| /* |
| * Copyright 2012 Google Inc. |
| * |
| * Use of this source code is governed by a BSD-style license that can be |
| * found in the LICENSE file. |
| */ |
| #include "src/pathops/SkPathOpsCubic.h" |
| |
| static bool rotate(const SkDCubic& cubic, int zero, int index, SkDCubic& rotPath) { |
| double dy = cubic[index].fY - cubic[zero].fY; |
| double dx = cubic[index].fX - cubic[zero].fX; |
| if (approximately_zero(dy)) { |
| if (approximately_zero(dx)) { |
| return false; |
| } |
| rotPath = cubic; |
| if (dy) { |
| rotPath[index].fY = cubic[zero].fY; |
| int mask = other_two(index, zero); |
| int side1 = index ^ mask; |
| int side2 = zero ^ mask; |
| if (approximately_equal(cubic[side1].fY, cubic[zero].fY)) { |
| rotPath[side1].fY = cubic[zero].fY; |
| } |
| if (approximately_equal(cubic[side2].fY, cubic[zero].fY)) { |
| rotPath[side2].fY = cubic[zero].fY; |
| } |
| } |
| return true; |
| } |
| for (int index = 0; index < 4; ++index) { |
| rotPath[index].fX = cubic[index].fX * dx + cubic[index].fY * dy; |
| rotPath[index].fY = cubic[index].fY * dx - cubic[index].fX * dy; |
| } |
| return true; |
| } |
| |
| |
| // Returns 0 if negative, 1 if zero, 2 if positive |
| static int side(double x) { |
| return (x > 0) + (x >= 0); |
| } |
| |
| /* Given a cubic, find the convex hull described by the end and control points. |
| The hull may have 3 or 4 points. Cubics that degenerate into a point or line |
| are not considered. |
| |
| The hull is computed by assuming that three points, if unique and non-linear, |
| form a triangle. The fourth point may replace one of the first three, may be |
| discarded if in the triangle or on an edge, or may be inserted between any of |
| the three to form a convex quadralateral. |
| |
| The indices returned in order describe the convex hull. |
| */ |
| int SkDCubic::convexHull(char order[4]) const { |
| size_t index; |
| // find top point |
| size_t yMin = 0; |
| for (index = 1; index < 4; ++index) { |
| if (fPts[yMin].fY > fPts[index].fY || (fPts[yMin].fY == fPts[index].fY |
| && fPts[yMin].fX > fPts[index].fX)) { |
| yMin = index; |
| } |
| } |
| order[0] = yMin; |
| int midX = -1; |
| int backupYMin = -1; |
| for (int pass = 0; pass < 2; ++pass) { |
| for (index = 0; index < 4; ++index) { |
| if (index == yMin) { |
| continue; |
| } |
| // rotate line from (yMin, index) to axis |
| // see if remaining two points are both above or below |
| // use this to find mid |
| int mask = other_two(yMin, index); |
| int side1 = yMin ^ mask; |
| int side2 = index ^ mask; |
| SkDCubic rotPath; |
| if (!rotate(*this, yMin, index, rotPath)) { // ! if cbc[yMin]==cbc[idx] |
| order[1] = side1; |
| order[2] = side2; |
| return 3; |
| } |
| int sides = side(rotPath[side1].fY - rotPath[yMin].fY); |
| sides ^= side(rotPath[side2].fY - rotPath[yMin].fY); |
| if (sides == 2) { // '2' means one remaining point <0, one >0 |
| if (midX >= 0) { |
| // one of the control points is equal to an end point |
| order[0] = 0; |
| order[1] = 3; |
| if (fPts[1] == fPts[0] || fPts[1] == fPts[3]) { |
| order[2] = 2; |
| return 3; |
| } |
| if (fPts[2] == fPts[0] || fPts[2] == fPts[3]) { |
| order[2] = 1; |
| return 3; |
| } |
| // one of the control points may be very nearly but not exactly equal -- |
| double dist1_0 = fPts[1].distanceSquared(fPts[0]); |
| double dist1_3 = fPts[1].distanceSquared(fPts[3]); |
| double dist2_0 = fPts[2].distanceSquared(fPts[0]); |
| double dist2_3 = fPts[2].distanceSquared(fPts[3]); |
| double smallest1distSq = SkTMin(dist1_0, dist1_3); |
| double smallest2distSq = SkTMin(dist2_0, dist2_3); |
| if (approximately_zero(SkTMin(smallest1distSq, smallest2distSq))) { |
| order[2] = smallest1distSq < smallest2distSq ? 2 : 1; |
| return 3; |
| } |
| } |
| midX = index; |
| } else if (sides == 0) { // '0' means both to one side or the other |
| backupYMin = index; |
| } |
| } |
| if (midX >= 0) { |
| break; |
| } |
| if (backupYMin < 0) { |
| break; |
| } |
| yMin = backupYMin; |
| backupYMin = -1; |
| } |
| if (midX < 0) { |
| midX = yMin ^ 3; // choose any other point |
| } |
| int mask = other_two(yMin, midX); |
| int least = yMin ^ mask; |
| int most = midX ^ mask; |
| order[0] = yMin; |
| order[1] = least; |
| |
| // see if mid value is on same side of line (least, most) as yMin |
| SkDCubic midPath; |
| if (!rotate(*this, least, most, midPath)) { // ! if cbc[least]==cbc[most] |
| order[2] = midX; |
| return 3; |
| } |
| int midSides = side(midPath[yMin].fY - midPath[least].fY); |
| midSides ^= side(midPath[midX].fY - midPath[least].fY); |
| if (midSides != 2) { // if mid point is not between |
| order[2] = most; |
| return 3; // result is a triangle |
| } |
| order[2] = midX; |
| order[3] = most; |
| return 4; // result is a quadralateral |
| } |