107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com/* 207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com * Copyright 2012 Google Inc. 307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com * 407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com * Use of this source code is governed by a BSD-style license that can be 507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com * found in the LICENSE file. 607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com */ 707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com#include "SkIntersections.h" 807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com#include "SkPathOpsLine.h" 907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com#include "SkPathOpsQuad.h" 1007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 1107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com/* 1207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comFind the interection of a line and quadratic by solving for valid t values. 1307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 1407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comFrom http://stackoverflow.com/questions/1853637/how-to-find-the-mathematical-function-defining-a-bezier-curve 1507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 1607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com"A Bezier curve is a parametric function. A quadratic Bezier curve (i.e. three 1707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comcontrol points) can be expressed as: F(t) = A(1 - t)^2 + B(1 - t)t + Ct^2 where 1807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comA, B and C are points and t goes from zero to one. 1907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 2007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comThis will give you two equations: 2107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 2207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com x = a(1 - t)^2 + b(1 - t)t + ct^2 2307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com y = d(1 - t)^2 + e(1 - t)t + ft^2 2407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 2507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comIf you add for instance the line equation (y = kx + m) to that, you'll end up 2607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comwith three equations and three unknowns (x, y and t)." 2707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 2807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comSimilar to above, the quadratic is represented as 2907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com x = a(1-t)^2 + 2b(1-t)t + ct^2 3007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com y = d(1-t)^2 + 2e(1-t)t + ft^2 3107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comand the line as 3207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com y = g*x + h 3307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 3407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comUsing Mathematica, solve for the values of t where the quadratic intersects the 3507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comline: 3607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 3707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com (in) t1 = Resultant[a*(1 - t)^2 + 2*b*(1 - t)*t + c*t^2 - x, 3807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com d*(1 - t)^2 + 2*e*(1 - t)*t + f*t^2 - g*x - h, x] 3907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com (out) -d + h + 2 d t - 2 e t - d t^2 + 2 e t^2 - f t^2 + 4007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com g (a - 2 a t + 2 b t + a t^2 - 2 b t^2 + c t^2) 4107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com (in) Solve[t1 == 0, t] 4207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com (out) { 4307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com {t -> (-2 d + 2 e + 2 a g - 2 b g - 4407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com Sqrt[(2 d - 2 e - 2 a g + 2 b g)^2 - 4507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 4 (-d + 2 e - f + a g - 2 b g + c g) (-d + a g + h)]) / 4607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com (2 (-d + 2 e - f + a g - 2 b g + c g)) 4707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com }, 4807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com {t -> (-2 d + 2 e + 2 a g - 2 b g + 4907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com Sqrt[(2 d - 2 e - 2 a g + 2 b g)^2 - 5007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 4 (-d + 2 e - f + a g - 2 b g + c g) (-d + a g + h)]) / 5107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com (2 (-d + 2 e - f + a g - 2 b g + c g)) 5207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 5307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 5407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 5507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comUsing the results above (when the line tends towards horizontal) 5607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com A = (-(d - 2*e + f) + g*(a - 2*b + c) ) 5707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com B = 2*( (d - e ) - g*(a - b ) ) 5807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com C = (-(d ) + g*(a ) + h ) 5907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 6007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comIf g goes to infinity, we can rewrite the line in terms of x. 6107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com x = g'*y + h' 6207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 6307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comAnd solve accordingly in Mathematica: 6407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 6507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com (in) t2 = Resultant[a*(1 - t)^2 + 2*b*(1 - t)*t + c*t^2 - g'*y - h', 6607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com d*(1 - t)^2 + 2*e*(1 - t)*t + f*t^2 - y, y] 6707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com (out) a - h' - 2 a t + 2 b t + a t^2 - 2 b t^2 + c t^2 - 6807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com g' (d - 2 d t + 2 e t + d t^2 - 2 e t^2 + f t^2) 6907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com (in) Solve[t2 == 0, t] 7007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com (out) { 7107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com {t -> (2 a - 2 b - 2 d g' + 2 e g' - 7207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com Sqrt[(-2 a + 2 b + 2 d g' - 2 e g')^2 - 7307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 4 (a - 2 b + c - d g' + 2 e g' - f g') (a - d g' - h')]) / 7407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com (2 (a - 2 b + c - d g' + 2 e g' - f g')) 7507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com }, 7607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com {t -> (2 a - 2 b - 2 d g' + 2 e g' + 7707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com Sqrt[(-2 a + 2 b + 2 d g' - 2 e g')^2 - 7807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 4 (a - 2 b + c - d g' + 2 e g' - f g') (a - d g' - h')])/ 7907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com (2 (a - 2 b + c - d g' + 2 e g' - f g')) 8007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 8107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 8207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 8307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comThus, if the slope of the line tends towards vertical, we use: 8407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com A = ( (a - 2*b + c) - g'*(d - 2*e + f) ) 8507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com B = 2*(-(a - b ) + g'*(d - e ) ) 8607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com C = ( (a ) - g'*(d ) - h' ) 8707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com */ 8807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 8907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comclass LineQuadraticIntersections { 9007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.compublic: 914fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com enum PinTPoint { 924fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com kPointUninitialized, 934fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com kPointInitialized 944fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com }; 954fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com 9607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com LineQuadraticIntersections(const SkDQuad& q, const SkDLine& l, SkIntersections* i) 974fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com : fQuad(q) 98624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark , fLine(&l) 994fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com , fIntersections(i) 100fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com , fAllowNear(true) { 1018cb1daaa1e4343eb60a7c4f21c12e33de30dad64commit-bot@chromium.org i->setMax(3); // allow short partial coincidence plus discrete intersection 102fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com } 103fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com 104624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark LineQuadraticIntersections(const SkDQuad& q) 105624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark : fQuad(q) 10696fcdcc219d2a0d3579719b84b28bede76efba64halcanary SkDEBUGPARAMS(fLine(nullptr)) 10796fcdcc219d2a0d3579719b84b28bede76efba64halcanary SkDEBUGPARAMS(fIntersections(nullptr)) 108624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark SkDEBUGPARAMS(fAllowNear(false)) { 109624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark } 110624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark 111fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com void allowNear(bool allow) { 112fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com fAllowNear = allow; 11307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 11407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 11554359294a7c9dc54802d512a5d891a35c1663392caryclark void checkCoincident() { 11654359294a7c9dc54802d512a5d891a35c1663392caryclark int last = fIntersections->used() - 1; 11754359294a7c9dc54802d512a5d891a35c1663392caryclark for (int index = 0; index < last; ) { 11854359294a7c9dc54802d512a5d891a35c1663392caryclark double quadMidT = ((*fIntersections)[0][index] + (*fIntersections)[0][index + 1]) / 2; 11954359294a7c9dc54802d512a5d891a35c1663392caryclark SkDPoint quadMidPt = fQuad.ptAtT(quadMidT); 12096fcdcc219d2a0d3579719b84b28bede76efba64halcanary double t = fLine->nearPoint(quadMidPt, nullptr); 12154359294a7c9dc54802d512a5d891a35c1663392caryclark if (t < 0) { 12254359294a7c9dc54802d512a5d891a35c1663392caryclark ++index; 12354359294a7c9dc54802d512a5d891a35c1663392caryclark continue; 12454359294a7c9dc54802d512a5d891a35c1663392caryclark } 12554359294a7c9dc54802d512a5d891a35c1663392caryclark if (fIntersections->isCoincident(index)) { 12654359294a7c9dc54802d512a5d891a35c1663392caryclark fIntersections->removeOne(index); 12754359294a7c9dc54802d512a5d891a35c1663392caryclark --last; 12854359294a7c9dc54802d512a5d891a35c1663392caryclark } else if (fIntersections->isCoincident(index + 1)) { 12954359294a7c9dc54802d512a5d891a35c1663392caryclark fIntersections->removeOne(index + 1); 13054359294a7c9dc54802d512a5d891a35c1663392caryclark --last; 13154359294a7c9dc54802d512a5d891a35c1663392caryclark } else { 13254359294a7c9dc54802d512a5d891a35c1663392caryclark fIntersections->setCoincident(index++); 13354359294a7c9dc54802d512a5d891a35c1663392caryclark } 13454359294a7c9dc54802d512a5d891a35c1663392caryclark fIntersections->setCoincident(index); 13554359294a7c9dc54802d512a5d891a35c1663392caryclark } 13654359294a7c9dc54802d512a5d891a35c1663392caryclark } 13754359294a7c9dc54802d512a5d891a35c1663392caryclark 13807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com int intersectRay(double roots[2]) { 13907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com /* 14007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com solve by rotating line+quad so line is horizontal, then finding the roots 14107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com set up matrix to rotate quad to x-axis 14207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com |cos(a) -sin(a)| 14307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com |sin(a) cos(a)| 14407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com note that cos(a) = A(djacent) / Hypoteneuse 14507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com sin(a) = O(pposite) / Hypoteneuse 14607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com since we are computing Ts, we can ignore hypoteneuse, the scale factor: 14707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com | A -O | 14807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com | O A | 14907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com A = line[1].fX - line[0].fX (adjacent side of the right triangle) 15007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com O = line[1].fY - line[0].fY (opposite side of the right triangle) 15107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com for each of the three points (e.g. n = 0 to 2) 15207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com quad[n].fY' = (quad[n].fY - line[0].fY) * A - (quad[n].fX - line[0].fX) * O 15307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com */ 154624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark double adj = (*fLine)[1].fX - (*fLine)[0].fX; 155624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark double opp = (*fLine)[1].fY - (*fLine)[0].fY; 15607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double r[3]; 15707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com for (int n = 0; n < 3; ++n) { 158624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark r[n] = (fQuad[n].fY - (*fLine)[0].fY) * adj - (fQuad[n].fX - (*fLine)[0].fX) * opp; 15907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 16007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double A = r[2]; 16107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double B = r[1]; 16207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double C = r[0]; 16307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com A += C - 2 * B; // A = a - 2*b + c 16407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com B -= C; // B = -(b - c) 16507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return SkDQuad::RootsValidT(A, 2 * B, C, roots); 16607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 16707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 16807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com int intersect() { 169fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com addExactEndPoints(); 170570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com if (fAllowNear) { 171570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com addNearEndPoints(); 172570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com } 17354359294a7c9dc54802d512a5d891a35c1663392caryclark double rootVals[2]; 17454359294a7c9dc54802d512a5d891a35c1663392caryclark int roots = intersectRay(rootVals); 17554359294a7c9dc54802d512a5d891a35c1663392caryclark for (int index = 0; index < roots; ++index) { 17654359294a7c9dc54802d512a5d891a35c1663392caryclark double quadT = rootVals[index]; 17754359294a7c9dc54802d512a5d891a35c1663392caryclark double lineT = findLineT(quadT); 17854359294a7c9dc54802d512a5d891a35c1663392caryclark SkDPoint pt; 17954359294a7c9dc54802d512a5d891a35c1663392caryclark if (pinTs(&quadT, &lineT, &pt, kPointUninitialized) && uniqueAnswer(quadT, pt)) { 18054359294a7c9dc54802d512a5d891a35c1663392caryclark fIntersections->insert(quadT, lineT, pt); 18107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 18207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 18354359294a7c9dc54802d512a5d891a35c1663392caryclark checkCoincident(); 1844fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com return fIntersections->used(); 18507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 18607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 18707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com int horizontalIntersect(double axisIntercept, double roots[2]) { 1884fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com double D = fQuad[2].fY; // f 1894fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com double E = fQuad[1].fY; // e 1904fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com double F = fQuad[0].fY; // d 19107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com D += F - 2 * E; // D = d - 2*e + f 19207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com E -= F; // E = -(d - e) 19307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com F -= axisIntercept; 19407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return SkDQuad::RootsValidT(D, 2 * E, F, roots); 19507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 19607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 19707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com int horizontalIntersect(double axisIntercept, double left, double right, bool flipped) { 198fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com addExactHorizontalEndPoints(left, right, axisIntercept); 199570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com if (fAllowNear) { 200570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com addNearHorizontalEndPoints(left, right, axisIntercept); 201570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com } 20207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double rootVals[2]; 20307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com int roots = horizontalIntersect(axisIntercept, rootVals); 20407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com for (int index = 0; index < roots; ++index) { 20507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double quadT = rootVals[index]; 2064fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com SkDPoint pt = fQuad.ptAtT(quadT); 20707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double lineT = (pt.fX - left) / (right - left); 20854359294a7c9dc54802d512a5d891a35c1663392caryclark if (pinTs(&quadT, &lineT, &pt, kPointInitialized) && uniqueAnswer(quadT, pt)) { 2094fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com fIntersections->insert(quadT, lineT, pt); 21007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 21107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 21207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com if (flipped) { 2134fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com fIntersections->flip(); 21407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 21554359294a7c9dc54802d512a5d891a35c1663392caryclark checkCoincident(); 2164fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com return fIntersections->used(); 21707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 21807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 21954359294a7c9dc54802d512a5d891a35c1663392caryclark bool uniqueAnswer(double quadT, const SkDPoint& pt) { 22054359294a7c9dc54802d512a5d891a35c1663392caryclark for (int inner = 0; inner < fIntersections->used(); ++inner) { 22154359294a7c9dc54802d512a5d891a35c1663392caryclark if (fIntersections->pt(inner) != pt) { 22254359294a7c9dc54802d512a5d891a35c1663392caryclark continue; 22354359294a7c9dc54802d512a5d891a35c1663392caryclark } 22454359294a7c9dc54802d512a5d891a35c1663392caryclark double existingQuadT = (*fIntersections)[0][inner]; 22554359294a7c9dc54802d512a5d891a35c1663392caryclark if (quadT == existingQuadT) { 22654359294a7c9dc54802d512a5d891a35c1663392caryclark return false; 22754359294a7c9dc54802d512a5d891a35c1663392caryclark } 22854359294a7c9dc54802d512a5d891a35c1663392caryclark // check if midway on quad is also same point. If so, discard this 22954359294a7c9dc54802d512a5d891a35c1663392caryclark double quadMidT = (existingQuadT + quadT) / 2; 23054359294a7c9dc54802d512a5d891a35c1663392caryclark SkDPoint quadMidPt = fQuad.ptAtT(quadMidT); 23154359294a7c9dc54802d512a5d891a35c1663392caryclark if (quadMidPt.approximatelyEqual(pt)) { 23254359294a7c9dc54802d512a5d891a35c1663392caryclark return false; 23354359294a7c9dc54802d512a5d891a35c1663392caryclark } 23454359294a7c9dc54802d512a5d891a35c1663392caryclark } 23554359294a7c9dc54802d512a5d891a35c1663392caryclark#if ONE_OFF_DEBUG 23654359294a7c9dc54802d512a5d891a35c1663392caryclark SkDPoint qPt = fQuad.ptAtT(quadT); 23754359294a7c9dc54802d512a5d891a35c1663392caryclark SkDebugf("%s pt=(%1.9g,%1.9g) cPt=(%1.9g,%1.9g)\n", __FUNCTION__, pt.fX, pt.fY, 23854359294a7c9dc54802d512a5d891a35c1663392caryclark qPt.fX, qPt.fY); 23954359294a7c9dc54802d512a5d891a35c1663392caryclark#endif 24054359294a7c9dc54802d512a5d891a35c1663392caryclark return true; 24154359294a7c9dc54802d512a5d891a35c1663392caryclark } 24254359294a7c9dc54802d512a5d891a35c1663392caryclark 24307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com int verticalIntersect(double axisIntercept, double roots[2]) { 2444fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com double D = fQuad[2].fX; // f 2454fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com double E = fQuad[1].fX; // e 2464fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com double F = fQuad[0].fX; // d 24707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com D += F - 2 * E; // D = d - 2*e + f 24807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com E -= F; // E = -(d - e) 24907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com F -= axisIntercept; 25007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return SkDQuad::RootsValidT(D, 2 * E, F, roots); 25107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 25207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 25307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com int verticalIntersect(double axisIntercept, double top, double bottom, bool flipped) { 254fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com addExactVerticalEndPoints(top, bottom, axisIntercept); 255570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com if (fAllowNear) { 256570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com addNearVerticalEndPoints(top, bottom, axisIntercept); 257570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com } 25807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double rootVals[2]; 25907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com int roots = verticalIntersect(axisIntercept, rootVals); 26007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com for (int index = 0; index < roots; ++index) { 26107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double quadT = rootVals[index]; 2624fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com SkDPoint pt = fQuad.ptAtT(quadT); 26307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double lineT = (pt.fY - top) / (bottom - top); 26454359294a7c9dc54802d512a5d891a35c1663392caryclark if (pinTs(&quadT, &lineT, &pt, kPointInitialized) && uniqueAnswer(quadT, pt)) { 2654fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com fIntersections->insert(quadT, lineT, pt); 26607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 26707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 26807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com if (flipped) { 2694fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com fIntersections->flip(); 27007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 27154359294a7c9dc54802d512a5d891a35c1663392caryclark checkCoincident(); 2724fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com return fIntersections->used(); 27307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 27407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 27507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comprotected: 27607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com // add endpoints first to get zero and one t values exactly 277fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com void addExactEndPoints() { 27807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com for (int qIndex = 0; qIndex < 3; qIndex += 2) { 279624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark double lineT = fLine->exactPoint(fQuad[qIndex]); 280fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com if (lineT < 0) { 28107e97fccd2d85076cd22ef411b0773ab92a18abecaryclark@google.com continue; 28207e97fccd2d85076cd22ef411b0773ab92a18abecaryclark@google.com } 283fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com double quadT = (double) (qIndex >> 1); 2844fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com fIntersections->insert(quadT, lineT, fQuad[qIndex]); 285fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com } 286fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com } 287fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com 288fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com void addNearEndPoints() { 289fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com for (int qIndex = 0; qIndex < 3; qIndex += 2) { 290fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com double quadT = (double) (qIndex >> 1); 2914fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com if (fIntersections->hasT(quadT)) { 29207e97fccd2d85076cd22ef411b0773ab92a18abecaryclark@google.com continue; 29307e97fccd2d85076cd22ef411b0773ab92a18abecaryclark@google.com } 29496fcdcc219d2a0d3579719b84b28bede76efba64halcanary double lineT = fLine->nearPoint(fQuad[qIndex], nullptr); 295fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com if (lineT < 0) { 29607e97fccd2d85076cd22ef411b0773ab92a18abecaryclark@google.com continue; 29707e97fccd2d85076cd22ef411b0773ab92a18abecaryclark@google.com } 2984fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com fIntersections->insert(quadT, lineT, fQuad[qIndex]); 299fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com } 300fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com // FIXME: see if line end is nearly on quad 301fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com } 302fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com 303fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com void addExactHorizontalEndPoints(double left, double right, double y) { 304fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com for (int qIndex = 0; qIndex < 3; qIndex += 2) { 3054fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com double lineT = SkDLine::ExactPointH(fQuad[qIndex], left, right, y); 306fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com if (lineT < 0) { 307fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com continue; 30807e97fccd2d85076cd22ef411b0773ab92a18abecaryclark@google.com } 309fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com double quadT = (double) (qIndex >> 1); 3104fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com fIntersections->insert(quadT, lineT, fQuad[qIndex]); 31107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 31207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 31307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 314fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com void addNearHorizontalEndPoints(double left, double right, double y) { 31507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com for (int qIndex = 0; qIndex < 3; qIndex += 2) { 316fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com double quadT = (double) (qIndex >> 1); 3174fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com if (fIntersections->hasT(quadT)) { 31807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com continue; 31907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 3204fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com double lineT = SkDLine::NearPointH(fQuad[qIndex], left, right, y); 321fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com if (lineT < 0) { 322fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com continue; 32307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 3244fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com fIntersections->insert(quadT, lineT, fQuad[qIndex]); 32507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 326fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com // FIXME: see if line end is nearly on quad 32707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 32807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 329fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com void addExactVerticalEndPoints(double top, double bottom, double x) { 33007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com for (int qIndex = 0; qIndex < 3; qIndex += 2) { 3314fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com double lineT = SkDLine::ExactPointV(fQuad[qIndex], top, bottom, x); 332fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com if (lineT < 0) { 33307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com continue; 33407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 335fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com double quadT = (double) (qIndex >> 1); 3364fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com fIntersections->insert(quadT, lineT, fQuad[qIndex]); 337fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com } 338fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com } 339fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com 340fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com void addNearVerticalEndPoints(double top, double bottom, double x) { 341fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com for (int qIndex = 0; qIndex < 3; qIndex += 2) { 342fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com double quadT = (double) (qIndex >> 1); 3434fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com if (fIntersections->hasT(quadT)) { 344fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com continue; 345fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com } 3464fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com double lineT = SkDLine::NearPointV(fQuad[qIndex], top, bottom, x); 347fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com if (lineT < 0) { 348fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com continue; 34907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 3504fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com fIntersections->insert(quadT, lineT, fQuad[qIndex]); 35107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 352fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com // FIXME: see if line end is nearly on quad 35307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 35407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 35507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double findLineT(double t) { 3564fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com SkDPoint xy = fQuad.ptAtT(t); 357624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark double dx = (*fLine)[1].fX - (*fLine)[0].fX; 358624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark double dy = (*fLine)[1].fY - (*fLine)[0].fY; 35928d219c5682af6dfacea2460b5ba2f9e98702de6caryclark@google.com if (fabs(dx) > fabs(dy)) { 360624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark return (xy.fX - (*fLine)[0].fX) / dx; 36107e97fccd2d85076cd22ef411b0773ab92a18abecaryclark@google.com } 362624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark return (xy.fY - (*fLine)[0].fY) / dy; 36307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 36407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 3654fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com bool pinTs(double* quadT, double* lineT, SkDPoint* pt, PinTPoint ptSet) { 3664431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org if (!approximately_one_or_less_double(*lineT)) { 36707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return false; 36807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 3694431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org if (!approximately_zero_or_more_double(*lineT)) { 37007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return false; 37107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 3724fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com double qT = *quadT = SkPinT(*quadT); 3734fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com double lT = *lineT = SkPinT(*lineT); 3744fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com if (lT == 0 || lT == 1 || (ptSet == kPointUninitialized && qT != 0 && qT != 1)) { 375624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark *pt = (*fLine).ptAtT(lT); 3764fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com } else if (ptSet == kPointUninitialized) { 3774fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com *pt = fQuad.ptAtT(qT); 3784fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com } 379570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com SkPoint gridPt = pt->asSkPoint(); 380624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark if (SkDPoint::ApproximatelyEqual(gridPt, (*fLine)[0].asSkPoint())) { 381624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark *pt = (*fLine)[0]; 382570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com *lineT = 0; 383624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark } else if (SkDPoint::ApproximatelyEqual(gridPt, (*fLine)[1].asSkPoint())) { 384624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark *pt = (*fLine)[1]; 385570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com *lineT = 1; 386570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com } 3878cb1daaa1e4343eb60a7c4f21c12e33de30dad64commit-bot@chromium.org if (fIntersections->used() > 0 && approximately_equal((*fIntersections)[1][0], *lineT)) { 3888cb1daaa1e4343eb60a7c4f21c12e33de30dad64commit-bot@chromium.org return false; 3898cb1daaa1e4343eb60a7c4f21c12e33de30dad64commit-bot@chromium.org } 390570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com if (gridPt == fQuad[0].asSkPoint()) { 3914431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org *pt = fQuad[0]; 392570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com *quadT = 0; 393570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com } else if (gridPt == fQuad[2].asSkPoint()) { 3944431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org *pt = fQuad[2]; 395570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com *quadT = 1; 396570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com } 39707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return true; 39807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 39907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 40007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comprivate: 4014fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com const SkDQuad& fQuad; 402624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark const SkDLine* fLine; 4034fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com SkIntersections* fIntersections; 404fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com bool fAllowNear; 40507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com}; 40607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 40707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comint SkIntersections::horizontal(const SkDQuad& quad, double left, double right, double y, 40807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com bool flipped) { 4094fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com SkDLine line = {{{ left, y }, { right, y }}}; 4104fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com LineQuadraticIntersections q(quad, line, this); 41107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return q.horizontalIntersect(y, left, right, flipped); 41207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 41307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 41407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comint SkIntersections::vertical(const SkDQuad& quad, double top, double bottom, double x, 41507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com bool flipped) { 4164fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com SkDLine line = {{{ x, top }, { x, bottom }}}; 4174fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com LineQuadraticIntersections q(quad, line, this); 41807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return q.verticalIntersect(x, top, bottom, flipped); 41907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 42007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 42107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comint SkIntersections::intersect(const SkDQuad& quad, const SkDLine& line) { 42207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com LineQuadraticIntersections q(quad, line, this); 423fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com q.allowNear(fAllowNear); 42407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return q.intersect(); 42507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 42607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 42707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comint SkIntersections::intersectRay(const SkDQuad& quad, const SkDLine& line) { 42807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com LineQuadraticIntersections q(quad, line, this); 429a5e55925ea03e76885804bda77408a1d6f04c335caryclark@google.com fUsed = q.intersectRay(fT[0]); 430a5e55925ea03e76885804bda77408a1d6f04c335caryclark@google.com for (int index = 0; index < fUsed; ++index) { 4314fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com fPt[index] = quad.ptAtT(fT[0][index]); 432a5e55925ea03e76885804bda77408a1d6f04c335caryclark@google.com } 433a5e55925ea03e76885804bda77408a1d6f04c335caryclark@google.com return fUsed; 43407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 435624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark 436624637cc8ec22c000409704d0b403ac1b81ad4b0caryclarkint SkIntersections::HorizontalIntercept(const SkDQuad& quad, SkScalar y, double* roots) { 437624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark LineQuadraticIntersections q(quad); 438624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark return q.horizontalIntersect(y, roots); 439624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark} 440624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark 441624637cc8ec22c000409704d0b403ac1b81ad4b0caryclarkint SkIntersections::VerticalIntercept(const SkDQuad& quad, SkScalar x, double* roots) { 442624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark LineQuadraticIntersections q(quad); 443624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark return q.verticalIntersect(x, roots); 444624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark} 4450449bcfb2fa1dd33cb3a4c0c8b17960d17edf01acaryclark 4460449bcfb2fa1dd33cb3a4c0c8b17960d17edf01acaryclark// SkDQuad accessors to Intersection utilities 4470449bcfb2fa1dd33cb3a4c0c8b17960d17edf01acaryclark 4480449bcfb2fa1dd33cb3a4c0c8b17960d17edf01acaryclarkint SkDQuad::horizontalIntersect(double yIntercept, double roots[2]) const { 4490449bcfb2fa1dd33cb3a4c0c8b17960d17edf01acaryclark return SkIntersections::HorizontalIntercept(*this, yIntercept, roots); 4500449bcfb2fa1dd33cb3a4c0c8b17960d17edf01acaryclark} 4510449bcfb2fa1dd33cb3a4c0c8b17960d17edf01acaryclark 4520449bcfb2fa1dd33cb3a4c0c8b17960d17edf01acaryclarkint SkDQuad::verticalIntersect(double xIntercept, double roots[2]) const { 4530449bcfb2fa1dd33cb3a4c0c8b17960d17edf01acaryclark return SkIntersections::VerticalIntercept(*this, xIntercept, roots); 4540449bcfb2fa1dd33cb3a4c0c8b17960d17edf01acaryclark} 455