121c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com/* 221c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com * Copyright 2012 Google Inc. 321c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com * 421c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com * Use of this source code is governed by a BSD-style license that can be 521c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com * found in the LICENSE file. 621c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com */ 721c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com#include "SkIntersections.h" 821c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com#include "SkPathOpsLine.h" 921c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com#include "SkPathOpsQuad.h" 1021c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com 1121c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com/* 1221c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.comFind the interection of a line and quadratic by solving for valid t values. 1321c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com 1421c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.comFrom http://stackoverflow.com/questions/1853637/how-to-find-the-mathematical-function-defining-a-bezier-curve 1521c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com 1621c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com"A Bezier curve is a parametric function. A quadratic Bezier curve (i.e. three 1721c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.comcontrol points) can be expressed as: F(t) = A(1 - t)^2 + B(1 - t)t + Ct^2 where 1821c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.comA, B and C are points and t goes from zero to one. 1921c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com 2021c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.comThis will give you two equations: 2121c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com 2221c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com x = a(1 - t)^2 + b(1 - t)t + ct^2 2321c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com y = d(1 - t)^2 + e(1 - t)t + ft^2 2421c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com 2521c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.comIf you add for instance the line equation (y = kx + m) to that, you'll end up 2621c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.comwith three equations and three unknowns (x, y and t)." 2721c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com 2821c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.comSimilar to above, the quadratic is represented as 2921c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com x = a(1-t)^2 + 2b(1-t)t + ct^2 3021c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com y = d(1-t)^2 + 2e(1-t)t + ft^2 3121c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.comand the line as 3221c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com y = g*x + h 3321c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com 3421c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.comUsing Mathematica, solve for the values of t where the quadratic intersects the 3521c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.comline: 3621c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com 3721c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com (in) t1 = Resultant[a*(1 - t)^2 + 2*b*(1 - t)*t + c*t^2 - x, 3821c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com d*(1 - t)^2 + 2*e*(1 - t)*t + f*t^2 - g*x - h, x] 3921c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com (out) -d + h + 2 d t - 2 e t - d t^2 + 2 e t^2 - f t^2 + 4021c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com g (a - 2 a t + 2 b t + a t^2 - 2 b t^2 + c t^2) 4121c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com (in) Solve[t1 == 0, t] 4221c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com (out) { 4321c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com {t -> (-2 d + 2 e + 2 a g - 2 b g - 4421c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com Sqrt[(2 d - 2 e - 2 a g + 2 b g)^2 - 4521c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com 4 (-d + 2 e - f + a g - 2 b g + c g) (-d + a g + h)]) / 4621c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com (2 (-d + 2 e - f + a g - 2 b g + c g)) 4721c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com }, 4821c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com {t -> (-2 d + 2 e + 2 a g - 2 b g + 4921c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com Sqrt[(2 d - 2 e - 2 a g + 2 b g)^2 - 5021c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com 4 (-d + 2 e - f + a g - 2 b g + c g) (-d + a g + h)]) / 5121c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com (2 (-d + 2 e - f + a g - 2 b g + c g)) 5221c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com } 5321c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com } 5421c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com 5521c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.comUsing the results above (when the line tends towards horizontal) 5621c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com A = (-(d - 2*e + f) + g*(a - 2*b + c) ) 5721c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com B = 2*( (d - e ) - g*(a - b ) ) 5821c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com C = (-(d ) + g*(a ) + h ) 5921c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com 6021c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.comIf g goes to infinity, we can rewrite the line in terms of x. 6121c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com x = g'*y + h' 6221c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com 6321c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.comAnd solve accordingly in Mathematica: 6421c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com 6521c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com (in) t2 = Resultant[a*(1 - t)^2 + 2*b*(1 - t)*t + c*t^2 - g'*y - h', 6621c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com d*(1 - t)^2 + 2*e*(1 - t)*t + f*t^2 - y, y] 6721c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com (out) a - h' - 2 a t + 2 b t + a t^2 - 2 b t^2 + c t^2 - 6821c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com g' (d - 2 d t + 2 e t + d t^2 - 2 e t^2 + f t^2) 6921c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com (in) Solve[t2 == 0, t] 7021c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com (out) { 7121c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com {t -> (2 a - 2 b - 2 d g' + 2 e g' - 7221c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com Sqrt[(-2 a + 2 b + 2 d g' - 2 e g')^2 - 7321c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com 4 (a - 2 b + c - d g' + 2 e g' - f g') (a - d g' - h')]) / 7421c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com (2 (a - 2 b + c - d g' + 2 e g' - f g')) 7521c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com }, 7621c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com {t -> (2 a - 2 b - 2 d g' + 2 e g' + 7721c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com Sqrt[(-2 a + 2 b + 2 d g' - 2 e g')^2 - 7821c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com 4 (a - 2 b + c - d g' + 2 e g' - f g') (a - d g' - h')])/ 7921c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com (2 (a - 2 b + c - d g' + 2 e g' - f g')) 8021c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com } 8121c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com } 8221c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com 8321c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.comThus, if the slope of the line tends towards vertical, we use: 8421c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com A = ( (a - 2*b + c) - g'*(d - 2*e + f) ) 8521c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com B = 2*(-(a - b ) + g'*(d - e ) ) 8621c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com C = ( (a ) - g'*(d ) - h' ) 8721c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com */ 8821c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com 8921c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com 9021c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.comclass LineQuadraticIntersections { 9121c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.compublic: 921a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com enum PinTPoint { 931a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com kPointUninitialized, 941a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com kPointInitialized 951a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com }; 961a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com 9721c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com LineQuadraticIntersections(const SkDQuad& q, const SkDLine& l, SkIntersections* i) 981a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com : fQuad(q) 991a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com , fLine(l) 1001a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com , fIntersections(i) 1012607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com , fAllowNear(true) { 1022607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com } 1032607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com 1042607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com void allowNear(bool allow) { 1052607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com fAllowNear = allow; 10621c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com } 10721c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com 10821c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com int intersectRay(double roots[2]) { 10921c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com /* 11021c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com solve by rotating line+quad so line is horizontal, then finding the roots 11121c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com set up matrix to rotate quad to x-axis 11221c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com |cos(a) -sin(a)| 11321c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com |sin(a) cos(a)| 11421c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com note that cos(a) = A(djacent) / Hypoteneuse 11521c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com sin(a) = O(pposite) / Hypoteneuse 11621c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com since we are computing Ts, we can ignore hypoteneuse, the scale factor: 11721c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com | A -O | 11821c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com | O A | 11921c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com A = line[1].fX - line[0].fX (adjacent side of the right triangle) 12021c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com O = line[1].fY - line[0].fY (opposite side of the right triangle) 12121c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com for each of the three points (e.g. n = 0 to 2) 12221c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com quad[n].fY' = (quad[n].fY - line[0].fY) * A - (quad[n].fX - line[0].fX) * O 12321c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com */ 1241a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com double adj = fLine[1].fX - fLine[0].fX; 1251a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com double opp = fLine[1].fY - fLine[0].fY; 12621c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com double r[3]; 12721c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com for (int n = 0; n < 3; ++n) { 1281a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com r[n] = (fQuad[n].fY - fLine[0].fY) * adj - (fQuad[n].fX - fLine[0].fX) * opp; 12921c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com } 13021c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com double A = r[2]; 13121c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com double B = r[1]; 13221c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com double C = r[0]; 13321c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com A += C - 2 * B; // A = a - 2*b + c 13421c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com B -= C; // B = -(b - c) 13521c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com return SkDQuad::RootsValidT(A, 2 * B, C, roots); 13621c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com } 13721c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com 13821c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com int intersect() { 1392607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com addExactEndPoints(); 14021c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com double rootVals[2]; 14121c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com int roots = intersectRay(rootVals); 14221c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com for (int index = 0; index < roots; ++index) { 14321c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com double quadT = rootVals[index]; 14421c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com double lineT = findLineT(quadT); 1451a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com SkDPoint pt; 1461a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com if (pinTs(&quadT, &lineT, &pt, kPointUninitialized)) { 1471a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com fIntersections->insert(quadT, lineT, pt); 14821c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com } 14921c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com } 1502607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com if (fAllowNear) { 1512607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com addNearEndPoints(); 1522607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com } 1531a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com return fIntersections->used(); 15421c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com } 15521c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com 15621c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com int horizontalIntersect(double axisIntercept, double roots[2]) { 1571a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com double D = fQuad[2].fY; // f 1581a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com double E = fQuad[1].fY; // e 1591a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com double F = fQuad[0].fY; // d 16021c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com D += F - 2 * E; // D = d - 2*e + f 16121c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com E -= F; // E = -(d - e) 16221c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com F -= axisIntercept; 16321c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com return SkDQuad::RootsValidT(D, 2 * E, F, roots); 16421c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com } 16521c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com 16621c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com int horizontalIntersect(double axisIntercept, double left, double right, bool flipped) { 1672607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com addExactHorizontalEndPoints(left, right, axisIntercept); 16821c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com double rootVals[2]; 16921c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com int roots = horizontalIntersect(axisIntercept, rootVals); 17021c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com for (int index = 0; index < roots; ++index) { 17121c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com double quadT = rootVals[index]; 1721a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com SkDPoint pt = fQuad.ptAtT(quadT); 17321c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com double lineT = (pt.fX - left) / (right - left); 1741a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com if (pinTs(&quadT, &lineT, &pt, kPointInitialized)) { 1751a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com fIntersections->insert(quadT, lineT, pt); 17621c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com } 17721c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com } 1782607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com if (fAllowNear) { 1792607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com addNearHorizontalEndPoints(left, right, axisIntercept); 1802607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com } 18121c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com if (flipped) { 1821a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com fIntersections->flip(); 18321c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com } 1841a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com return fIntersections->used(); 18521c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com } 18621c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com 18721c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com int verticalIntersect(double axisIntercept, double roots[2]) { 1881a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com double D = fQuad[2].fX; // f 1891a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com double E = fQuad[1].fX; // e 1901a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com double F = fQuad[0].fX; // d 19121c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com D += F - 2 * E; // D = d - 2*e + f 19221c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com E -= F; // E = -(d - e) 19321c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com F -= axisIntercept; 19421c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com return SkDQuad::RootsValidT(D, 2 * E, F, roots); 19521c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com } 19621c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com 19721c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com int verticalIntersect(double axisIntercept, double top, double bottom, bool flipped) { 1982607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com addExactVerticalEndPoints(top, bottom, axisIntercept); 19921c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com double rootVals[2]; 20021c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com int roots = verticalIntersect(axisIntercept, rootVals); 20121c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com for (int index = 0; index < roots; ++index) { 20221c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com double quadT = rootVals[index]; 2031a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com SkDPoint pt = fQuad.ptAtT(quadT); 20421c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com double lineT = (pt.fY - top) / (bottom - top); 2051a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com if (pinTs(&quadT, &lineT, &pt, kPointInitialized)) { 2061a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com fIntersections->insert(quadT, lineT, pt); 20721c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com } 20821c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com } 2092607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com if (fAllowNear) { 2102607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com addNearVerticalEndPoints(top, bottom, axisIntercept); 2112607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com } 21221c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com if (flipped) { 2131a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com fIntersections->flip(); 21421c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com } 2151a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com return fIntersections->used(); 21621c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com } 21721c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com 21821c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.comprotected: 21921c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com // add endpoints first to get zero and one t values exactly 2202607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com void addExactEndPoints() { 22121c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com for (int qIndex = 0; qIndex < 3; qIndex += 2) { 2221a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com double lineT = fLine.exactPoint(fQuad[qIndex]); 2232607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com if (lineT < 0) { 22446e3086c1837da6ab13b48f852bd7bfbab3dc44fcaryclark@google.com continue; 22546e3086c1837da6ab13b48f852bd7bfbab3dc44fcaryclark@google.com } 2262607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com double quadT = (double) (qIndex >> 1); 2271a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com fIntersections->insert(quadT, lineT, fQuad[qIndex]); 2282607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com } 2292607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com } 2302607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com 2312607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com void addNearEndPoints() { 2322607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com for (int qIndex = 0; qIndex < 3; qIndex += 2) { 2332607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com double quadT = (double) (qIndex >> 1); 2341a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com if (fIntersections->hasT(quadT)) { 23546e3086c1837da6ab13b48f852bd7bfbab3dc44fcaryclark@google.com continue; 23646e3086c1837da6ab13b48f852bd7bfbab3dc44fcaryclark@google.com } 2371a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com double lineT = fLine.nearPoint(fQuad[qIndex]); 2382607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com if (lineT < 0) { 23946e3086c1837da6ab13b48f852bd7bfbab3dc44fcaryclark@google.com continue; 24046e3086c1837da6ab13b48f852bd7bfbab3dc44fcaryclark@google.com } 2411a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com fIntersections->insert(quadT, lineT, fQuad[qIndex]); 2422607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com } 2432607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com // FIXME: see if line end is nearly on quad 2442607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com } 2452607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com 2462607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com void addExactHorizontalEndPoints(double left, double right, double y) { 2472607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com for (int qIndex = 0; qIndex < 3; qIndex += 2) { 2481a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com double lineT = SkDLine::ExactPointH(fQuad[qIndex], left, right, y); 2492607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com if (lineT < 0) { 2502607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com continue; 25146e3086c1837da6ab13b48f852bd7bfbab3dc44fcaryclark@google.com } 2522607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com double quadT = (double) (qIndex >> 1); 2531a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com fIntersections->insert(quadT, lineT, fQuad[qIndex]); 25421c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com } 25521c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com } 25621c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com 2572607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com void addNearHorizontalEndPoints(double left, double right, double y) { 25821c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com for (int qIndex = 0; qIndex < 3; qIndex += 2) { 2592607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com double quadT = (double) (qIndex >> 1); 2601a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com if (fIntersections->hasT(quadT)) { 26121c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com continue; 26221c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com } 2631a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com double lineT = SkDLine::NearPointH(fQuad[qIndex], left, right, y); 2642607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com if (lineT < 0) { 2652607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com continue; 26621c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com } 2671a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com fIntersections->insert(quadT, lineT, fQuad[qIndex]); 26821c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com } 2692607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com // FIXME: see if line end is nearly on quad 27021c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com } 27121c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com 2722607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com void addExactVerticalEndPoints(double top, double bottom, double x) { 27321c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com for (int qIndex = 0; qIndex < 3; qIndex += 2) { 2741a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com double lineT = SkDLine::ExactPointV(fQuad[qIndex], top, bottom, x); 2752607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com if (lineT < 0) { 27621c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com continue; 27721c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com } 2782607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com double quadT = (double) (qIndex >> 1); 2791a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com fIntersections->insert(quadT, lineT, fQuad[qIndex]); 2802607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com } 2812607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com } 2822607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com 2832607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com void addNearVerticalEndPoints(double top, double bottom, double x) { 2842607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com for (int qIndex = 0; qIndex < 3; qIndex += 2) { 2852607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com double quadT = (double) (qIndex >> 1); 2861a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com if (fIntersections->hasT(quadT)) { 2872607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com continue; 2882607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com } 2891a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com double lineT = SkDLine::NearPointV(fQuad[qIndex], top, bottom, x); 2902607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com if (lineT < 0) { 2912607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com continue; 29221c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com } 2931a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com fIntersections->insert(quadT, lineT, fQuad[qIndex]); 29421c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com } 2952607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com // FIXME: see if line end is nearly on quad 29621c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com } 29721c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com 29821c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com double findLineT(double t) { 2991a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com SkDPoint xy = fQuad.ptAtT(t); 3001a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com double dx = fLine[1].fX - fLine[0].fX; 3011a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com double dy = fLine[1].fY - fLine[0].fY; 3021a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com double dxT = (xy.fX - fLine[0].fX) / dx; 3031a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com double dyT = (xy.fY - fLine[0].fY) / dy; 30446e3086c1837da6ab13b48f852bd7bfbab3dc44fcaryclark@google.com if (!between(FLT_EPSILON, dxT, 1 - FLT_EPSILON) && between(0, dyT, 1)) { 30546e3086c1837da6ab13b48f852bd7bfbab3dc44fcaryclark@google.com return dyT; 30646e3086c1837da6ab13b48f852bd7bfbab3dc44fcaryclark@google.com } 30746e3086c1837da6ab13b48f852bd7bfbab3dc44fcaryclark@google.com if (!between(FLT_EPSILON, dyT, 1 - FLT_EPSILON) && between(0, dxT, 1)) { 30846e3086c1837da6ab13b48f852bd7bfbab3dc44fcaryclark@google.com return dxT; 30946e3086c1837da6ab13b48f852bd7bfbab3dc44fcaryclark@google.com } 31046e3086c1837da6ab13b48f852bd7bfbab3dc44fcaryclark@google.com return fabs(dx) > fabs(dy) ? dxT : dyT; 31121c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com } 31221c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com 3131a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com bool pinTs(double* quadT, double* lineT, SkDPoint* pt, PinTPoint ptSet) { 31421c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com if (!approximately_one_or_less(*lineT)) { 31521c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com return false; 31621c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com } 31721c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com if (!approximately_zero_or_more(*lineT)) { 31821c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com return false; 31921c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com } 3201a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com double qT = *quadT = SkPinT(*quadT); 3211a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com double lT = *lineT = SkPinT(*lineT); 3221a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com if (lT == 0 || lT == 1 || (ptSet == kPointUninitialized && qT != 0 && qT != 1)) { 3231a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com *pt = fLine.ptAtT(lT); 3241a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com } else if (ptSet == kPointUninitialized) { 3251a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com *pt = fQuad.ptAtT(qT); 3261a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com } 32721c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com return true; 32821c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com } 32921c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com 33021c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.comprivate: 3311a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com const SkDQuad& fQuad; 3321a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com const SkDLine& fLine; 3331a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com SkIntersections* fIntersections; 3342607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com bool fAllowNear; 33521c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com}; 33621c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com 33721c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com// utility for pairs of coincident quads 33821c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.comstatic double horizontalIntersect(const SkDQuad& quad, const SkDPoint& pt) { 33921c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com LineQuadraticIntersections q(quad, *(static_cast<SkDLine*>(0)), 34021c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com static_cast<SkIntersections*>(0)); 34121c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com double rootVals[2]; 34221c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com int roots = q.horizontalIntersect(pt.fY, rootVals); 34321c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com for (int index = 0; index < roots; ++index) { 34421c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com double t = rootVals[index]; 3451a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com SkDPoint qPt = quad.ptAtT(t); 34621c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com if (AlmostEqualUlps(qPt.fX, pt.fX)) { 34721c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com return t; 34821c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com } 34921c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com } 35021c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com return -1; 35121c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com} 35221c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com 35321c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.comstatic double verticalIntersect(const SkDQuad& quad, const SkDPoint& pt) { 35421c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com LineQuadraticIntersections q(quad, *(static_cast<SkDLine*>(0)), 35521c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com static_cast<SkIntersections*>(0)); 35621c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com double rootVals[2]; 35721c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com int roots = q.verticalIntersect(pt.fX, rootVals); 35821c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com for (int index = 0; index < roots; ++index) { 35921c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com double t = rootVals[index]; 3601a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com SkDPoint qPt = quad.ptAtT(t); 36121c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com if (AlmostEqualUlps(qPt.fY, pt.fY)) { 36221c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com return t; 36321c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com } 36421c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com } 36521c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com return -1; 36621c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com} 36721c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com 36821c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.comdouble SkIntersections::Axial(const SkDQuad& q1, const SkDPoint& p, bool vertical) { 36921c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com if (vertical) { 37021c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com return verticalIntersect(q1, p); 37121c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com } 37221c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com return horizontalIntersect(q1, p); 37321c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com} 37421c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com 37521c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.comint SkIntersections::horizontal(const SkDQuad& quad, double left, double right, double y, 37621c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com bool flipped) { 3771a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com SkDLine line = {{{ left, y }, { right, y }}}; 3781a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com LineQuadraticIntersections q(quad, line, this); 37921c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com return q.horizontalIntersect(y, left, right, flipped); 38021c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com} 38121c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com 38221c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.comint SkIntersections::vertical(const SkDQuad& quad, double top, double bottom, double x, 38321c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com bool flipped) { 3841a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com SkDLine line = {{{ x, top }, { x, bottom }}}; 3851a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com LineQuadraticIntersections q(quad, line, this); 38621c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com return q.verticalIntersect(x, top, bottom, flipped); 38721c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com} 38821c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com 38921c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.comint SkIntersections::intersect(const SkDQuad& quad, const SkDLine& line) { 39021c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com LineQuadraticIntersections q(quad, line, this); 3912607e2e5a8f13275d86e2242f9906f2106a2fa79caryclark@google.com q.allowNear(fAllowNear); 39221c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com return q.intersect(); 39321c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com} 39421c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com 39521c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.comint SkIntersections::intersectRay(const SkDQuad& quad, const SkDLine& line) { 39621c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com LineQuadraticIntersections q(quad, line, this); 3972274f123b56c02b1d0f195c6a980e6cfacc239bfcaryclark@google.com fUsed = q.intersectRay(fT[0]); 3982274f123b56c02b1d0f195c6a980e6cfacc239bfcaryclark@google.com for (int index = 0; index < fUsed; ++index) { 3991a4d09d786e54862a38f367490a7e4769f7e73adcaryclark@google.com fPt[index] = quad.ptAtT(fT[0][index]); 4002274f123b56c02b1d0f195c6a980e6cfacc239bfcaryclark@google.com } 4012274f123b56c02b1d0f195c6a980e6cfacc239bfcaryclark@google.com return fUsed; 40221c2924b178f0d4c298d6631e568401473ed8d16caryclark@google.com} 403