bool SkXRayCrossesLine(const SkXRay& pt, const SkPoint pts[2]) {
// Determine quick discards.
// Consider query line going exactly through point 0 to not
// intersect, for symmetry with SkXRayCrossesMonotonicCubic.
if (pt.fY == pts[0].fY)
return false;
if (pt.fY < pts[0].fY && pt.fY < pts[1].fY)
return false;
if (pt.fY > pts[0].fY && pt.fY > pts[1].fY)
return false;
if (pt.fX > pts[0].fX && pt.fX > pts[1].fX)
return false;
// Determine degenerate cases
if (SkScalarNearlyZero(pts[0].fY - pts[1].fY))
return false;
if (SkScalarNearlyZero(pts[0].fX - pts[1].fX))
// We've already determined the query point lies within the
// vertical range of the line segment.
return pt.fX <= pts[0].fX;
// Full line segment evaluation
SkScalar delta_y = pts[1].fY - pts[0].fY;
SkScalar delta_x = pts[1].fX - pts[0].fX;
SkScalar slope = SkScalarDiv(delta_y, delta_x);
SkScalar b = pts[0].fY - SkScalarMul(slope, pts[0].fX);
// Solve for x coordinate at y = pt.fY
SkScalar x = SkScalarDiv(pt.fY - b, slope);
return pt.fX <= x;
}
/**
* For the purposes of drawing bitmaps, if a matrix is "almost" translate
* go ahead and treat it as if it were, so that subsequent code can go fast.
*/
static bool just_trans_general(const SkMatrix& matrix) {
SkASSERT(matrix_only_scale_translate(matrix));
const SkScalar tol = SK_Scalar1 / 32768;
return SkScalarNearlyZero(matrix[SkMatrix::kMScaleX] - SK_Scalar1, tol)
&& SkScalarNearlyZero(matrix[SkMatrix::kMScaleY] - SK_Scalar1, tol);
}
static AngleType Dot2AngleType(SkScalar dot)
{
// need more precise fixed normalization
// SkASSERT(SkScalarAbs(dot) <= SK_Scalar1 + SK_ScalarNearlyZero);
if (dot >= 0) // shallow or line
return SkScalarNearlyZero(SK_Scalar1 - dot) ? kNearlyLine_AngleType : kShallow_AngleType;
else // sharp or 180
return SkScalarNearlyZero(SK_Scalar1 + dot) ? kNearly180_AngleType : kSharp_AngleType;
}
SkColor SkHSVToColor(U8CPU a, const SkScalar hsv[3]) {
SkASSERT(hsv);
SkScalar s = SkScalarPin(hsv[1], 0, 1);
SkScalar v = SkScalarPin(hsv[2], 0, 1);
U8CPU v_byte = SkScalarRoundToInt(v * 255);
if (SkScalarNearlyZero(s)) { // shade of gray
return SkColorSetARGB(a, v_byte, v_byte, v_byte);
}
SkScalar hx = (hsv[0] < 0 || hsv[0] >= SkIntToScalar(360)) ? 0 : hsv[0]/60;
SkScalar w = SkScalarFloorToScalar(hx);
SkScalar f = hx - w;
unsigned p = SkScalarRoundToInt((SK_Scalar1 - s) * v * 255);
unsigned q = SkScalarRoundToInt((SK_Scalar1 - (s * f)) * v * 255);
unsigned t = SkScalarRoundToInt((SK_Scalar1 - (s * (SK_Scalar1 - f))) * v * 255);
unsigned r, g, b;
SkASSERT((unsigned)(w) < 6);
switch ((unsigned)(w)) {
case 0: r = v_byte; g = t; b = p; break;
case 1: r = q; g = v_byte; b = p; break;
case 2: r = p; g = v_byte; b = t; break;
case 3: r = p; g = q; b = v_byte; break;
case 4: r = t; g = p; b = v_byte; break;
default: r = v_byte; g = p; b = q; break;
}
return SkColorSetARGB(a, r, g, b);
}
static bool just_trans_general(const SkMatrix& matrix) {
SkASSERT(matrix_only_scale_translate(matrix));
if (matrix.getType() & SkMatrix::kScale_Mask) {
const SkScalar tol = SK_Scalar1 / 32768;
if (!SkScalarNearlyZero(matrix[SkMatrix::kMScaleX] - SK_Scalar1, tol)) {
return false;
}
if (!SkScalarNearlyZero(matrix[SkMatrix::kMScaleY] - SK_Scalar1, tol)) {
return false;
}
}
// if we got here, treat us as either kTranslate_Mask or identity
return true;
}
// Finds affine and persp such that in = affine * persp.
// but it returns the inverse of perspective matrix.
static bool split_perspective(const SkMatrix in, SkMatrix* affine,
SkMatrix* perspectiveInverse) {
const SkScalar p2 = in[SkMatrix::kMPersp2];
if (SkScalarNearlyZero(p2)) {
return false;
}
const SkScalar zero = SkIntToScalar(0);
const SkScalar one = SkIntToScalar(1);
const SkScalar sx = in[SkMatrix::kMScaleX];
const SkScalar kx = in[SkMatrix::kMSkewX];
const SkScalar tx = in[SkMatrix::kMTransX];
const SkScalar ky = in[SkMatrix::kMSkewY];
const SkScalar sy = in[SkMatrix::kMScaleY];
const SkScalar ty = in[SkMatrix::kMTransY];
const SkScalar p0 = in[SkMatrix::kMPersp0];
const SkScalar p1 = in[SkMatrix::kMPersp1];
// Perspective matrix would be:
// 1 0 0
// 0 1 0
// p0 p1 p2
// But we need the inverse of persp.
perspectiveInverse->setAll(one, zero, zero,
zero, one, zero,
-p0/p2, -p1/p2, 1/p2);
affine->setAll(sx - p0 * tx / p2, kx - p1 * tx / p2, tx / p2,
ky - p0 * ty / p2, sy - p1 * ty / p2, ty / p2,
zero, zero, one);
return true;
}
static IntersectionType intersection(const SkPoint& p1, const SkPoint& p2,
const SkPoint& p3, const SkPoint& p4,
SkPoint& res) {
// Store the values for fast access and easy
// equations-to-code conversion
SkScalar x1 = p1.x(), x2 = p2.x(), x3 = p3.x(), x4 = p4.x();
SkScalar y1 = p1.y(), y2 = p2.y(), y3 = p3.y(), y4 = p4.y();
SkScalar d = SkScalarMul(x1 - x2, y3 - y4) - SkScalarMul(y1 - y2, x3 - x4);
// If d is zero, there is no intersection
if (SkScalarNearlyZero(d)) {
return kNone_IntersectionType;
}
// Get the x and y
SkScalar pre = SkScalarMul(x1, y2) - SkScalarMul(y1, x2),
post = SkScalarMul(x3, y4) - SkScalarMul(y3, x4);
// Compute the point of intersection
res.set(SkScalarDiv(SkScalarMul(pre, x3 - x4) - SkScalarMul(x1 - x2, post), d),
SkScalarDiv(SkScalarMul(pre, y3 - y4) - SkScalarMul(y1 - y2, post), d));
// Check if the x and y coordinates are within both lines
return (res.x() < GrMin(x1, x2) || res.x() > GrMax(x1, x2) ||
res.x() < GrMin(x3, x4) || res.x() > GrMax(x3, x4) ||
res.y() < GrMin(y1, y2) || res.y() > GrMax(y1, y2) ||
res.y() < GrMin(y3, y4) || res.y() > GrMax(y3, y4)) ?
kOut_IntersectionType : kIn_IntersectionType;
}
bool SkPathContainsPoint(const SkPath& originalPath, const FloatPoint& point, SkPath::FillType ft)
{
SkRect bounds = originalPath.getBounds();
// We can immediately return false if the point is outside the bounding
// rect. We don't use bounds.contains() here, since it would exclude
// points on the right and bottom edges of the bounding rect, and we want
// to include them.
SkScalar fX = SkFloatToScalar(point.x());
SkScalar fY = SkFloatToScalar(point.y());
if (fX < bounds.fLeft || fX > bounds.fRight || fY < bounds.fTop || fY > bounds.fBottom)
return false;
// Scale the path to a large size before hit testing for two reasons:
// 1) Skia has trouble with coordinates close to the max signed 16-bit values, so we scale larger paths down.
// TODO: when Skia is patched to work properly with large values, this will not be necessary.
// 2) Skia does not support analytic hit testing, so we scale paths up to do raster hit testing with subpixel accuracy.
// 3) Scale the x/y axis separately so an extreme large/small scale factor on one axis won't
// ruin the resolution of the other axis.
SkScalar biggestCoordX = std::max(bounds.fRight, -bounds.fLeft);
SkScalar biggestCoordY = std::max(bounds.fBottom, -bounds.fTop);
if (SkScalarNearlyZero(biggestCoordX) || SkScalarNearlyZero(biggestCoordY))
return false;
biggestCoordX = std::max(biggestCoordX, std::fabs(fX) + 1);
biggestCoordY = std::max(biggestCoordY, std::fabs(fY) + 1);
const SkScalar kMaxCoordinate = SkIntToScalar(1 << 15);
SkScalar scaleX = kMaxCoordinate / biggestCoordX;
SkScalar scaleY = kMaxCoordinate / biggestCoordY;
SkRegion rgn;
SkRegion clip;
SkMatrix m;
SkPath scaledPath(originalPath);
scaledPath.setFillType(ft);
m.setScale(scaleX, scaleY);
scaledPath.transform(m, 0);
int x = static_cast<int>(floorf(0.5f + point.x() * scaleX));
int y = static_cast<int>(floorf(0.5f + point.y() * scaleY));
clip.setRect(x - 1, y - 1, x + 1, y + 1);
return rgn.setPath(scaledPath, clip);
}
void onSetData(const GrGLSLProgramDataManager& pdman, const GrFragmentProcessor& p) override {
INHERITED::onSetData(pdman, p);
const TwoPointConicalEffect& effect = p.cast<TwoPointConicalEffect>();
// kRadialType should imply |r1 - r0| = 1 (after our transformation)
SkASSERT(effect.getType() == Type::kStrip ||
SkScalarNearlyZero(SkTAbs(effect.diffRadius()) - 1));
pdman.set1f(fParamUni, effect.getType() == Type::kRadial ? effect.r0()
: effect.r0() * effect.r0());
}
// return X coordinate of intersection with horizontal line at Y
static SkScalar sect_with_horizontal(const SkPoint src[2], SkScalar Y) {
SkScalar dy = src[1].fY - src[0].fY;
if (SkScalarNearlyZero(dy)) {
return SkScalarAve(src[0].fX, src[1].fX);
} else {
return src[0].fX + SkScalarMulDiv(Y - src[0].fY, src[1].fX - src[0].fX,
dy);
}
}
// return Y coordinate of intersection with vertical line at X
static SkScalar sect_with_vertical(const SkPoint src[2], SkScalar X) {
SkScalar dx = src[1].fX - src[0].fX;
if (SkScalarNearlyZero(dx)) {
return SkScalarAve(src[0].fY, src[1].fY);
} else {
return src[0].fY + SkScalarMulDiv(X - src[0].fX, src[1].fY - src[0].fY,
dx);
}
}
static void test_conic_tangents(skiatest::Reporter* reporter) {
SkPoint pts[] = {
{ 10, 20}, {10, 20}, {20, 30},
{ 10, 20}, {15, 25}, {20, 30},
{ 10, 20}, {20, 30}, {20, 30}
};
int count = (int) SK_ARRAY_COUNT(pts) / 3;
for (int index = 0; index < count; ++index) {
SkConic conic(&pts[index * 3], 0.707f);
SkVector start = conic.evalTangentAt(0);
SkVector mid = conic.evalTangentAt(.5f);
SkVector end = conic.evalTangentAt(1);
REPORTER_ASSERT(reporter, start.fX && start.fY);
REPORTER_ASSERT(reporter, mid.fX && mid.fY);
REPORTER_ASSERT(reporter, end.fX && end.fY);
REPORTER_ASSERT(reporter, SkScalarNearlyZero(start.cross(mid)));
REPORTER_ASSERT(reporter, SkScalarNearlyZero(mid.cross(end)));
}
}
static bool just_trans_general(const SkMatrix& matrix) {
SkMatrix::TypeMask mask = matrix.getType();
if (mask & (SkMatrix::kAffine_Mask | SkMatrix::kPerspective_Mask)) {
return false;
}
if (mask & SkMatrix::kScale_Mask) {
const SkScalar tol = SK_Scalar1 / 32768;
if (!SkScalarNearlyZero(matrix[SkMatrix::kMScaleX] - SK_Scalar1, tol)) {
return false;
}
if (!SkScalarNearlyZero(matrix[SkMatrix::kMScaleY] - SK_Scalar1, tol)) {
return false;
}
}
// if we got here, treat us as either kTranslate_Mask or identity
return true;
}
// Computes perpDot for point compared to segment.
// A positive value means the point is to the left of the segment,
// negative is to the right, 0 is collinear.
static int compute_side(const SkPoint& s0, const SkPoint& s1, const SkPoint& p) {
SkVector v0 = s1 - s0;
SkVector v1 = p - s0;
SkScalar perpDot = v0.cross(v1);
if (!SkScalarNearlyZero(perpDot)) {
return ((perpDot > 0) ? 1 : -1);
}
return 0;
}
/* Solve coeff(t) == 0, returning the number of roots that
lie withing 0 < t < 1.
coeff[0]t^3 + coeff[1]t^2 + coeff[2]t + coeff[3]
Eliminates repeated roots (so that all tValues are distinct, and are always
in increasing order.
*/
static int solve_cubic_polynomial(const SkFP coeff[4], SkScalar tValues[3])
{
#ifndef SK_SCALAR_IS_FLOAT
return 0; // this is not yet implemented for software float
#endif
if (SkScalarNearlyZero(coeff[0])) // we're just a quadratic
{
return SkFindUnitQuadRoots(coeff[1], coeff[2], coeff[3], tValues);
}
SkFP a, b, c, Q, R;
{
SkASSERT(coeff[0] != 0);
SkFP inva = SkFPInvert(coeff[0]);
a = SkFPMul(coeff[1], inva);
b = SkFPMul(coeff[2], inva);
c = SkFPMul(coeff[3], inva);
}
Q = SkFPDivInt(SkFPSub(SkFPMul(a,a), SkFPMulInt(b, 3)), 9);
// R = (2*a*a*a - 9*a*b + 27*c) / 54;
R = SkFPMulInt(SkFPMul(SkFPMul(a, a), a), 2);
R = SkFPSub(R, SkFPMulInt(SkFPMul(a, b), 9));
R = SkFPAdd(R, SkFPMulInt(c, 27));
R = SkFPDivInt(R, 54);
SkFP Q3 = SkFPMul(SkFPMul(Q, Q), Q);
SkFP R2MinusQ3 = SkFPSub(SkFPMul(R,R), Q3);
SkFP adiv3 = SkFPDivInt(a, 3);
SkScalar* roots = tValues;
SkScalar r;
if (SkFPLT(R2MinusQ3, 0)) // we have 3 real roots
{
#ifdef SK_SCALAR_IS_FLOAT
float theta = sk_float_acos(R / sk_float_sqrt(Q3));
float neg2RootQ = -2 * sk_float_sqrt(Q);
r = neg2RootQ * sk_float_cos(theta/3) - adiv3;
if (is_unit_interval(r))
*roots++ = r;
r = neg2RootQ * sk_float_cos((theta + 2*SK_ScalarPI)/3) - adiv3;
if (is_unit_interval(r))
*roots++ = r;
r = neg2RootQ * sk_float_cos((theta - 2*SK_ScalarPI)/3) - adiv3;
if (is_unit_interval(r))
*roots++ = r;
SkDEBUGCODE(test_collaps_duplicates();)
static void test_cubic_tangents(skiatest::Reporter* reporter) {
SkPoint pts[] = {
{ 10, 20}, {10, 20}, {20, 30}, {30, 40},
{ 10, 20}, {15, 25}, {20, 30}, {30, 40},
{ 10, 20}, {20, 30}, {30, 40}, {30, 40},
};
int count = (int) SK_ARRAY_COUNT(pts) / 4;
for (int index = 0; index < count; ++index) {
SkConic conic(&pts[index * 3], 0.707f);
SkVector start, mid, end;
SkEvalCubicAt(&pts[index * 4], 0, nullptr, &start, nullptr);
SkEvalCubicAt(&pts[index * 4], .5f, nullptr, &mid, nullptr);
SkEvalCubicAt(&pts[index * 4], 1, nullptr, &end, nullptr);
REPORTER_ASSERT(reporter, start.fX && start.fY);
REPORTER_ASSERT(reporter, mid.fX && mid.fY);
REPORTER_ASSERT(reporter, end.fX && end.fY);
REPORTER_ASSERT(reporter, SkScalarNearlyZero(start.cross(mid)));
REPORTER_ASSERT(reporter, SkScalarNearlyZero(mid.cross(end)));
}
}
static void center_of_mass(const SegmentArray& segments, SkPoint* c) {
SkScalar area = 0;
SkPoint center = {0, 0};
int count = segments.count();
SkPoint p0 = {0, 0};
if (count > 2) {
// We translate the polygon so that the first point is at the origin.
// This avoids some precision issues with small area polygons far away
// from the origin.
p0 = segments[0].endPt();
SkPoint pi;
SkPoint pj;
// the first and last iteration of the below loop would compute
// zeros since the starting / ending point is (0,0). So instead we start
// at i=1 and make the last iteration i=count-2.
pj = segments[1].endPt() - p0;
for (int i = 1; i < count - 1; ++i) {
pi = pj;
const SkPoint pj = segments[i + 1].endPt() - p0;
SkScalar t = SkScalarMul(pi.fX, pj.fY) - SkScalarMul(pj.fX, pi.fY);
area += t;
center.fX += (pi.fX + pj.fX) * t;
center.fY += (pi.fY + pj.fY) * t;
}
}
// If the poly has no area then we instead return the average of
// its points.
if (SkScalarNearlyZero(area)) {
SkPoint avg;
avg.set(0, 0);
for (int i = 0; i < count; ++i) {
const SkPoint& pt = segments[i].endPt();
avg.fX += pt.fX;
avg.fY += pt.fY;
}
SkScalar denom = SK_Scalar1 / count;
avg.scale(denom);
*c = avg;
} else {
area *= 3;
area = SkScalarDiv(SK_Scalar1, area);
center.fX = SkScalarMul(center.fX, area);
center.fY = SkScalarMul(center.fY, area);
// undo the translate of p0 to the origin.
*c = center + p0;
}
SkASSERT(!SkScalarIsNaN(c->fX) && !SkScalarIsNaN(c->fY));
}
// return Y coordinate of intersection with vertical line at X
static SkScalar sect_with_vertical(const SkPoint src[2], SkScalar X) {
SkScalar dx = src[1].fX - src[0].fX;
if (SkScalarNearlyZero(dx)) {
return SkScalarAve(src[0].fY, src[1].fY);
} else {
// need the extra precision so we don't compute a value that exceeds
// our original limits
double X0 = src[0].fX;
double Y0 = src[0].fY;
double X1 = src[1].fX;
double Y1 = src[1].fY;
double result = Y0 + ((double)X - X0) * (Y1 - Y0) / (X1 - X0);
return (float)result;
}
}
void SkLinearGradient::
LinearGradient4fContext::shadeSpanInternal(int x, int y, dstType dst[], int count,
float bias0, float bias1) const {
SkPoint pt;
fDstToPosProc(fDstToPos,
x + SK_ScalarHalf,
y + SK_ScalarHalf,
&pt);
const SkScalar fx = pinFx<tileMode>(pt.x());
const SkScalar dx = fDstToPos.getScaleX();
LinearIntervalProcessor<dstType, premul, tileMode> proc(fIntervals->begin(),
fIntervals->end() - 1,
this->findInterval(fx),
fx,
dx,
SkScalarNearlyZero(dx * count));
Sk4f bias4f0(bias0),
bias4f1(bias1);
while (count > 0) {
// What we really want here is SkTPin(advance, 1, count)
// but that's a significant perf hit for >> stops; investigate.
const int n = SkScalarTruncToInt(
SkTMin<SkScalar>(proc.currentAdvance() + 1, SkIntToScalar(count)));
// The current interval advance can be +inf (e.g. when reaching
// the clamp mode end intervals) - when that happens, we expect to
// a) consume all remaining count in one swoop
// b) return a zero color gradient
SkASSERT(SkScalarIsFinite(proc.currentAdvance())
|| (n == count && proc.currentRampIsZero()));
if (proc.currentRampIsZero()) {
DstTraits<dstType, premul>::store(proc.currentColor(), dst, n);
} else {
ramp<dstType, premul>(proc.currentColor(), proc.currentColorGrad(), dst, n,
bias4f0, bias4f1);
}
proc.advance(SkIntToScalar(n));
count -= n;
dst += n;
if (n & 1) {
SkTSwap(bias4f0, bias4f1);
}
}
}
static SkXfermode* Create(SkScalar k1, SkScalar k2, SkScalar k3, SkScalar k4,
bool enforcePMColor) {
if (SkScalarNearlyZero(k1) && SkScalarNearlyEqual(k2, SK_Scalar1) &&
SkScalarNearlyZero(k3) && SkScalarNearlyZero(k4)) {
return SkXfermode::Create(SkXfermode::kSrc_Mode);
} else if (SkScalarNearlyZero(k1) && SkScalarNearlyZero(k2) &&
SkScalarNearlyEqual(k3, SK_Scalar1) && SkScalarNearlyZero(k4)) {
return SkXfermode::Create(SkXfermode::kDst_Mode);
}
return new SkArithmeticMode_scalar(k1, k2, k3, k4, enforcePMColor);
}
bool SkPathContainsPoint(SkPath* originalPath, const FloatPoint& point, SkPath::FillType ft)
{
SkRect bounds = originalPath->getBounds();
// We can immediately return false if the point is outside the bounding
// rect. We don't use bounds.contains() here, since it would exclude
// points on the right and bottom edges of the bounding rect, and we want
// to include them.
SkScalar fX = SkFloatToScalar(point.x());
SkScalar fY = SkFloatToScalar(point.y());
if (fX < bounds.fLeft || fX > bounds.fRight || fY < bounds.fTop || fY > bounds.fBottom)
return false;
// Scale the path to a large size before hit testing for two reasons:
// 1) Skia has trouble with coordinates close to the max signed 16-bit values, so we scale larger paths down.
// TODO: when Skia is patched to work properly with large values, this will not be necessary.
// 2) Skia does not support analytic hit testing, so we scale paths up to do raster hit testing with subpixel accuracy.
SkScalar biggestCoord = std::max(std::max(std::max(bounds.fRight, bounds.fBottom), -bounds.fLeft), -bounds.fTop);
if (SkScalarNearlyZero(biggestCoord))
return false;
biggestCoord = std::max(std::max(biggestCoord, fX + 1), fY + 1);
const SkScalar kMaxCoordinate = SkIntToScalar(1 << 15);
SkScalar scale = SkScalarDiv(kMaxCoordinate, biggestCoord);
SkRegion rgn;
SkRegion clip;
SkMatrix m;
SkPath scaledPath;
SkPath::FillType originalFillType = originalPath->getFillType();
originalPath->setFillType(ft);
m.setScale(scale, scale);
originalPath->transform(m, &scaledPath);
int x = static_cast<int>(floorf(0.5f + point.x() * scale));
int y = static_cast<int>(floorf(0.5f + point.y() * scale));
clip.setRect(x - 1, y - 1, x + 1, y + 1);
bool contains = rgn.setPath(scaledPath, clip);
originalPath->setFillType(originalFillType);
return contains;
}
// return X coordinate of intersection with horizontal line at Y
static SkScalar sect_with_horizontal(const SkPoint src[2], SkScalar Y) {
SkScalar dy = src[1].fY - src[0].fY;
if (SkScalarNearlyZero(dy)) {
return SkScalarAve(src[0].fX, src[1].fX);
} else {
// need the extra precision so we don't compute a value that exceeds
// our original limits
double X0 = src[0].fX;
double Y0 = src[0].fY;
double X1 = src[1].fX;
double Y1 = src[1].fY;
double result = X0 + ((double)Y - Y0) * (X1 - X0) / (Y1 - Y0);
// The computed X value might still exceed [X0..X1] due to quantum flux
// when the doubles were added and subtracted, so we have to pin the
// answer :(
return (float)pin_unsorted(result, X0, X1);
}
}
// Compute the intersection 'p' between segments s0 and s1, if any.
// 's' is the parametric value for the intersection along 's0' & 't' is the same for 's1'.
// Returns false if there is no intersection.
static bool compute_intersection(const InsetSegment& s0, const InsetSegment& s1,
SkPoint* p, SkScalar* s, SkScalar* t) {
SkVector v0 = s0.fP1 - s0.fP0;
SkVector v1 = s1.fP1 - s1.fP0;
SkScalar perpDot = v0.cross(v1);
if (SkScalarNearlyZero(perpDot)) {
// segments are parallel
// check if endpoints are touching
if (s0.fP1.equalsWithinTolerance(s1.fP0)) {
*p = s0.fP1;
*s = SK_Scalar1;
*t = 0;
return true;
}
if (s1.fP1.equalsWithinTolerance(s0.fP0)) {
*p = s1.fP1;
*s = 0;
*t = SK_Scalar1;
return true;
}
return false;
}
SkVector d = s1.fP0 - s0.fP0;
SkScalar localS = d.cross(v1) / perpDot;
if (localS < 0 || localS > SK_Scalar1) {
return false;
}
SkScalar localT = d.cross(v0) / perpDot;
if (localT < 0 || localT > SK_Scalar1) {
return false;
}
v0 *= localS;
*p = s0.fP0 + v0;
*s = localS;
*t = localT;
return true;
}
/* Solve coeff(t) == 0, returning the number of roots that
lie withing 0 < t < 1.
coeff[0]t^3 + coeff[1]t^2 + coeff[2]t + coeff[3]
Eliminates repeated roots (so that all tValues are distinct, and are always
in increasing order.
*/
static int solve_cubic_poly(const SkScalar coeff[4], SkScalar tValues[3]) {
if (SkScalarNearlyZero(coeff[0])) { // we're just a quadratic
return SkFindUnitQuadRoots(coeff[1], coeff[2], coeff[3], tValues);
}
SkScalar a, b, c, Q, R;
{
SkASSERT(coeff[0] != 0);
SkScalar inva = SkScalarInvert(coeff[0]);
a = coeff[1] * inva;
b = coeff[2] * inva;
c = coeff[3] * inva;
}
Q = (a*a - b*3) / 9;
R = (2*a*a*a - 9*a*b + 27*c) / 54;
SkScalar Q3 = Q * Q * Q;
SkScalar R2MinusQ3 = R * R - Q3;
SkScalar adiv3 = a / 3;
SkScalar* roots = tValues;
SkScalar r;
if (R2MinusQ3 < 0) { // we have 3 real roots
SkScalar theta = SkScalarACos(R / SkScalarSqrt(Q3));
SkScalar neg2RootQ = -2 * SkScalarSqrt(Q);
r = neg2RootQ * SkScalarCos(theta/3) - adiv3;
if (is_unit_interval(r)) {
*roots++ = r;
}
r = neg2RootQ * SkScalarCos((theta + 2*SK_ScalarPI)/3) - adiv3;
if (is_unit_interval(r)) {
*roots++ = r;
}
r = neg2RootQ * SkScalarCos((theta - 2*SK_ScalarPI)/3) - adiv3;
if (is_unit_interval(r)) {
*roots++ = r;
}
SkDEBUGCODE(test_collaps_duplicates();)
// return X coordinate of intersection with horizontal line at Y
static SkScalar sect_with_horizontal(const SkPoint src[2], SkScalar Y) {
SkScalar dy = src[1].fY - src[0].fY;
if (SkScalarNearlyZero(dy)) {
return SkScalarAve(src[0].fX, src[1].fX);
} else {
#ifdef SK_SCALAR_IS_FLOAT
// need the extra precision so we don't compute a value that exceeds
// our original limits
double X0 = src[0].fX;
double Y0 = src[0].fY;
double X1 = src[1].fX;
double Y1 = src[1].fY;
double result = X0 + ((double)Y - Y0) * (X1 - X0) / (Y1 - Y0);
return (float)result;
#else
return src[0].fX + SkScalarMulDiv(Y - src[0].fY, src[1].fX - src[0].fX,
dy);
#endif
}
}
bool SkSetPoly3To3(SkMatrix* matrix, const SkPoint src[3], const SkPoint dst[3]) {
const SkPoint& srcAve = src[0];
const SkPoint& dstAve = dst[0];
SkScalar srcOP[4], dstOP[4];
computeOuterProduct(srcOP, src, srcAve, src, srcAve);
computeOuterProduct(dstOP, src, srcAve, dst, dstAve);
SkScalar det = SkScalarMul(srcOP[0], srcOP[3]) - SkScalarMul(srcOP[1], srcOP[2]);
// need SkScalarNearlyZeroSquared for this (to match Chrome's fix)
if (SkScalarNearlyZero(det)) {
return false;
}
SkScalar invDet = SkScalarInvert(det);
// now compute invDet * [srcOP]T * [dstOP]
// scale and transpose
const SkScalar srcOP0 = SkScalarMul( srcOP[3], invDet);
const SkScalar srcOP1 = SkScalarMul(-srcOP[1], invDet);
const SkScalar srcOP2 = SkScalarMul(-srcOP[2], invDet);
const SkScalar srcOP3 = SkScalarMul( srcOP[0], invDet);
matrix->reset();
matrix->setScaleX(dot(srcOP0, srcOP1, dstOP[0], dstOP[2]));
matrix->setSkewX( dot(srcOP2, srcOP3, dstOP[0], dstOP[2]));
matrix->setSkewY (dot(srcOP0, srcOP1, dstOP[1], dstOP[3]));
matrix->setScaleY(dot(srcOP2, srcOP3, dstOP[1], dstOP[3]));
matrix->setTranslateX(dstAve.fX - dot(srcAve.fX, srcAve.fY,
matrix->getScaleX(), matrix->getSkewX()));
matrix->setTranslateY(dstAve.fY - dot(srcAve.fX, srcAve.fY,
matrix->getSkewY(), matrix->getScaleY()));
return true;
}
static void test_matrix_decomposition(skiatest::Reporter* reporter) {
SkMatrix mat;
SkPoint rotation1, scale, rotation2;
const float kRotation0 = 15.5f;
const float kRotation1 = -50.f;
const float kScale0 = 5000.f;
const float kScale1 = 0.001f;
// identity
mat.reset();
REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation1, &scale, &rotation2));
REPORTER_ASSERT(reporter, check_matrix_recomposition(mat, rotation1, scale, rotation2));
// make sure it doesn't crash if we pass in NULLs
REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, NULL, NULL, NULL));
// rotation only
mat.setRotate(kRotation0);
REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation1, &scale, &rotation2));
REPORTER_ASSERT(reporter, check_matrix_recomposition(mat, rotation1, scale, rotation2));
// uniform scale only
mat.setScale(kScale0, kScale0);
REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation1, &scale, &rotation2));
REPORTER_ASSERT(reporter, check_matrix_recomposition(mat, rotation1, scale, rotation2));
// anisotropic scale only
mat.setScale(kScale1, kScale0);
REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation1, &scale, &rotation2));
REPORTER_ASSERT(reporter, check_matrix_recomposition(mat, rotation1, scale, rotation2));
// rotation then uniform scale
mat.setRotate(kRotation1);
mat.postScale(kScale0, kScale0);
REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation1, &scale, &rotation2));
REPORTER_ASSERT(reporter, check_matrix_recomposition(mat, rotation1, scale, rotation2));
// uniform scale then rotation
mat.setScale(kScale0, kScale0);
mat.postRotate(kRotation1);
REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation1, &scale, &rotation2));
REPORTER_ASSERT(reporter, check_matrix_recomposition(mat, rotation1, scale, rotation2));
// rotation then uniform scale+reflection
mat.setRotate(kRotation0);
mat.postScale(kScale1, -kScale1);
REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation1, &scale, &rotation2));
REPORTER_ASSERT(reporter, check_matrix_recomposition(mat, rotation1, scale, rotation2));
// uniform scale+reflection, then rotate
mat.setScale(kScale0, -kScale0);
mat.postRotate(kRotation1);
REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation1, &scale, &rotation2));
REPORTER_ASSERT(reporter, check_matrix_recomposition(mat, rotation1, scale, rotation2));
// rotation then anisotropic scale
mat.setRotate(kRotation1);
mat.postScale(kScale1, kScale0);
REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation1, &scale, &rotation2));
REPORTER_ASSERT(reporter, check_matrix_recomposition(mat, rotation1, scale, rotation2));
// rotation then anisotropic scale
mat.setRotate(90);
mat.postScale(kScale1, kScale0);
REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation1, &scale, &rotation2));
REPORTER_ASSERT(reporter, check_matrix_recomposition(mat, rotation1, scale, rotation2));
// anisotropic scale then rotation
mat.setScale(kScale1, kScale0);
mat.postRotate(kRotation0);
REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation1, &scale, &rotation2));
REPORTER_ASSERT(reporter, check_matrix_recomposition(mat, rotation1, scale, rotation2));
// anisotropic scale then rotation
mat.setScale(kScale1, kScale0);
mat.postRotate(90);
REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation1, &scale, &rotation2));
REPORTER_ASSERT(reporter, check_matrix_recomposition(mat, rotation1, scale, rotation2));
// rotation, uniform scale, then different rotation
mat.setRotate(kRotation1);
mat.postScale(kScale0, kScale0);
mat.postRotate(kRotation0);
REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation1, &scale, &rotation2));
REPORTER_ASSERT(reporter, check_matrix_recomposition(mat, rotation1, scale, rotation2));
// rotation, anisotropic scale, then different rotation
mat.setRotate(kRotation0);
mat.postScale(kScale1, kScale0);
mat.postRotate(kRotation1);
REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation1, &scale, &rotation2));
REPORTER_ASSERT(reporter, check_matrix_recomposition(mat, rotation1, scale, rotation2));
// rotation, anisotropic scale + reflection, then different rotation
mat.setRotate(kRotation0);
mat.postScale(-kScale1, kScale0);
mat.postRotate(kRotation1);
REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation1, &scale, &rotation2));
REPORTER_ASSERT(reporter, check_matrix_recomposition(mat, rotation1, scale, rotation2));
// try some random matrices
SkRandom rand;
for (int m = 0; m < 1000; ++m) {
SkScalar rot0 = rand.nextRangeF(-180, 180);
SkScalar sx = rand.nextRangeF(-3000.f, 3000.f);
SkScalar sy = rand.nextRangeF(-3000.f, 3000.f);
SkScalar rot1 = rand.nextRangeF(-180, 180);
mat.setRotate(rot0);
mat.postScale(sx, sy);
mat.postRotate(rot1);
if (SkDecomposeUpper2x2(mat, &rotation1, &scale, &rotation2)) {
REPORTER_ASSERT(reporter, check_matrix_recomposition(mat, rotation1, scale, rotation2));
} else {
// if the matrix is degenerate, the basis vectors should be near-parallel or near-zero
SkScalar perpdot = mat[SkMatrix::kMScaleX]*mat[SkMatrix::kMScaleY] -
mat[SkMatrix::kMSkewX]*mat[SkMatrix::kMSkewY];
REPORTER_ASSERT(reporter, SkScalarNearlyZero(perpdot));
}
}
// translation shouldn't affect this
mat.postTranslate(-1000.f, 1000.f);
REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation1, &scale, &rotation2));
REPORTER_ASSERT(reporter, check_matrix_recomposition(mat, rotation1, scale, rotation2));
// perspective shouldn't affect this
mat[SkMatrix::kMPersp0] = 12.f;
mat[SkMatrix::kMPersp1] = 4.f;
mat[SkMatrix::kMPersp2] = 1872.f;
REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation1, &scale, &rotation2));
REPORTER_ASSERT(reporter, check_matrix_recomposition(mat, rotation1, scale, rotation2));
// degenerate matrices
// mostly zero entries
mat.reset();
mat[SkMatrix::kMScaleX] = 0.f;
REPORTER_ASSERT(reporter, !SkDecomposeUpper2x2(mat, &rotation1, &scale, &rotation2));
mat.reset();
mat[SkMatrix::kMScaleY] = 0.f;
REPORTER_ASSERT(reporter, !SkDecomposeUpper2x2(mat, &rotation1, &scale, &rotation2));
mat.reset();
// linearly dependent entries
mat[SkMatrix::kMScaleX] = 1.f;
mat[SkMatrix::kMSkewX] = 2.f;
mat[SkMatrix::kMSkewY] = 4.f;
mat[SkMatrix::kMScaleY] = 8.f;
REPORTER_ASSERT(reporter, !SkDecomposeUpper2x2(mat, &rotation1, &scale, &rotation2));
}
static void test_matrix_decomposition(skiatest::Reporter* reporter) {
SkMatrix mat;
SkScalar rotation0, scaleX, scaleY, rotation1;
const float kRotation0 = 15.5f;
const float kRotation1 = -50.f;
const float kScale0 = 5000.f;
const float kScale1 = 0.001f;
// identity
mat.reset();
REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation0, &scaleX, &scaleY, &rotation1));
REPORTER_ASSERT(reporter, SkScalarNearlyZero(rotation0));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(scaleX, SK_Scalar1));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(scaleY, SK_Scalar1));
REPORTER_ASSERT(reporter, SkScalarNearlyZero(rotation1));
// make sure it doesn't crash if we pass in NULLs
REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, NULL, NULL, NULL, NULL));
// rotation only
mat.setRotate(kRotation0);
REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation0, &scaleX, &scaleY, &rotation1));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(rotation0, SkDegreesToRadians(kRotation0)));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(scaleX, SK_Scalar1));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(scaleY, SK_Scalar1));
REPORTER_ASSERT(reporter, SkScalarNearlyZero(rotation1));
// uniform scale only
mat.setScale(kScale0, kScale0);
REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation0, &scaleX, &scaleY, &rotation1));
REPORTER_ASSERT(reporter, SkScalarNearlyZero(rotation0));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(scaleX, kScale0));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(scaleY, kScale0));
REPORTER_ASSERT(reporter, SkScalarNearlyZero(rotation1));
// anisotropic scale only
mat.setScale(kScale1, kScale0);
REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation0, &scaleX, &scaleY, &rotation1));
REPORTER_ASSERT(reporter, SkScalarNearlyZero(rotation0));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(scaleX, kScale1));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(scaleY, kScale0));
REPORTER_ASSERT(reporter, SkScalarNearlyZero(rotation1));
// rotation then uniform scale
mat.setRotate(kRotation1);
mat.postScale(kScale0, kScale0);
REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation0, &scaleX, &scaleY, &rotation1));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(rotation0, SkDegreesToRadians(kRotation1)));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(scaleX, kScale0));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(scaleY, kScale0));
REPORTER_ASSERT(reporter, SkScalarNearlyZero(rotation1));
// uniform scale then rotation
mat.setScale(kScale0, kScale0);
mat.postRotate(kRotation1);
REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation0, &scaleX, &scaleY, &rotation1));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(rotation0, SkDegreesToRadians(kRotation1)));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(scaleX, kScale0));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(scaleY, kScale0));
REPORTER_ASSERT(reporter, SkScalarNearlyZero(rotation1));
// rotation then uniform scale+reflection
mat.setRotate(kRotation0);
mat.postScale(kScale1, -kScale1);
REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation0, &scaleX, &scaleY, &rotation1));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(rotation0, SkDegreesToRadians(kRotation0)));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(scaleX, kScale1));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(scaleY, -kScale1));
REPORTER_ASSERT(reporter, SkScalarNearlyZero(rotation1));
// uniform scale+reflection, then rotate
mat.setScale(kScale0, -kScale0);
mat.postRotate(kRotation1);
REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation0, &scaleX, &scaleY, &rotation1));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(rotation0, SkDegreesToRadians(-kRotation1)));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(scaleX, kScale0));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(scaleY, -kScale0));
REPORTER_ASSERT(reporter, SkScalarNearlyZero(rotation1));
// rotation then anisotropic scale
mat.setRotate(kRotation1);
mat.postScale(kScale1, kScale0);
REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation0, &scaleX, &scaleY, &rotation1));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(rotation0, SkDegreesToRadians(kRotation1)));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(scaleX, kScale1));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(scaleY, kScale0));
REPORTER_ASSERT(reporter, SkScalarNearlyZero(rotation1));
// anisotropic scale then rotation
mat.setScale(kScale1, kScale0);
mat.postRotate(kRotation0);
REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation0, &scaleX, &scaleY, &rotation1));
REPORTER_ASSERT(reporter, SkScalarNearlyZero(rotation0));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(scaleX, kScale1));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(scaleY, kScale0));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(rotation1, SkDegreesToRadians(kRotation0)));
// rotation, uniform scale, then different rotation
mat.setRotate(kRotation1);
mat.postScale(kScale0, kScale0);
mat.postRotate(kRotation0);
REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation0, &scaleX, &scaleY, &rotation1));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(rotation0,
SkDegreesToRadians(kRotation0 + kRotation1)));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(scaleX, kScale0));
REPORTER_ASSERT(reporter, SkScalarNearlyEqual(scaleY, kScale0));
REPORTER_ASSERT(reporter, SkScalarNearlyZero(rotation1));
// rotation, anisotropic scale, then different rotation
mat.setRotate(kRotation0);
mat.postScale(kScale1, kScale0);
mat.postRotate(kRotation1);
REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation0, &scaleX, &scaleY, &rotation1));
// Because of the shear/skew we won't get the same results, so we need to multiply it out.
// Generating the matrices requires doing a radian-to-degree calculation, then degree-to-radian
// calculation (in setRotate()), which adds error, so this just computes the matrix elements
// directly.
SkScalar c0;
SkScalar s0 = SkScalarSinCos(rotation0, &c0);
SkScalar c1;
SkScalar s1 = SkScalarSinCos(rotation1, &c1);
// We do a relative check here because large scale factors cause problems with an absolute check
REPORTER_ASSERT(reporter, scalar_nearly_equal_relative(mat[SkMatrix::kMScaleX],
scaleX*c0*c1 - scaleY*s0*s1));
REPORTER_ASSERT(reporter, scalar_nearly_equal_relative(mat[SkMatrix::kMSkewX],
-scaleX*s0*c1 - scaleY*c0*s1));
REPORTER_ASSERT(reporter, scalar_nearly_equal_relative(mat[SkMatrix::kMSkewY],
scaleX*c0*s1 + scaleY*s0*c1));
REPORTER_ASSERT(reporter, scalar_nearly_equal_relative(mat[SkMatrix::kMScaleY],
-scaleX*s0*s1 + scaleY*c0*c1));
// try some random matrices
SkMWCRandom rand;
for (int m = 0; m < 1000; ++m) {
SkScalar rot0 = rand.nextRangeF(-SK_ScalarPI, SK_ScalarPI);
SkScalar sx = rand.nextRangeF(-3000.f, 3000.f);
SkScalar sy = rand.nextRangeF(-3000.f, 3000.f);
SkScalar rot1 = rand.nextRangeF(-SK_ScalarPI, SK_ScalarPI);
mat.setRotate(rot0);
mat.postScale(sx, sy);
mat.postRotate(rot1);
if (SkDecomposeUpper2x2(mat, &rotation0, &scaleX, &scaleY, &rotation1)) {
SkScalar c0;
SkScalar s0 = SkScalarSinCos(rotation0, &c0);
SkScalar c1;
SkScalar s1 = SkScalarSinCos(rotation1, &c1);
REPORTER_ASSERT(reporter, scalar_nearly_equal_relative(mat[SkMatrix::kMScaleX],
scaleX*c0*c1 - scaleY*s0*s1));
REPORTER_ASSERT(reporter, scalar_nearly_equal_relative(mat[SkMatrix::kMSkewX],
-scaleX*s0*c1 - scaleY*c0*s1));
REPORTER_ASSERT(reporter, scalar_nearly_equal_relative(mat[SkMatrix::kMSkewY],
scaleX*c0*s1 + scaleY*s0*c1));
REPORTER_ASSERT(reporter, scalar_nearly_equal_relative(mat[SkMatrix::kMScaleY],
-scaleX*s0*s1 + scaleY*c0*c1));
} else {
// if the matrix is degenerate, the basis vectors should be near-parallel or near-zero
SkScalar perpdot = mat[SkMatrix::kMScaleX]*mat[SkMatrix::kMScaleY] -
mat[SkMatrix::kMSkewX]*mat[SkMatrix::kMSkewY];
REPORTER_ASSERT(reporter, SkScalarNearlyZero(perpdot));
}
}
// translation shouldn't affect this
mat.postTranslate(-1000.f, 1000.f);
REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation0, &scaleX, &scaleY, &rotation1));
s0 = SkScalarSinCos(rotation0, &c0);
s1 = SkScalarSinCos(rotation1, &c1);
REPORTER_ASSERT(reporter, scalar_nearly_equal_relative(mat[SkMatrix::kMScaleX],
scaleX*c0*c1 - scaleY*s0*s1));
REPORTER_ASSERT(reporter, scalar_nearly_equal_relative(mat[SkMatrix::kMSkewX],
-scaleX*s0*c1 - scaleY*c0*s1));
REPORTER_ASSERT(reporter, scalar_nearly_equal_relative(mat[SkMatrix::kMSkewY],
scaleX*c0*s1 + scaleY*s0*c1));
REPORTER_ASSERT(reporter, scalar_nearly_equal_relative(mat[SkMatrix::kMScaleY],
-scaleX*s0*s1 + scaleY*c0*c1));
// perspective shouldn't affect this
mat[SkMatrix::kMPersp0] = 12.f;
mat[SkMatrix::kMPersp1] = 4.f;
mat[SkMatrix::kMPersp2] = 1872.f;
REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation0, &scaleX, &scaleY, &rotation1));
s0 = SkScalarSinCos(rotation0, &c0);
s1 = SkScalarSinCos(rotation1, &c1);
REPORTER_ASSERT(reporter, scalar_nearly_equal_relative(mat[SkMatrix::kMScaleX],
scaleX*c0*c1 - scaleY*s0*s1));
REPORTER_ASSERT(reporter, scalar_nearly_equal_relative(mat[SkMatrix::kMSkewX],
-scaleX*s0*c1 - scaleY*c0*s1));
REPORTER_ASSERT(reporter, scalar_nearly_equal_relative(mat[SkMatrix::kMSkewY],
scaleX*c0*s1 + scaleY*s0*c1));
REPORTER_ASSERT(reporter, scalar_nearly_equal_relative(mat[SkMatrix::kMScaleY],
-scaleX*s0*s1 + scaleY*c0*c1));
// rotation, anisotropic scale + reflection, then different rotation
mat.setRotate(kRotation0);
mat.postScale(-kScale1, kScale0);
mat.postRotate(kRotation1);
REPORTER_ASSERT(reporter, SkDecomposeUpper2x2(mat, &rotation0, &scaleX, &scaleY, &rotation1));
s0 = SkScalarSinCos(rotation0, &c0);
s1 = SkScalarSinCos(rotation1, &c1);
REPORTER_ASSERT(reporter, scalar_nearly_equal_relative(mat[SkMatrix::kMScaleX],
scaleX*c0*c1 - scaleY*s0*s1));
REPORTER_ASSERT(reporter, scalar_nearly_equal_relative(mat[SkMatrix::kMSkewX],
-scaleX*s0*c1 - scaleY*c0*s1));
REPORTER_ASSERT(reporter, scalar_nearly_equal_relative(mat[SkMatrix::kMSkewY],
scaleX*c0*s1 + scaleY*s0*c1));
REPORTER_ASSERT(reporter, scalar_nearly_equal_relative(mat[SkMatrix::kMScaleY],
-scaleX*s0*s1 + scaleY*c0*c1));
// degenerate matrices
// mostly zero entries
mat.reset();
mat[SkMatrix::kMScaleX] = 0.f;
REPORTER_ASSERT(reporter, !SkDecomposeUpper2x2(mat, &rotation0, &scaleX, &scaleY, &rotation1));
mat.reset();
mat[SkMatrix::kMScaleY] = 0.f;
REPORTER_ASSERT(reporter, !SkDecomposeUpper2x2(mat, &rotation0, &scaleX, &scaleY, &rotation1));
mat.reset();
// linearly dependent entries
mat[SkMatrix::kMScaleX] = 1.f;
mat[SkMatrix::kMSkewX] = 2.f;
mat[SkMatrix::kMSkewY] = 4.f;
mat[SkMatrix::kMScaleY] = 8.f;
REPORTER_ASSERT(reporter, !SkDecomposeUpper2x2(mat, &rotation0, &scaleX, &scaleY, &rotation1));
}
void SkPathStroker::cubicTo(const SkPoint& pt1, const SkPoint& pt2,
const SkPoint& pt3) {
bool degenerateAB = SkPath::IsLineDegenerate(fPrevPt, pt1);
bool degenerateBC = SkPath::IsLineDegenerate(pt1, pt2);
bool degenerateCD = SkPath::IsLineDegenerate(pt2, pt3);
if (degenerateAB + degenerateBC + degenerateCD >= 2) {
this->lineTo(pt3);
return;
}
SkVector normalAB, unitAB, normalCD, unitCD;
// find the first tangent (which might be pt1 or pt2
{
const SkPoint* nextPt = &pt1;
if (degenerateAB)
nextPt = &pt2;
this->preJoinTo(*nextPt, &normalAB, &unitAB, false);
}
{
SkPoint pts[4], tmp[13];
int i, count;
SkVector n, u;
SkScalar tValues[3];
pts[0] = fPrevPt;
pts[1] = pt1;
pts[2] = pt2;
pts[3] = pt3;
#if 1
count = SkChopCubicAtMaxCurvature(pts, tmp, tValues);
#else
count = 1;
memcpy(tmp, pts, 4 * sizeof(SkPoint));
#endif
n = normalAB;
u = unitAB;
for (i = 0; i < count; i++) {
this->cubic_to(&tmp[i * 3], n, u, &normalCD, &unitCD,
kMaxCubicSubdivide);
if (i == count - 1) {
break;
}
n = normalCD;
u = unitCD;
}
// check for too pinchy
for (i = 1; i < count; i++) {
SkPoint p;
SkVector v, c;
SkEvalCubicAt(pts, tValues[i - 1], &p, &v, &c);
SkScalar dot = SkPoint::DotProduct(c, c);
v.scale(SkScalarInvert(dot));
if (SkScalarNearlyZero(v.fX) && SkScalarNearlyZero(v.fY)) {
fExtra.addCircle(p.fX, p.fY, fRadius, SkPath::kCW_Direction);
}
}
}
this->postJoinTo(pt3, normalCD, unitCD);
}
bool SkXRayCrossesMonotonicCubic(const SkXRay& pt, const SkPoint cubic[4]) {
// Find the minimum and maximum y of the extrema, which are the
// first and last points since this cubic is monotonic
SkScalar min_y = SkMinScalar(cubic[0].fY, cubic[3].fY);
SkScalar max_y = SkMaxScalar(cubic[0].fY, cubic[3].fY);
if (pt.fY == cubic[0].fY
|| pt.fY < min_y
|| pt.fY > max_y) {
// The query line definitely does not cross the curve
return false;
}
SkScalar min_x =
SkMinScalar(
SkMinScalar(
SkMinScalar(cubic[0].fX, cubic[1].fX),
cubic[2].fX),
cubic[3].fX);
if (pt.fX < min_x) {
// The query line definitely crosses the curve
return true;
}
SkScalar max_x =
SkMaxScalar(
SkMaxScalar(
SkMaxScalar(cubic[0].fX, cubic[1].fX),
cubic[2].fX),
cubic[3].fX);
if (pt.fX > max_x) {
// The query line definitely does not cross the curve
return false;
}
// Do a binary search to find the parameter value which makes y as
// close as possible to the query point. See whether the query
// line's origin is to the left of the associated x coordinate.
// kMaxIter is chosen as the number of mantissa bits for a float,
// since there's no way we are going to get more precision by
// iterating more times than that.
const int kMaxIter = 23;
SkPoint eval;
int iter = 0;
SkScalar upper_t;
SkScalar lower_t;
// Need to invert direction of t parameter if cubic goes up
// instead of down
if (cubic[3].fY > cubic[0].fY) {
upper_t = SK_Scalar1;
lower_t = SkFloatToScalar(0);
} else {
upper_t = SkFloatToScalar(0);
lower_t = SK_Scalar1;
}
do {
SkScalar t = SkScalarAve(upper_t, lower_t);
SkEvalCubicAt(cubic, t, &eval, NULL, NULL);
if (pt.fY > eval.fY) {
lower_t = t;
} else {
upper_t = t;
}
} while (++iter < kMaxIter
&& !SkScalarNearlyZero(eval.fY - pt.fY));
if (pt.fX <= eval.fX) {
return true;
}
return false;
}
