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| 1 /* | |
| 2 * Copyright 2012 Google Inc. | |
| 3 * | |
| 4 * Use of this source code is governed by a BSD-style license that can be | |
| 5 * found in the LICENSE file. | |
| 6 */ | |
| 7 #include "CurveIntersection.h" | |
| 8 | |
| 9 /* This rejects coincidence with two muls, two adds, and one cmp. | |
| 10 Coincident candidates will take another four muls and two adds, but may still | |
| 11 fail if they don't overlap. (The overlap test isn't performed here.) | |
| 12 */ | |
| 13 bool implicit_matches(const _Line& one, const _Line& two) { | |
| 14 _Point oneD, twoD; | |
| 15 tangent(one, oneD); | |
| 16 tangent(two, twoD); | |
| 17 /* See if the slopes match, i.e. | |
| 18 dx1 / dy1 == dx2 / dy2 | |
| 19 (dy1 * dy2) * dx1 / dy1 == (dy1 * dy2) * dx2 / dy2 | |
| 20 dy2 * dx1 == dy1 * dx2 | |
| 21 */ | |
| 22 if (!AlmostEqualUlps(oneD.x * twoD.y, twoD.x * oneD.y)) { | |
| 23 return false; | |
| 24 } | |
| 25 /* See if the axis intercepts match, i.e. | |
| 26 y0 - x0 * dy / dx == y1 - x1 * dy / dx | |
| 27 dx * (y0 - x0 * dy / dx) == dx * (y1 - x1 * dy / dx) | |
| 28 dx * y0 - x0 * dy == dx * y1 - x1 * dy | |
| 29 */ | |
| 30 if (!AlmostEqualUlps(oneD.x * one[0].y - oneD.y * one[0].x, | |
| 31 oneD.x * two[0].y - oneD.y * two[0].x)) { | |
| 32 return false; | |
| 33 } | |
| 34 return true; | |
| 35 } | |
| 36 | |
| 37 bool implicit_matches_ulps(const _Line& one, const _Line& two, int ulps) { | |
| 38 _Point oneD, twoD; | |
| 39 tangent(one, oneD); | |
| 40 tangent(two, twoD); | |
| 41 /* See if the slopes match, i.e. | |
| 42 dx1 / dy1 == dx2 / dy2 | |
| 43 (dy1 * dy2) * dx1 / dy1 == (dy1 * dy2) * dx2 / dy2 | |
| 44 dy2 * dx1 == dy1 * dx2 | |
| 45 */ | |
| 46 int diff = UlpsDiff((float) (oneD.x * twoD.y), (float) (twoD.x * oneD.y)); | |
| 47 if (diff < 0 || diff > ulps) { | |
| 48 return false; | |
| 49 } | |
| 50 /* See if the axis intercepts match, i.e. | |
| 51 y0 - x0 * dy / dx == y1 - x1 * dy / dx | |
| 52 dx * (y0 - x0 * dy / dx) == dx * (y1 - x1 * dy / dx) | |
| 53 dx * y0 - x0 * dy == dx * y1 - x1 * dy | |
| 54 */ | |
| 55 diff = UlpsDiff((float) (oneD.x * one[0].y - oneD.y * one[0].x), | |
| 56 (float) (oneD.x * two[0].y - oneD.y * two[0].x)); | |
| 57 return diff >= 0 && diff <= ulps; | |
| 58 } | |
| 59 | |
| 60 void tangent(const _Line& line, _Point& result) { | |
| 61 result.x = line[0].x - line[1].x; | |
| 62 result.y = line[0].y - line[1].y; | |
| 63 } | |
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