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) 984fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com , 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 104fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com void allowNear(bool allow) { 105fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com fAllowNear = allow; 10607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 10707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 10807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com int intersectRay(double roots[2]) { 10907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com /* 11007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com solve by rotating line+quad so line is horizontal, then finding the roots 11107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com set up matrix to rotate quad to x-axis 11207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com |cos(a) -sin(a)| 11307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com |sin(a) cos(a)| 11407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com note that cos(a) = A(djacent) / Hypoteneuse 11507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com sin(a) = O(pposite) / Hypoteneuse 11607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com since we are computing Ts, we can ignore hypoteneuse, the scale factor: 11707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com | A -O | 11807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com | O A | 11907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com A = line[1].fX - line[0].fX (adjacent side of the right triangle) 12007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com O = line[1].fY - line[0].fY (opposite side of the right triangle) 12107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com for each of the three points (e.g. n = 0 to 2) 12207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com quad[n].fY' = (quad[n].fY - line[0].fY) * A - (quad[n].fX - line[0].fX) * O 12307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com */ 1244fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com double adj = fLine[1].fX - fLine[0].fX; 1254fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com double opp = fLine[1].fY - fLine[0].fY; 12607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double r[3]; 12707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com for (int n = 0; n < 3; ++n) { 1284fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com r[n] = (fQuad[n].fY - fLine[0].fY) * adj - (fQuad[n].fX - fLine[0].fX) * opp; 12907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 13007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double A = r[2]; 13107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double B = r[1]; 13207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double C = r[0]; 13307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com A += C - 2 * B; // A = a - 2*b + c 13407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com B -= C; // B = -(b - c) 13507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return SkDQuad::RootsValidT(A, 2 * B, C, roots); 13607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 13707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 13807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com int intersect() { 139fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com addExactEndPoints(); 140570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com if (fAllowNear) { 141570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com addNearEndPoints(); 142570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com } 143a2bbc6e19d5332e81784e582c290cc060f40c4c7caryclark@google.com if (fIntersections->used() == 2) { 144a2bbc6e19d5332e81784e582c290cc060f40c4c7caryclark@google.com // FIXME : need sharable code that turns spans into coincident if middle point is on 145a2bbc6e19d5332e81784e582c290cc060f40c4c7caryclark@google.com } else { 146a2bbc6e19d5332e81784e582c290cc060f40c4c7caryclark@google.com double rootVals[2]; 147a2bbc6e19d5332e81784e582c290cc060f40c4c7caryclark@google.com int roots = intersectRay(rootVals); 148a2bbc6e19d5332e81784e582c290cc060f40c4c7caryclark@google.com for (int index = 0; index < roots; ++index) { 149a2bbc6e19d5332e81784e582c290cc060f40c4c7caryclark@google.com double quadT = rootVals[index]; 150a2bbc6e19d5332e81784e582c290cc060f40c4c7caryclark@google.com double lineT = findLineT(quadT); 151a2bbc6e19d5332e81784e582c290cc060f40c4c7caryclark@google.com SkDPoint pt; 152a2bbc6e19d5332e81784e582c290cc060f40c4c7caryclark@google.com if (pinTs(&quadT, &lineT, &pt, kPointUninitialized)) { 153a2bbc6e19d5332e81784e582c290cc060f40c4c7caryclark@google.com fIntersections->insert(quadT, lineT, pt); 154a2bbc6e19d5332e81784e582c290cc060f40c4c7caryclark@google.com } 15507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 15607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 1574fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com return fIntersections->used(); 15807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 15907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 16007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com int horizontalIntersect(double axisIntercept, double roots[2]) { 1614fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com double D = fQuad[2].fY; // f 1624fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com double E = fQuad[1].fY; // e 1634fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com double F = fQuad[0].fY; // d 16407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com D += F - 2 * E; // D = d - 2*e + f 16507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com E -= F; // E = -(d - e) 16607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com F -= axisIntercept; 16707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return SkDQuad::RootsValidT(D, 2 * E, F, roots); 16807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 16907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 17007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com int horizontalIntersect(double axisIntercept, double left, double right, bool flipped) { 171fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com addExactHorizontalEndPoints(left, right, axisIntercept); 172570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com if (fAllowNear) { 173570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com addNearHorizontalEndPoints(left, right, axisIntercept); 174570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com } 17507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double rootVals[2]; 17607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com int roots = horizontalIntersect(axisIntercept, rootVals); 17707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com for (int index = 0; index < roots; ++index) { 17807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double quadT = rootVals[index]; 1794fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com SkDPoint pt = fQuad.ptAtT(quadT); 18007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double lineT = (pt.fX - left) / (right - left); 1814fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com if (pinTs(&quadT, &lineT, &pt, kPointInitialized)) { 1824fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com fIntersections->insert(quadT, lineT, pt); 18307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 18407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 18507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com if (flipped) { 1864fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com fIntersections->flip(); 18707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 1884fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com return fIntersections->used(); 18907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 19007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 19107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com int verticalIntersect(double axisIntercept, double roots[2]) { 1924fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com double D = fQuad[2].fX; // f 1934fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com double E = fQuad[1].fX; // e 1944fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com double F = fQuad[0].fX; // d 19507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com D += F - 2 * E; // D = d - 2*e + f 19607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com E -= F; // E = -(d - e) 19707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com F -= axisIntercept; 19807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return SkDQuad::RootsValidT(D, 2 * E, F, roots); 19907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 20007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 20107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com int verticalIntersect(double axisIntercept, double top, double bottom, bool flipped) { 202fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com addExactVerticalEndPoints(top, bottom, axisIntercept); 203570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com if (fAllowNear) { 204570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com addNearVerticalEndPoints(top, bottom, axisIntercept); 205570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com } 20607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double rootVals[2]; 20707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com int roots = verticalIntersect(axisIntercept, rootVals); 20807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com for (int index = 0; index < roots; ++index) { 20907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double quadT = rootVals[index]; 2104fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com SkDPoint pt = fQuad.ptAtT(quadT); 21107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double lineT = (pt.fY - top) / (bottom - top); 2124fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com if (pinTs(&quadT, &lineT, &pt, kPointInitialized)) { 2134fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com fIntersections->insert(quadT, lineT, pt); 21407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 21507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 21607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com if (flipped) { 2174fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com fIntersections->flip(); 21807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 2194fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com return fIntersections->used(); 22007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 22107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 22207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comprotected: 22307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com // add endpoints first to get zero and one t values exactly 224fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com void addExactEndPoints() { 22507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com for (int qIndex = 0; qIndex < 3; qIndex += 2) { 2264fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com double lineT = fLine.exactPoint(fQuad[qIndex]); 227fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com if (lineT < 0) { 22807e97fccd2d85076cd22ef411b0773ab92a18abecaryclark@google.com continue; 22907e97fccd2d85076cd22ef411b0773ab92a18abecaryclark@google.com } 230fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com double quadT = (double) (qIndex >> 1); 2314fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com fIntersections->insert(quadT, lineT, fQuad[qIndex]); 232fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com } 233fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com } 234fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com 235fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com void addNearEndPoints() { 236fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com for (int qIndex = 0; qIndex < 3; qIndex += 2) { 237fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com double quadT = (double) (qIndex >> 1); 2384fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com if (fIntersections->hasT(quadT)) { 23907e97fccd2d85076cd22ef411b0773ab92a18abecaryclark@google.com continue; 24007e97fccd2d85076cd22ef411b0773ab92a18abecaryclark@google.com } 241dac1d17027dcaa5596885a9f333979418b35001ccaryclark double lineT = fLine.nearPoint(fQuad[qIndex], NULL); 242fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com if (lineT < 0) { 24307e97fccd2d85076cd22ef411b0773ab92a18abecaryclark@google.com continue; 24407e97fccd2d85076cd22ef411b0773ab92a18abecaryclark@google.com } 2454fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com fIntersections->insert(quadT, lineT, fQuad[qIndex]); 246fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com } 247fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com // FIXME: see if line end is nearly on quad 248fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com } 249fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com 250fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com void addExactHorizontalEndPoints(double left, double right, double y) { 251fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com for (int qIndex = 0; qIndex < 3; qIndex += 2) { 2524fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com double lineT = SkDLine::ExactPointH(fQuad[qIndex], left, right, y); 253fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com if (lineT < 0) { 254fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com continue; 25507e97fccd2d85076cd22ef411b0773ab92a18abecaryclark@google.com } 256fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com double quadT = (double) (qIndex >> 1); 2574fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com fIntersections->insert(quadT, lineT, fQuad[qIndex]); 25807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 25907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 26007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 261fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com void addNearHorizontalEndPoints(double left, double right, double y) { 26207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com for (int qIndex = 0; qIndex < 3; qIndex += 2) { 263fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com double quadT = (double) (qIndex >> 1); 2644fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com if (fIntersections->hasT(quadT)) { 26507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com continue; 26607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 2674fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com double lineT = SkDLine::NearPointH(fQuad[qIndex], left, right, y); 268fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com if (lineT < 0) { 269fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com continue; 27007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 2714fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com fIntersections->insert(quadT, lineT, fQuad[qIndex]); 27207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 273fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com // FIXME: see if line end is nearly on quad 27407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 27507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 276fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com void addExactVerticalEndPoints(double top, double bottom, double x) { 27707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com for (int qIndex = 0; qIndex < 3; qIndex += 2) { 2784fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com double lineT = SkDLine::ExactPointV(fQuad[qIndex], top, bottom, x); 279fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com if (lineT < 0) { 28007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com continue; 28107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 282fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com double quadT = (double) (qIndex >> 1); 2834fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com fIntersections->insert(quadT, lineT, fQuad[qIndex]); 284fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com } 285fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com } 286fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com 287fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com void addNearVerticalEndPoints(double top, double bottom, double x) { 288fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com for (int qIndex = 0; qIndex < 3; qIndex += 2) { 289fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com double quadT = (double) (qIndex >> 1); 2904fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com if (fIntersections->hasT(quadT)) { 291fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com continue; 292fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com } 2934fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com double lineT = SkDLine::NearPointV(fQuad[qIndex], top, bottom, x); 294fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com if (lineT < 0) { 295fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com continue; 29607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 2974fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com fIntersections->insert(quadT, lineT, fQuad[qIndex]); 29807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 299fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com // FIXME: see if line end is nearly on quad 30007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 30107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 30207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double findLineT(double t) { 3034fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com SkDPoint xy = fQuad.ptAtT(t); 3044fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com double dx = fLine[1].fX - fLine[0].fX; 3054fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com double dy = fLine[1].fY - fLine[0].fY; 30628d219c5682af6dfacea2460b5ba2f9e98702de6caryclark@google.com if (fabs(dx) > fabs(dy)) { 30728d219c5682af6dfacea2460b5ba2f9e98702de6caryclark@google.com return (xy.fX - fLine[0].fX) / dx; 30807e97fccd2d85076cd22ef411b0773ab92a18abecaryclark@google.com } 30928d219c5682af6dfacea2460b5ba2f9e98702de6caryclark@google.com return (xy.fY - fLine[0].fY) / dy; 31007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 31107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 3124fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com bool pinTs(double* quadT, double* lineT, SkDPoint* pt, PinTPoint ptSet) { 3134431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org if (!approximately_one_or_less_double(*lineT)) { 31407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return false; 31507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 3164431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org if (!approximately_zero_or_more_double(*lineT)) { 31707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return false; 31807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 3194fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com double qT = *quadT = SkPinT(*quadT); 3204fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com double lT = *lineT = SkPinT(*lineT); 3214fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com if (lT == 0 || lT == 1 || (ptSet == kPointUninitialized && qT != 0 && qT != 1)) { 3224fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com *pt = fLine.ptAtT(lT); 3234fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com } else if (ptSet == kPointUninitialized) { 3244fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com *pt = fQuad.ptAtT(qT); 3254fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com } 326570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com SkPoint gridPt = pt->asSkPoint(); 327dac1d17027dcaa5596885a9f333979418b35001ccaryclark if (SkDPoint::ApproximatelyEqual(gridPt, fLine[0].asSkPoint())) { 3284431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org *pt = fLine[0]; 329570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com *lineT = 0; 330dac1d17027dcaa5596885a9f333979418b35001ccaryclark } else if (SkDPoint::ApproximatelyEqual(gridPt, fLine[1].asSkPoint())) { 3314431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org *pt = fLine[1]; 332570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com *lineT = 1; 333570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com } 3348cb1daaa1e4343eb60a7c4f21c12e33de30dad64commit-bot@chromium.org if (fIntersections->used() > 0 && approximately_equal((*fIntersections)[1][0], *lineT)) { 3358cb1daaa1e4343eb60a7c4f21c12e33de30dad64commit-bot@chromium.org return false; 3368cb1daaa1e4343eb60a7c4f21c12e33de30dad64commit-bot@chromium.org } 337570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com if (gridPt == fQuad[0].asSkPoint()) { 3384431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org *pt = fQuad[0]; 339570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com *quadT = 0; 340570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com } else if (gridPt == fQuad[2].asSkPoint()) { 3414431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org *pt = fQuad[2]; 342570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com *quadT = 1; 343570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com } 34407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return true; 34507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 34607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 34707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comprivate: 3484fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com const SkDQuad& fQuad; 3494fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com const SkDLine& fLine; 3504fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com SkIntersections* fIntersections; 351fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com bool fAllowNear; 35207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com}; 35307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 35407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comint SkIntersections::horizontal(const SkDQuad& quad, double left, double right, double y, 35507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com bool flipped) { 3564fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com SkDLine line = {{{ left, y }, { right, y }}}; 3574fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com LineQuadraticIntersections q(quad, line, this); 35807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return q.horizontalIntersect(y, left, right, flipped); 35907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 36007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 36107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comint SkIntersections::vertical(const SkDQuad& quad, double top, double bottom, double x, 36207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com bool flipped) { 3634fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com SkDLine line = {{{ x, top }, { x, bottom }}}; 3644fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com LineQuadraticIntersections q(quad, line, this); 36507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return q.verticalIntersect(x, top, bottom, flipped); 36607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 36707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 36807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comint SkIntersections::intersect(const SkDQuad& quad, const SkDLine& line) { 36907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com LineQuadraticIntersections q(quad, line, this); 370fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com q.allowNear(fAllowNear); 37107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return q.intersect(); 37207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 37307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 37407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comint SkIntersections::intersectRay(const SkDQuad& quad, const SkDLine& line) { 37507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com LineQuadraticIntersections q(quad, line, this); 376a5e55925ea03e76885804bda77408a1d6f04c335caryclark@google.com fUsed = q.intersectRay(fT[0]); 377a5e55925ea03e76885804bda77408a1d6f04c335caryclark@google.com for (int index = 0; index < fUsed; ++index) { 3784fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com fPt[index] = quad.ptAtT(fT[0][index]); 379a5e55925ea03e76885804bda77408a1d6f04c335caryclark@google.com } 380a5e55925ea03e76885804bda77408a1d6f04c335caryclark@google.com return fUsed; 38107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 382