| 1 | /* | 
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| 2 | * Copyright 2015 Google Inc. | 
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| 3 | * | 
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| 4 | * Use of this source code is governed by a BSD-style license that can be | 
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| 5 | * found in the LICENSE file. | 
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| 6 | */ | 
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| 7 |  | 
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| 8 | /* | 
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| 9 | http://stackoverflow.com/questions/2009160/how-do-i-convert-the-2-control-points-of-a-cubic-curve-to-the-single-control-poi | 
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| 10 | */ | 
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| 11 |  | 
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| 12 | /* | 
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| 13 | Let's call the control points of the cubic Q0..Q3 and the control points of the quadratic P0..P2. | 
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| 14 | Then for degree elevation, the equations are: | 
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| 15 |  | 
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| 16 | Q0 = P0 | 
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| 17 | Q1 = 1/3 P0 + 2/3 P1 | 
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| 18 | Q2 = 2/3 P1 + 1/3 P2 | 
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| 19 | Q3 = P2 | 
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| 20 | In your case you have Q0..Q3 and you're solving for P0..P2. There are two ways to compute P1 from | 
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| 21 | the equations above: | 
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| 22 |  | 
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| 23 | P1 = 3/2 Q1 - 1/2 Q0 | 
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| 24 | P1 = 3/2 Q2 - 1/2 Q3 | 
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| 25 | If this is a degree-elevated cubic, then both equations will give the same answer for P1. Since | 
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| 26 | it's likely not, your best bet is to average them. So, | 
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| 27 |  | 
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| 28 | P1 = -1/4 Q0 + 3/4 Q1 + 3/4 Q2 - 1/4 Q3 | 
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| 29 | */ | 
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| 30 |  | 
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| 31 | #include "src/pathops/SkPathOpsCubic.h" | 
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| 32 | #include "src/pathops/SkPathOpsQuad.h" | 
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| 33 |  | 
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| 34 | // used for testing only | 
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| 35 | SkDQuad SkDCubic::toQuad() const { | 
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| 36 | SkDQuad quad; | 
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| 37 | quad[0] = fPts[0]; | 
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| 38 | const SkDPoint fromC1 = {(3 * fPts[1].fX - fPts[0].fX) / 2, (3 * fPts[1].fY - fPts[0].fY) / 2}; | 
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| 39 | const SkDPoint fromC2 = {(3 * fPts[2].fX - fPts[3].fX) / 2, (3 * fPts[2].fY - fPts[3].fY) / 2}; | 
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| 40 | quad[1].fX = (fromC1.fX + fromC2.fX) / 2; | 
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| 41 | quad[1].fY = (fromC1.fY + fromC2.fY) / 2; | 
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| 42 | quad[2] = fPts[3]; | 
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| 43 | return quad; | 
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| 44 | } | 
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| 45 |  | 
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