar detABSqd = ab.cross(da); |
| detABSqd = SkScalarSquare(detABSqd); |
| SkScalar detDCSqd = dc.cross(da); |
| detDCSqd = SkScalarSquare(detDCSqd); |
| if (SkScalarMul(detABSqd, invDALengthSqd) < toleranceSqd && |
| SkScalarMul(detDCSqd, invDALengthSqd) < toleranceSqd) { |
| SkPoint b = p[0] + ab; |
| SkPoint c = p[3] + dc; |
| SkPoint mid = b + c; |
| mid.scale(SK_ScalarHalf); |
| // Insert two quadratics to cover the case when ab points away from d and/or dc |
| // points away from a. |
| if (SkVector::DotProduct(da, dc) < 0 || SkVector::DotProduct(ab,da) > 0) { |
| SkPoint* qpts = quads->push_back_n(6); |
| qpts[0] = p[0]; |
| qpts[1] = b; |
| qpts[2] = mid; |
| qpts[3] = mid; |
| qpts[4] = c; |
| qpts[5] = p[3]; |
| } else { |
| SkPoint* qpts = quads->push_back_n(3); |
| qpts[0] = p[0]; |
| qpts[1] = mid; |
| qpts[2] = p[3]; |
| } |
| return; |
| } |
| } |
| } |
| |
| static const SkScalar kLengthScale = 3 * SK_Scalar1 / 2; |
| static const int kMaxSubdivs = 10; |
| |
| ab.scale(kLengthScale); |
| dc.scale(kLengthScale); |
| |
| // e0 and e1 are extrapolations along vectors ab and dc. |
| SkVector c0 = p[0]; |
| c0 += ab; |
| SkVector c1 = p[3]; |
| c1 += dc; |
| |
| SkScalar dSqd = sublevel > kMaxSubdivs ? 0 : c0.distanceToSqd(c1); |
| if (dSqd < toleranceSqd) { |
| SkPoint cAvg = c0; |
| cAvg += c1; |
| cAvg.scale(SK_ScalarHalf); |
| |
| bool subdivide = false; |
| |
| if (constrainWithinTangents && |
| !is_point_within_cubic_tangents(p[0], ab, dc, p[3], dir, cAvg)) { |
| // choose a new cAvg that is the intersection of the two tangent lines. |
| ab.setOrthog(ab); |
| SkScalar z0 = -ab.dot(p[0]); |
| dc.setOrthog(dc); |
| SkScalar z1 = -dc.dot(p[3]); |
| cAvg.fX = SkScalarMul(ab.fY, z1) - SkScalarMul(z0, dc.fY); |
| cAvg.fY = SkScalarMul(z0, dc.fX) - SkScalarMul(ab.fX, z1); |
| SkScalar z = SkScalarMul(ab.fX, dc.fY) - SkScalarMul(ab.fY, dc.fX); |
| z = SkScalarInvert(z); |
| cAvg.fX *= z; |
| cAvg.fY *= z; |
| if (sublevel <= kMaxSubdivs) { |
| SkScalar d0Sqd = c0.distanceToSqd(cAvg); |
| SkScalar d1Sqd = c1.distanceToSqd(cAvg); |
| // We need to subdivide if d0 + d1 > tolerance but we have the sqd values. We know |
| // the distances and tolerance can't be negative. |
| // (d0 + d1)^2 > toleranceSqd |
| // d0Sqd + 2*d0*d1 + d1Sqd > toleranceSqd |
| SkScalar d0d1 = SkScalarSqrt(SkScalarMul(d0Sqd, d1Sqd)); |
| subdivide = 2 * d0d1 + d0Sqd + d1Sqd > toleranceSqd; |
| } |
| } |
| if (!subdivide) { |
| SkPoint* pts = quads->push_back_n(3); |
| pts[0] = p[0]; |
| pts[1] = cAvg; |
| pts[2] = p[3]; |
| return; |
| } |
| } |
| SkPoint choppedPts[7]; |
| SkChopCubicAtHalf(p, choppedPts); |
| convert_noninflect_cubic_to_quads(choppedPts + 0, |
| toleranceSqd, |
| constrainWithinTangents, |
| dir, |
| quads, |
| sublevel + 1); |
| convert_noninflect_cubic_to_quads(choppedPts + 3, |
| toleranceSqd, |
| constrainWithinTangents, |
| dir, |
| quads, |
| sublevel + 1); |
| } |
| } |
| |
| void GrPathUtils::convertCubicToQuads(const GrPoint p[4], |
| SkScalar tolScale, |
| bool constrainWithinTangents, |
| SkPath::Direction dir, |
| SkTArray<SkPoint, true>* quads) { |
| SkPoint chopped[10]; |
| int count = SkChopCubicAtInflections(p, chopped); |
| |
| // base tolerance is 1 pixel. |
| static const SkScalar kTolerance = SK_Scalar1; |
| const SkScalar tolSqd = SkScalarSquare(SkScalarMul(tolScale, kTolerance)); |
| |
| for (int i = 0; i < count; ++i) { |
| SkPoint* cubic = chopped + 3*i; |
| convert_noninflect_cubic_to_quads(cubic, tolSqd, constrainWithinTangents, dir, quads); |
| } |
| |
| } |
