double SkDLine::nearPoint(const SkDPoint& xy) const {
if (!AlmostBetweenUlps(fPts[0].fX, xy.fX, fPts[1].fX)
|| !AlmostBetweenUlps(fPts[0].fY, xy.fY, fPts[1].fY)) {
return -1;
}
// project a perpendicular ray from the point to the line; find the T on the line
SkDVector len = fPts[1] - fPts[0]; // the x/y magnitudes of the line
double denom = len.fX * len.fX + len.fY * len.fY; // see DLine intersectRay
SkDVector ab0 = xy - fPts[0];
double numer = len.fX * ab0.fX + ab0.fY * len.fY;
if (!between(0, numer, denom)) {
return -1;
}
double t = numer / denom;
SkDPoint realPt = ptAtT(t);
double dist = realPt.distance(xy); // OPTIMIZATION: can we compare against distSq instead ?
// find the ordinal in the original line with the largest unsigned exponent
double tiniest = SkTMin(SkTMin(SkTMin(fPts[0].fX, fPts[0].fY), fPts[1].fX), fPts[1].fY);
double largest = SkTMax(SkTMax(SkTMax(fPts[0].fX, fPts[0].fY), fPts[1].fX), fPts[1].fY);
largest = SkTMax(largest, -tiniest);
if (!AlmostEqualUlps(largest, largest + dist)) { // is the dist within ULPS tolerance?
return -1;
}
t = SkPinT(t);
SkASSERT(between(0, t, 1));
return t;
}
// from http://blog.gludion.com/2009/08/distance-to-quadratic-bezier-curve.html
// (currently only used by testing)
double SkDQuad::nearestT(const SkDPoint& pt) const {
SkDVector pos = fPts[0] - pt;
// search points P of bezier curve with PM.(dP / dt) = 0
// a calculus leads to a 3d degree equation :
SkDVector A = fPts[1] - fPts[0];
SkDVector B = fPts[2] - fPts[1];
B -= A;
double a = B.dot(B);
double b = 3 * A.dot(B);
double c = 2 * A.dot(A) + pos.dot(B);
double d = pos.dot(A);
double ts[3];
int roots = SkDCubic::RootsValidT(a, b, c, d, ts);
double d0 = pt.distanceSquared(fPts[0]);
double d2 = pt.distanceSquared(fPts[2]);
double distMin = SkTMin(d0, d2);
int bestIndex = -1;
for (int index = 0; index < roots; ++index) {
SkDPoint onQuad = ptAtT(ts[index]);
double dist = pt.distanceSquared(onQuad);
if (distMin > dist) {
distMin = dist;
bestIndex = index;
}
}
if (bestIndex >= 0) {
return ts[bestIndex];
}
return d0 < d2 ? 0 : 1;
}
// give up when changing t no longer moves point
// also, copy point rather than recompute it when it does change
double SkDCubic::binarySearch(double min, double max, double axisIntercept,
SearchAxis xAxis) const {
double t = (min + max) / 2;
double step = (t - min) / 2;
SkDPoint cubicAtT = ptAtT(t);
double calcPos = (&cubicAtT.fX)[xAxis];
double calcDist = calcPos - axisIntercept;
do {
double priorT = t - step;
SkOPASSERT(priorT >= min);
SkDPoint lessPt = ptAtT(priorT);
if (approximately_equal_half(lessPt.fX, cubicAtT.fX)
&& approximately_equal_half(lessPt.fY, cubicAtT.fY)) {
return -1; // binary search found no point at this axis intercept
}
double lessDist = (&lessPt.fX)[xAxis] - axisIntercept;
#if DEBUG_CUBIC_BINARY_SEARCH
SkDebugf("t=%1.9g calc=%1.9g dist=%1.9g step=%1.9g less=%1.9g\n", t, calcPos, calcDist,
step, lessDist);
#endif
double lastStep = step;
step /= 2;
if (calcDist > 0 ? calcDist > lessDist : calcDist < lessDist) {
t = priorT;
} else {
double nextT = t + lastStep;
if (nextT > max) {
return -1;
}
SkDPoint morePt = ptAtT(nextT);
if (approximately_equal_half(morePt.fX, cubicAtT.fX)
&& approximately_equal_half(morePt.fY, cubicAtT.fY)) {
return -1; // binary search found no point at this axis intercept
}
double moreDist = (&morePt.fX)[xAxis] - axisIntercept;
if (calcDist > 0 ? calcDist <= moreDist : calcDist >= moreDist) {
continue;
}
t = nextT;
}
SkDPoint testAtT = ptAtT(t);
cubicAtT = testAtT;
calcPos = (&cubicAtT.fX)[xAxis];
calcDist = calcPos - axisIntercept;
} while (!approximately_equal(calcPos, axisIntercept));
return t;
}
bool SkDLine::nearRay(const SkDPoint& xy) const {
// project a perpendicular ray from the point to the line; find the T on the line
SkDVector len = fPts[1] - fPts[0]; // the x/y magnitudes of the line
double denom = len.fX * len.fX + len.fY * len.fY; // see DLine intersectRay
SkDVector ab0 = xy - fPts[0];
double numer = len.fX * ab0.fX + ab0.fY * len.fY;
double t = numer / denom;
SkDPoint realPt = ptAtT(t);
double dist = realPt.distance(xy); // OPTIMIZATION: can we compare against distSq instead ?
// find the ordinal in the original line with the largest unsigned exponent
double tiniest = SkTMin(SkTMin(SkTMin(fPts[0].fX, fPts[0].fY), fPts[1].fX), fPts[1].fY);
double largest = SkTMax(SkTMax(SkTMax(fPts[0].fX, fPts[0].fY), fPts[1].fX), fPts[1].fY);
largest = SkTMax(largest, -tiniest);
return RoughlyEqualUlps(largest, largest + dist); // is the dist within ULPS tolerance?
}
SkDPoint SkDQuad::top(double startT, double endT) const {
SkDQuad sub = subDivide(startT, endT);
SkDPoint topPt = sub[0];
if (topPt.fY > sub[2].fY || (topPt.fY == sub[2].fY && topPt.fX > sub[2].fX)) {
topPt = sub[2];
}
if (!between(sub[0].fY, sub[1].fY, sub[2].fY)) {
double extremeT;
if (FindExtrema(sub[0].fY, sub[1].fY, sub[2].fY, &extremeT)) {
extremeT = startT + (endT - startT) * extremeT;
SkDPoint test = ptAtT(extremeT);
if (topPt.fY > test.fY || (topPt.fY == test.fY && topPt.fX > test.fX)) {
topPt = test;
}
}
}
return topPt;
}
SkDPoint SkDCubic::top(double startT, double endT) const {
SkDCubic sub = subDivide(startT, endT);
SkDPoint topPt = sub[0];
if (topPt.fY > sub[3].fY || (topPt.fY == sub[3].fY && topPt.fX > sub[3].fX)) {
topPt = sub[3];
}
double extremeTs[2];
if (!sub.monotonicInY()) {
int roots = FindExtrema(sub[0].fY, sub[1].fY, sub[2].fY, sub[3].fY, extremeTs);
for (int index = 0; index < roots; ++index) {
double t = startT + (endT - startT) * extremeTs[index];
SkDPoint mid = ptAtT(t);
if (topPt.fY > mid.fY || (topPt.fY == mid.fY && topPt.fX > mid.fX)) {
topPt = mid;
}
}
}
return topPt;
}
