int main () {
// FILE *f = fopen(INP, "r");
FILE *f = stdin;
fscanf(f,"%d",&T);
for(int i = 1; i <= T; i++){
for(int j = 1; j <= 4; j++){
fscanf(f,"%d%d",&P[j].x,&P[j].y);
}
//process
Result = 6;
memset(Used,false,sizeof Used);
Used[1] = true;
for(int j = 2; j <= 4; j++){
if(Result != 6) break;
Used[j] = true;
pair <int, int> line (0,0);
for(int k = 2; k <= 4; k++){
if(!Used[k]){
if(line.first == 0) line.first = k;
else line.second = k;
}
}
if(!checkParallel(P[1],P[j],P[line.first],P[line.second])) {Used[j] = false; continue;}
else{
Result = 5;
if(checkParallel(P[1],P[line.first],P[j],P[line.second])){
Result = 4;
whatIsIt(P[1],P[line.first],P[j],P[line.second]);
}
else{
if(checkParallel(P[1],P[line.second],P[j],P[line.first])){
Result = 4;
whatIsIt(P[1],P[line.second],P[j],P[line.first]);
}
else break;
}
}
Used[j] = false;
}
//output
printf("Case %d: %s\n",i,Shape[Result]);
}
// getchar();
return 0;
}
/* returns
-1 if overlaps
0 if no overlap cw
1 if no overlap ccw
*/
static int quadHullsOverlap(skiatest::Reporter* reporter, const SkDQuad& quad1,
const SkDQuad& quad2) {
SkDVector sweep[2], tweep[2];
setQuadHullSweep(quad1, sweep);
setQuadHullSweep(quad2, tweep);
double s0xs1 = sweep[0].crossCheck(sweep[1]);
double s0xt0 = sweep[0].crossCheck(tweep[0]);
double s1xt0 = sweep[1].crossCheck(tweep[0]);
bool tBetweenS = s0xs1 > 0 ? s0xt0 > 0 && s1xt0 < 0 : s0xt0 < 0 && s1xt0 > 0;
double s0xt1 = sweep[0].crossCheck(tweep[1]);
double s1xt1 = sweep[1].crossCheck(tweep[1]);
tBetweenS |= s0xs1 > 0 ? s0xt1 > 0 && s1xt1 < 0 : s0xt1 < 0 && s1xt1 > 0;
double t0xt1 = tweep[0].crossCheck(tweep[1]);
if (tBetweenS) {
return -1;
}
if ((s0xt0 == 0 && s1xt1 == 0) || (s1xt0 == 0 && s0xt1 == 0)) { // s0 to s1 equals t0 to t1
return -1;
}
bool sBetweenT = t0xt1 > 0 ? s0xt0 < 0 && s0xt1 > 0 : s0xt0 > 0 && s0xt1 < 0;
sBetweenT |= t0xt1 > 0 ? s1xt0 < 0 && s1xt1 > 0 : s1xt0 > 0 && s1xt1 < 0;
if (sBetweenT) {
return -1;
}
// if all of the sweeps are in the same half plane, then the order of any pair is enough
if (s0xt0 >= 0 && s0xt1 >= 0 && s1xt0 >= 0 && s1xt1 >= 0) {
return 0;
}
if (s0xt0 <= 0 && s0xt1 <= 0 && s1xt0 <= 0 && s1xt1 <= 0) {
return 1;
}
// if the outside sweeps are greater than 180 degress:
// first assume the inital tangents are the ordering
// if the midpoint direction matches the inital order, that is enough
SkDVector m0 = quad1.ptAtT(0.5) - quad1[0];
SkDVector m1 = quad2.ptAtT(0.5) - quad2[0];
double m0xm1 = m0.crossCheck(m1);
if (s0xt0 > 0 && m0xm1 > 0) {
return 0;
}
if (s0xt0 < 0 && m0xm1 < 0) {
return 1;
}
REPORTER_ASSERT(reporter, s0xt0 != 0);
return checkParallel(reporter, quad1, quad2);
}
bool SkOpAngle::endsIntersect(const SkOpAngle& rh) const {
SkPath::Verb lVerb = fSegment->verb();
SkPath::Verb rVerb = rh.fSegment->verb();
int lPts = SkPathOpsVerbToPoints(lVerb);
int rPts = SkPathOpsVerbToPoints(rVerb);
SkDLine rays[] = {{{fCurvePart[0], rh.fCurvePart[rPts]}},
{{fCurvePart[0], fCurvePart[lPts]}}};
if (rays[0][1] == rays[1][1]) {
return checkParallel(rh);
}
double smallTs[2] = {-1, -1};
bool limited[2] = {false, false};
for (int index = 0; index < 2; ++index) {
const SkOpSegment& segment = index ? *rh.fSegment : *fSegment;
SkIntersections i;
(*CurveIntersectRay[index ? rPts : lPts])(segment.pts(), rays[index], &i);
// SkASSERT(i.used() >= 1);
// if (i.used() <= 1) {
// continue;
// }
double tStart = segment.t(index ? rh.fStart : fStart);
double tEnd = segment.t(index ? rh.fComputedEnd : fComputedEnd);
bool testAscends = index ? rh.fStart < rh.fComputedEnd : fStart < fComputedEnd;
double t = testAscends ? 0 : 1;
for (int idx2 = 0; idx2 < i.used(); ++idx2) {
double testT = i[0][idx2];
if (!approximately_between_orderable(tStart, testT, tEnd)) {
continue;
}
if (approximately_equal_orderable(tStart, testT)) {
continue;
}
smallTs[index] = t = testAscends ? SkTMax(t, testT) : SkTMin(t, testT);
limited[index] = approximately_equal_orderable(t, tEnd);
}
}
#if 0
if (smallTs[0] < 0 && smallTs[1] < 0) { // if neither ray intersects, do endpoint sort
double m0xm1 = 0;
if (lVerb == SkPath::kLine_Verb) {
SkASSERT(rVerb != SkPath::kLine_Verb);
SkDVector m0 = rays[1][1] - fCurvePart[0];
SkDPoint endPt;
endPt.set(rh.fSegment->pts()[rh.fStart < rh.fEnd ? rPts : 0]);
SkDVector m1 = endPt - fCurvePart[0];
m0xm1 = m0.crossCheck(m1);
}
if (rVerb == SkPath::kLine_Verb) {
SkDPoint endPt;
endPt.set(fSegment->pts()[fStart < fEnd ? lPts : 0]);
SkDVector m0 = endPt - fCurvePart[0];
SkDVector m1 = rays[0][1] - fCurvePart[0];
m0xm1 = m0.crossCheck(m1);
}
if (m0xm1 != 0) {
return m0xm1 < 0;
}
}
#endif
bool sRayLonger = false;
SkDVector sCept = {0, 0};
double sCeptT = -1;
int sIndex = -1;
bool useIntersect = false;
for (int index = 0; index < 2; ++index) {
if (smallTs[index] < 0) {
continue;
}
const SkOpSegment& segment = index ? *rh.fSegment : *fSegment;
const SkDPoint& dPt = segment.dPtAtT(smallTs[index]);
SkDVector cept = dPt - rays[index][0];
// If this point is on the curve, it should have been detected earlier by ordinary
// curve intersection. This may be hard to determine in general, but for lines,
// the point could be close to or equal to its end, but shouldn't be near the start.
if ((index ? lPts : rPts) == 1) {
SkDVector total = rays[index][1] - rays[index][0];
if (cept.lengthSquared() * 2 < total.lengthSquared()) {
continue;
}
}
SkDVector end = rays[index][1] - rays[index][0];
if (cept.fX * end.fX < 0 || cept.fY * end.fY < 0) {
continue;
}
double rayDist = cept.length();
double endDist = end.length();
bool rayLonger = rayDist > endDist;
if (limited[0] && limited[1] && rayLonger) {
useIntersect = true;
sRayLonger = rayLonger;
sCept = cept;
sCeptT = smallTs[index];
sIndex = index;
break;
}
double delta = fabs(rayDist - endDist);
double minX, minY, maxX, maxY;
minX = minY = SK_ScalarInfinity;
maxX = maxY = -SK_ScalarInfinity;
const SkDCubic& curve = index ? rh.fCurvePart : fCurvePart;
int ptCount = index ? rPts : lPts;
for (int idx2 = 0; idx2 <= ptCount; ++idx2) {
minX = SkTMin(minX, curve[idx2].fX);
minY = SkTMin(minY, curve[idx2].fY);
maxX = SkTMax(maxX, curve[idx2].fX);
maxY = SkTMax(maxY, curve[idx2].fY);
}
double maxWidth = SkTMax(maxX - minX, maxY - minY);
delta /= maxWidth;
if (delta > 1e-4 && (useIntersect ^= true)) { // FIXME: move this magic number
sRayLonger = rayLonger;
sCept = cept;
sCeptT = smallTs[index];
sIndex = index;
}
}
if (useIntersect) {
const SkDCubic& curve = sIndex ? rh.fCurvePart : fCurvePart;
const SkOpSegment& segment = sIndex ? *rh.fSegment : *fSegment;
double tStart = segment.t(sIndex ? rh.fStart : fStart);
SkDVector mid = segment.dPtAtT(tStart + (sCeptT - tStart) / 2) - curve[0];
double septDir = mid.crossCheck(sCept);
if (!septDir) {
return checkParallel(rh);
}
return sRayLonger ^ (sIndex == 0) ^ (septDir < 0);
} else {
return checkParallel(rh);
}
}
static void testQuadAngles(skiatest::Reporter* reporter, const SkDQuad& quad1, const SkDQuad& quad2,
int testNo, SkChunkAlloc* allocator) {
SkPoint shortQuads[2][3];
SkOpContour contour;
SkOpGlobalState state(NULL PATH_OPS_DEBUG_PARAMS(&contour));
contour.init(&state, false, false);
makeSegment(&contour, quad1, shortQuads[0], allocator);
makeSegment(&contour, quad1, shortQuads[1], allocator);
SkOpSegment* seg1 = contour.first();
seg1->debugAddAngle(0, 1, allocator);
SkOpSegment* seg2 = seg1->next();
seg2->debugAddAngle(0, 1, allocator);
int realOverlap = PathOpsAngleTester::ConvexHullOverlaps(*seg1->debugLastAngle(),
*seg2->debugLastAngle());
const SkDPoint& origin = quad1[0];
REPORTER_ASSERT(reporter, origin == quad2[0]);
double a1s = atan2(origin.fY - quad1[1].fY, quad1[1].fX - origin.fX);
double a1e = atan2(origin.fY - quad1[2].fY, quad1[2].fX - origin.fX);
double a2s = atan2(origin.fY - quad2[1].fY, quad2[1].fX - origin.fX);
double a2e = atan2(origin.fY - quad2[2].fY, quad2[2].fX - origin.fX);
bool oldSchoolOverlap = radianBetween(a1s, a2s, a1e)
|| radianBetween(a1s, a2e, a1e) || radianBetween(a2s, a1s, a2e)
|| radianBetween(a2s, a1e, a2e);
int overlap = quadHullsOverlap(reporter, quad1, quad2);
bool realMatchesOverlap = realOverlap == overlap || SK_ScalarPI - fabs(a2s - a1s) < 0.002;
if (realOverlap != overlap) {
SkDebugf("\nSK_ScalarPI - fabs(a2s - a1s) = %1.9g\n", SK_ScalarPI - fabs(a2s - a1s));
}
if (!realMatchesOverlap) {
DumpQ(quad1, quad2, testNo);
}
REPORTER_ASSERT(reporter, realMatchesOverlap);
if (oldSchoolOverlap != (overlap < 0)) {
overlap = quadHullsOverlap(reporter, quad1, quad2); // set a breakpoint and debug if assert fires
REPORTER_ASSERT(reporter, oldSchoolOverlap == (overlap < 0));
}
SkDVector v1s = quad1[1] - quad1[0];
SkDVector v1e = quad1[2] - quad1[0];
SkDVector v2s = quad2[1] - quad2[0];
SkDVector v2e = quad2[2] - quad2[0];
double vDir[2] = { v1s.cross(v1e), v2s.cross(v2e) };
bool ray1In2 = v1s.cross(v2s) * vDir[1] <= 0 && v1s.cross(v2e) * vDir[1] >= 0;
bool ray2In1 = v2s.cross(v1s) * vDir[0] <= 0 && v2s.cross(v1e) * vDir[0] >= 0;
if (overlap >= 0) {
// verify that hulls really don't overlap
REPORTER_ASSERT(reporter, !ray1In2);
REPORTER_ASSERT(reporter, !ray2In1);
bool ctrl1In2 = v1e.cross(v2s) * vDir[1] <= 0 && v1e.cross(v2e) * vDir[1] >= 0;
REPORTER_ASSERT(reporter, !ctrl1In2);
bool ctrl2In1 = v2e.cross(v1s) * vDir[0] <= 0 && v2e.cross(v1e) * vDir[0] >= 0;
REPORTER_ASSERT(reporter, !ctrl2In1);
// check answer against reference
bruteForce(reporter, quad1, quad2, overlap > 0);
}
// continue end point rays and see if they intersect the opposite curve
SkDLine rays[] = {{{origin, quad2[2]}}, {{origin, quad1[2]}}};
const SkDQuad* quads[] = {&quad1, &quad2};
SkDVector midSpokes[2];
SkIntersections intersect[2];
double minX, minY, maxX, maxY;
minX = minY = SK_ScalarInfinity;
maxX = maxY = -SK_ScalarInfinity;
double maxWidth = 0;
bool useIntersect = false;
double smallestTs[] = {1, 1};
for (unsigned index = 0; index < SK_ARRAY_COUNT(quads); ++index) {
const SkDQuad& q = *quads[index];
midSpokes[index] = q.ptAtT(0.5) - origin;
minX = SkTMin(SkTMin(SkTMin(minX, origin.fX), q[1].fX), q[2].fX);
minY = SkTMin(SkTMin(SkTMin(minY, origin.fY), q[1].fY), q[2].fY);
maxX = SkTMax(SkTMax(SkTMax(maxX, origin.fX), q[1].fX), q[2].fX);
maxY = SkTMax(SkTMax(SkTMax(maxY, origin.fY), q[1].fY), q[2].fY);
maxWidth = SkTMax(maxWidth, SkTMax(maxX - minX, maxY - minY));
intersect[index].intersectRay(q, rays[index]);
const SkIntersections& i = intersect[index];
REPORTER_ASSERT(reporter, i.used() >= 1);
bool foundZero = false;
double smallT = 1;
for (int idx2 = 0; idx2 < i.used(); ++idx2) {
double t = i[0][idx2];
if (t == 0) {
foundZero = true;
continue;
}
if (smallT > t) {
smallT = t;
}
}
REPORTER_ASSERT(reporter, foundZero == true);
if (smallT == 1) {
continue;
}
SkDVector ray = q.ptAtT(smallT) - origin;
SkDVector end = rays[index][1] - origin;
if (ray.fX * end.fX < 0 || ray.fY * end.fY < 0) {
continue;
}
double rayDist = ray.length();
double endDist = end.length();
double delta = fabs(rayDist - endDist) / maxWidth;
if (delta > 1e-4) {
useIntersect ^= true;
}
smallestTs[index] = smallT;
}
bool firstInside;
if (useIntersect) {
int sIndex = (int) (smallestTs[1] < 1);
REPORTER_ASSERT(reporter, smallestTs[sIndex ^ 1] == 1);
double t = smallestTs[sIndex];
const SkDQuad& q = *quads[sIndex];
SkDVector ray = q.ptAtT(t) - origin;
SkDVector end = rays[sIndex][1] - origin;
double rayDist = ray.length();
double endDist = end.length();
SkDVector mid = q.ptAtT(t / 2) - origin;
double midXray = mid.crossCheck(ray);
if (gPathOpsAngleIdeasVerbose) {
SkDebugf("rayDist>endDist:%d sIndex==0:%d vDir[sIndex]<0:%d midXray<0:%d\n",
rayDist > endDist, sIndex == 0, vDir[sIndex] < 0, midXray < 0);
}
SkASSERT(SkScalarSignAsInt(SkDoubleToScalar(midXray))
== SkScalarSignAsInt(SkDoubleToScalar(vDir[sIndex])));
firstInside = (rayDist > endDist) ^ (sIndex == 0) ^ (vDir[sIndex] < 0);
} else if (overlap >= 0) {
return; // answer has already been determined
} else {
firstInside = checkParallel(reporter, quad1, quad2);
}
if (overlap < 0) {
SkDEBUGCODE(int realEnds =)
PathOpsAngleTester::EndsIntersect(*seg1->debugLastAngle(),
*seg2->debugLastAngle());
SkASSERT(realEnds == (firstInside ? 1 : 0));
}