// note that this only works if both lines are neither horizontal nor vertical
int SkIntersections::intersect(const SkDLine& a, const SkDLine& b) {
// see if end points intersect the opposite line
double t;
for (int iA = 0; iA < 2; ++iA) {
if (!checkEndPoint(a[iA].fX, a[iA].fY, b, &t, -1)) {
continue;
}
insert(iA, t, a[iA]);
}
for (int iB = 0; iB < 2; ++iB) {
if (!checkEndPoint(b[iB].fX, b[iB].fY, a, &t, -1)) {
continue;
}
insert(t, iB, b[iB]);
}
if (used() > 0) {
SkASSERT(fUsed <= 2);
return used(); // coincident lines are returned here
}
/* Determine the intersection point of two line segments
Return FALSE if the lines don't intersect
from: http://paulbourke.net/geometry/lineline2d/ */
double axLen = a[1].fX - a[0].fX;
double ayLen = a[1].fY - a[0].fY;
double bxLen = b[1].fX - b[0].fX;
double byLen = b[1].fY - b[0].fY;
/* Slopes match when denom goes to zero:
axLen / ayLen == bxLen / byLen
(ayLen * byLen) * axLen / ayLen == (ayLen * byLen) * bxLen / byLen
byLen * axLen == ayLen * bxLen
byLen * axLen - ayLen * bxLen == 0 ( == denom )
*/
double denom = byLen * axLen - ayLen * bxLen;
double ab0y = a[0].fY - b[0].fY;
double ab0x = a[0].fX - b[0].fX;
double numerA = ab0y * bxLen - byLen * ab0x;
double numerB = ab0y * axLen - ayLen * ab0x;
bool mayNotOverlap = (numerA < 0 && denom > numerA) || (numerA > 0 && denom < numerA)
|| (numerB < 0 && denom > numerB) || (numerB > 0 && denom < numerB);
numerA /= denom;
numerB /= denom;
if ((!approximately_zero(denom) || (!approximately_zero_inverse(numerA)
&& !approximately_zero_inverse(numerB))) && !sk_double_isnan(numerA)
&& !sk_double_isnan(numerB)) {
if (mayNotOverlap) {
return 0;
}
fT[0][0] = numerA;
fT[1][0] = numerB;
fPt[0] = a.xyAtT(numerA);
return computePoints(a, 1);
}
return 0;
}
// unlike quadratic roots, this does not discard real roots <= 0 or >= 1
int quadraticRootsReal(const double A, const double B, const double C, double s[2]) {
const double p = B / (2 * A);
const double q = C / A;
if (approximately_zero(A) && (approximately_zero_inverse(p) || approximately_zero_inverse(q))) {
if (approximately_zero(B)) {
s[0] = 0;
return C == 0;
}
s[0] = -C / B;
return 1;
}
/* normal form: x^2 + px + q = 0 */
const double p2 = p * p;
#if 0
double D = AlmostEqualUlps(p2, q) ? 0 : p2 - q;
if (D <= 0) {
if (D < 0) {
return 0;
}
s[0] = -p;
SkDebugf("[%d] %1.9g\n", 1, s[0]);
return 1;
}
double sqrt_D = sqrt(D);
s[0] = sqrt_D - p;
s[1] = -sqrt_D - p;
SkDebugf("[%d] %1.9g %1.9g\n", 2, s[0], s[1]);
return 2;
#else
if (!AlmostEqualUlps(p2, q) && p2 < q) {
return 0;
}
double sqrt_D = 0;
if (p2 > q) {
sqrt_D = sqrt(p2 - q);
}
s[0] = sqrt_D - p;
s[1] = -sqrt_D - p;
#if 0
if (AlmostEqualUlps(s[0], s[1])) {
SkDebugf("[%d] %1.9g\n", 1, s[0]);
} else {
SkDebugf("[%d] %1.9g %1.9g\n", 2, s[0], s[1]);
}
#endif
return 1 + !AlmostEqualUlps(s[0], s[1]);
#endif
}
// this does not discard real roots <= 0 or >= 1
int SkDQuad::RootsReal(const double A, const double B, const double C, double s[2]) {
const double p = B / (2 * A);
const double q = C / A;
if (approximately_zero(A) && (approximately_zero_inverse(p) || approximately_zero_inverse(q))) {
if (approximately_zero(B)) {
s[0] = 0;
return C == 0;
}
s[0] = -C / B;
return 1;
}
/* normal form: x^2 + px + q = 0 */
const double p2 = p * p;
if (!AlmostDequalUlps(p2, q) && p2 < q) {
return 0;
}
double sqrt_D = 0;
if (p2 > q) {
sqrt_D = sqrt(p2 - q);
}
s[0] = sqrt_D - p;
s[1] = -sqrt_D - p;
return 1 + !AlmostDequalUlps(s[0], s[1]);
}
int SkIntersections::intersect(const SkDLine& a, const SkDLine& b) {
double axLen = a[1].fX - a[0].fX;
double ayLen = a[1].fY - a[0].fY;
double bxLen = b[1].fX - b[0].fX;
double byLen = b[1].fY - b[0].fY;
/* Slopes match when denom goes to zero:
axLen / ayLen == bxLen / byLen
(ayLen * byLen) * axLen / ayLen == (ayLen * byLen) * bxLen / byLen
byLen * axLen == ayLen * bxLen
byLen * axLen - ayLen * bxLen == 0 ( == denom )
*/
double denom = byLen * axLen - ayLen * bxLen;
double ab0y = a[0].fY - b[0].fY;
double ab0x = a[0].fX - b[0].fX;
double numerA = ab0y * bxLen - byLen * ab0x;
double numerB = ab0y * axLen - ayLen * ab0x;
bool mayNotOverlap = (numerA < 0 && denom > numerA) || (numerA > 0 && denom < numerA)
|| (numerB < 0 && denom > numerB) || (numerB > 0 && denom < numerB);
numerA /= denom;
numerB /= denom;
if ((!approximately_zero(denom) || (!approximately_zero_inverse(numerA)
&& !approximately_zero_inverse(numerB))) && !sk_double_isnan(numerA)
&& !sk_double_isnan(numerB)) {
if (mayNotOverlap) {
return fUsed = 0;
}
fT[0][0] = numerA;
fT[1][0] = numerB;
fPt[0] = a.xyAtT(numerA);
return computePoints(a, 1);
}
/* See if the axis intercepts match:
ay - ax * ayLen / axLen == by - bx * ayLen / axLen
axLen * (ay - ax * ayLen / axLen) == axLen * (by - bx * ayLen / axLen)
axLen * ay - ax * ayLen == axLen * by - bx * ayLen
*/
if (!AlmostEqualUlps(axLen * a[0].fY - ayLen * a[0].fX,
axLen * b[0].fY - ayLen * b[0].fX)) {
return fUsed = 0;
}
const double* aPtr;
const double* bPtr;
if (fabs(axLen) > fabs(ayLen) || fabs(bxLen) > fabs(byLen)) {
aPtr = &a[0].fX;
bPtr = &b[0].fX;
} else {
aPtr = &a[0].fY;
bPtr = &b[0].fY;
}
double a0 = aPtr[0];
double a1 = aPtr[2];
double b0 = bPtr[0];
double b1 = bPtr[2];
// OPTIMIZATION: restructure to reject before the divide
// e.g., if ((a0 - b0) * (a0 - a1) < 0 || abs(a0 - b0) > abs(a0 - a1))
// (except efficient)
double aDenom = a0 - a1;
if (approximately_zero(aDenom)) {
if (!between(b0, a0, b1)) {
return fUsed = 0;
}
fT[0][0] = fT[0][1] = 0;
} else {
double at0 = (a0 - b0) / aDenom;
double at1 = (a0 - b1) / aDenom;
if ((at0 < 0 && at1 < 0) || (at0 > 1 && at1 > 1)) {
return fUsed = 0;
}
fT[0][0] = SkTMax(SkTMin(at0, 1.0), 0.0);
fT[0][1] = SkTMax(SkTMin(at1, 1.0), 0.0);
}
double bDenom = b0 - b1;
if (approximately_zero(bDenom)) {
fT[1][0] = fT[1][1] = 0;
} else {
int bIn = aDenom * bDenom < 0;
fT[1][bIn] = SkTMax(SkTMin((b0 - a0) / bDenom, 1.0), 0.0);
fT[1][!bIn] = SkTMax(SkTMin((b0 - a1) / bDenom, 1.0), 0.0);
}
bool second = fabs(fT[0][0] - fT[0][1]) > FLT_EPSILON;
SkASSERT((fabs(fT[1][0] - fT[1][1]) <= FLT_EPSILON) ^ second);
return computePoints(a, 1 + second);
}
