SkDQuadLineIntersection.cpp revision a5e55925ea03e76885804bda77408a1d6f04c335
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.com 9007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comclass LineQuadraticIntersections { 9107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.compublic: 9207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com LineQuadraticIntersections(const SkDQuad& q, const SkDLine& l, SkIntersections* i) 9307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com : quad(q) 9407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com , line(l) 9507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com , intersections(i) { 9607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 9707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 9807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com int intersectRay(double roots[2]) { 9907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com /* 10007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com solve by rotating line+quad so line is horizontal, then finding the roots 10107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com set up matrix to rotate quad to x-axis 10207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com |cos(a) -sin(a)| 10307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com |sin(a) cos(a)| 10407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com note that cos(a) = A(djacent) / Hypoteneuse 10507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com sin(a) = O(pposite) / Hypoteneuse 10607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com since we are computing Ts, we can ignore hypoteneuse, the scale factor: 10707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com | A -O | 10807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com | O A | 10907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com A = line[1].fX - line[0].fX (adjacent side of the right triangle) 11007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com O = line[1].fY - line[0].fY (opposite side of the right triangle) 11107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com for each of the three points (e.g. n = 0 to 2) 11207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com quad[n].fY' = (quad[n].fY - line[0].fY) * A - (quad[n].fX - line[0].fX) * O 11307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com */ 11407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double adj = line[1].fX - line[0].fX; 11507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double opp = line[1].fY - line[0].fY; 11607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double r[3]; 11707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com for (int n = 0; n < 3; ++n) { 11807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com r[n] = (quad[n].fY - line[0].fY) * adj - (quad[n].fX - line[0].fX) * opp; 11907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 12007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double A = r[2]; 12107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double B = r[1]; 12207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double C = r[0]; 12307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com A += C - 2 * B; // A = a - 2*b + c 12407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com B -= C; // B = -(b - c) 12507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return SkDQuad::RootsValidT(A, 2 * B, C, roots); 12607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 12707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 12807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com int intersect() { 12907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com addEndPoints(); 13007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double rootVals[2]; 13107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com int roots = intersectRay(rootVals); 13207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com for (int index = 0; index < roots; ++index) { 13307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double quadT = rootVals[index]; 13407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double lineT = findLineT(quadT); 13507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com if (PinTs(&quadT, &lineT)) { 13607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com SkDPoint pt = line.xyAtT(lineT); 13707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com intersections->insert(quadT, lineT, pt); 13807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 13907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 14007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return intersections->used(); 14107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 14207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 14307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com int horizontalIntersect(double axisIntercept, double roots[2]) { 14407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double D = quad[2].fY; // f 14507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double E = quad[1].fY; // e 14607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double F = quad[0].fY; // d 14707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com D += F - 2 * E; // D = d - 2*e + f 14807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com E -= F; // E = -(d - e) 14907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com F -= axisIntercept; 15007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return SkDQuad::RootsValidT(D, 2 * E, F, roots); 15107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 15207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 15307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com int horizontalIntersect(double axisIntercept, double left, double right, bool flipped) { 15407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com addHorizontalEndPoints(left, right, axisIntercept); 15507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double rootVals[2]; 15607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com int roots = horizontalIntersect(axisIntercept, rootVals); 15707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com for (int index = 0; index < roots; ++index) { 15807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double quadT = rootVals[index]; 15907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com SkDPoint pt = quad.xyAtT(quadT); 16007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double lineT = (pt.fX - left) / (right - left); 16107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com if (PinTs(&quadT, &lineT)) { 16207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com intersections->insert(quadT, lineT, pt); 16307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 16407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 16507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com if (flipped) { 16607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com intersections->flip(); 16707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 16807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return intersections->used(); 16907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 17007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 17107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com int verticalIntersect(double axisIntercept, double roots[2]) { 17207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double D = quad[2].fX; // f 17307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double E = quad[1].fX; // e 17407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double F = quad[0].fX; // d 17507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com D += F - 2 * E; // D = d - 2*e + f 17607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com E -= F; // E = -(d - e) 17707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com F -= axisIntercept; 17807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return SkDQuad::RootsValidT(D, 2 * E, F, roots); 17907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 18007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 18107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com int verticalIntersect(double axisIntercept, double top, double bottom, bool flipped) { 18207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com addVerticalEndPoints(top, bottom, axisIntercept); 18307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double rootVals[2]; 18407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com int roots = verticalIntersect(axisIntercept, rootVals); 18507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com for (int index = 0; index < roots; ++index) { 18607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double quadT = rootVals[index]; 18707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com SkDPoint pt = quad.xyAtT(quadT); 18807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double lineT = (pt.fY - top) / (bottom - top); 18907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com if (PinTs(&quadT, &lineT)) { 19007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com intersections->insert(quadT, lineT, pt); 19107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 19207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 19307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com if (flipped) { 19407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com intersections->flip(); 19507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 19607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return intersections->used(); 19707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 19807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 19907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comprotected: 20007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com // add endpoints first to get zero and one t values exactly 20107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com void addEndPoints() { 20207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com for (int qIndex = 0; qIndex < 3; qIndex += 2) { 20307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com for (int lIndex = 0; lIndex < 2; lIndex++) { 20407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com if (quad[qIndex] == line[lIndex]) { 20507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com intersections->insert(qIndex >> 1, lIndex, line[lIndex]); 20607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 20707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 20807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 20907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 21007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 21107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com void addHorizontalEndPoints(double left, double right, double y) { 21207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com for (int qIndex = 0; qIndex < 3; qIndex += 2) { 21307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com if (quad[qIndex].fY != y) { 21407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com continue; 21507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 21607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com if (quad[qIndex].fX == left) { 21707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com intersections->insert(qIndex >> 1, 0, quad[qIndex]); 21807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 21907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com if (quad[qIndex].fX == right) { 22007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com intersections->insert(qIndex >> 1, 1, quad[qIndex]); 22107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 22207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 22307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 22407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 22507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com void addVerticalEndPoints(double top, double bottom, double x) { 22607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com for (int qIndex = 0; qIndex < 3; qIndex += 2) { 22707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com if (quad[qIndex].fX != x) { 22807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com continue; 22907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 23007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com if (quad[qIndex].fY == top) { 23107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com intersections->insert(qIndex >> 1, 0, quad[qIndex]); 23207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 23307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com if (quad[qIndex].fY == bottom) { 23407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com intersections->insert(qIndex >> 1, 1, quad[qIndex]); 23507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 23607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 23707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 23807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 23907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double findLineT(double t) { 24007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com SkDPoint xy = quad.xyAtT(t); 24107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double dx = line[1].fX - line[0].fX; 24207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double dy = line[1].fY - line[0].fY; 24307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com if (fabs(dx) > fabs(dy)) { 24407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return (xy.fX - line[0].fX) / dx; 24507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 24607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return (xy.fY - line[0].fY) / dy; 24707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 24807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 24907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com static bool PinTs(double* quadT, double* lineT) { 25007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com if (!approximately_one_or_less(*lineT)) { 25107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return false; 25207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 25307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com if (!approximately_zero_or_more(*lineT)) { 25407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return false; 25507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 25607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com if (precisely_less_than_zero(*quadT)) { 25707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com *quadT = 0; 25807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } else if (precisely_greater_than_one(*quadT)) { 25907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com *quadT = 1; 26007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 26107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com if (precisely_less_than_zero(*lineT)) { 26207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com *lineT = 0; 26307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } else if (precisely_greater_than_one(*lineT)) { 26407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com *lineT = 1; 26507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 26607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return true; 26707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 26807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 26907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comprivate: 27007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com const SkDQuad& quad; 27107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com const SkDLine& line; 27207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com SkIntersections* intersections; 27307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com}; 27407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 27507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// utility for pairs of coincident quads 27607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comstatic double horizontalIntersect(const SkDQuad& quad, const SkDPoint& pt) { 27707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com LineQuadraticIntersections q(quad, *(static_cast<SkDLine*>(0)), 27807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com static_cast<SkIntersections*>(0)); 27907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double rootVals[2]; 28007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com int roots = q.horizontalIntersect(pt.fY, rootVals); 28107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com for (int index = 0; index < roots; ++index) { 28207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double t = rootVals[index]; 28307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com SkDPoint qPt = quad.xyAtT(t); 28407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com if (AlmostEqualUlps(qPt.fX, pt.fX)) { 28507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return t; 28607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 28707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 28807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return -1; 28907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 29007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 29107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comstatic double verticalIntersect(const SkDQuad& quad, const SkDPoint& pt) { 29207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com LineQuadraticIntersections q(quad, *(static_cast<SkDLine*>(0)), 29307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com static_cast<SkIntersections*>(0)); 29407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double rootVals[2]; 29507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com int roots = q.verticalIntersect(pt.fX, rootVals); 29607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com for (int index = 0; index < roots; ++index) { 29707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double t = rootVals[index]; 29807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com SkDPoint qPt = quad.xyAtT(t); 29907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com if (AlmostEqualUlps(qPt.fY, pt.fY)) { 30007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return t; 30107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 30207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 30307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return -1; 30407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 30507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 30607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comdouble SkIntersections::Axial(const SkDQuad& q1, const SkDPoint& p, bool vertical) { 30707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com if (vertical) { 30807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return verticalIntersect(q1, p); 30907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 31007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return horizontalIntersect(q1, p); 31107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 31207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 31307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comint SkIntersections::horizontal(const SkDQuad& quad, double left, double right, double y, 31407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com bool flipped) { 31507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com LineQuadraticIntersections q(quad, *(static_cast<SkDLine*>(0)), this); 31607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return q.horizontalIntersect(y, left, right, flipped); 31707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 31807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 31907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comint SkIntersections::vertical(const SkDQuad& quad, double top, double bottom, double x, 32007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com bool flipped) { 32107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com LineQuadraticIntersections q(quad, *(static_cast<SkDLine*>(0)), this); 32207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return q.verticalIntersect(x, top, bottom, flipped); 32307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 32407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 32507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comint SkIntersections::intersect(const SkDQuad& quad, const SkDLine& line) { 32607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com LineQuadraticIntersections q(quad, line, this); 32707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return q.intersect(); 32807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 32907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 33007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comint SkIntersections::intersectRay(const SkDQuad& quad, const SkDLine& line) { 33107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com LineQuadraticIntersections q(quad, line, this); 332a5e55925ea03e76885804bda77408a1d6f04c335caryclark@google.com fUsed = q.intersectRay(fT[0]); 333a5e55925ea03e76885804bda77408a1d6f04c335caryclark@google.com for (int index = 0; index < fUsed; ++index) { 334a5e55925ea03e76885804bda77408a1d6f04c335caryclark@google.com fPt[index] = quad.xyAtT(fT[0][index]); 335a5e55925ea03e76885804bda77408a1d6f04c335caryclark@google.com } 336a5e55925ea03e76885804bda77408a1d6f04c335caryclark@google.com return fUsed; 33707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 338