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1 /* | 1 /* |
2 http://stackoverflow.com/questions/2009160/how-do-i-convert-the-2-control-points
-of-a-cubic-curve-to-the-single-control-poi | 2 http://stackoverflow.com/questions/2009160/how-do-i-convert-the-2-control-points
-of-a-cubic-curve-to-the-single-control-poi |
3 */ | 3 */ |
4 | 4 |
5 /* | 5 /* |
6 Let's call the control points of the cubic Q0..Q3 and the control points of the
quadratic P0..P2. | 6 Let's call the control points of the cubic Q0..Q3 and the control points of the
quadratic P0..P2. |
7 Then for degree elevation, the equations are: | 7 Then for degree elevation, the equations are: |
8 | 8 |
9 Q0 = P0 | 9 Q0 = P0 |
10 Q1 = 1/3 P0 + 2/3 P1 | 10 Q1 = 1/3 P0 + 2/3 P1 |
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42 http://www.caffeineowl.com/graphics/2d/vectorial/cubic2quad01.html | 42 http://www.caffeineowl.com/graphics/2d/vectorial/cubic2quad01.html |
43 // maybe in turn derived from http://www.cccg.ca/proceedings/2004/36.pdf | 43 // maybe in turn derived from http://www.cccg.ca/proceedings/2004/36.pdf |
44 // also stored at http://www.cis.usouthal.edu/~hain/general/Publications/Bezier/
bezier%20cccg04%20paper.pdf | 44 // also stored at http://www.cis.usouthal.edu/~hain/general/Publications/Bezier/
bezier%20cccg04%20paper.pdf |
45 | 45 |
46 */ | 46 */ |
47 | 47 |
48 #include "SkPathOpsCubic.h" | 48 #include "SkPathOpsCubic.h" |
49 #include "SkPathOpsLine.h" | 49 #include "SkPathOpsLine.h" |
50 #include "SkPathOpsQuad.h" | 50 #include "SkPathOpsQuad.h" |
51 #include "SkReduceOrder.h" | 51 #include "SkReduceOrder.h" |
52 #include "SkTDArray.h" | 52 #include "SkTArray.h" |
53 #include "SkTSort.h" | 53 #include "SkTSort.h" |
54 | 54 |
55 #define USE_CUBIC_END_POINTS 1 | 55 #define USE_CUBIC_END_POINTS 1 |
56 | 56 |
57 static double calc_t_div(const SkDCubic& cubic, double precision, double start)
{ | 57 static double calc_t_div(const SkDCubic& cubic, double precision, double start)
{ |
58 const double adjust = sqrt(3.) / 36; | 58 const double adjust = sqrt(3.) / 36; |
59 SkDCubic sub; | 59 SkDCubic sub; |
60 const SkDCubic* cPtr; | 60 const SkDCubic* cPtr; |
61 if (start == 0) { | 61 if (start == 0) { |
62 cPtr = &cubic; | 62 cPtr = &cubic; |
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81 SkDQuad quad; | 81 SkDQuad quad; |
82 quad[0] = fPts[0]; | 82 quad[0] = fPts[0]; |
83 const SkDPoint fromC1 = {(3 * fPts[1].fX - fPts[0].fX) / 2, (3 * fPts[1].fY
- fPts[0].fY) / 2}; | 83 const SkDPoint fromC1 = {(3 * fPts[1].fX - fPts[0].fX) / 2, (3 * fPts[1].fY
- fPts[0].fY) / 2}; |
84 const SkDPoint fromC2 = {(3 * fPts[2].fX - fPts[3].fX) / 2, (3 * fPts[2].fY
- fPts[3].fY) / 2}; | 84 const SkDPoint fromC2 = {(3 * fPts[2].fX - fPts[3].fX) / 2, (3 * fPts[2].fY
- fPts[3].fY) / 2}; |
85 quad[1].fX = (fromC1.fX + fromC2.fX) / 2; | 85 quad[1].fX = (fromC1.fX + fromC2.fX) / 2; |
86 quad[1].fY = (fromC1.fY + fromC2.fY) / 2; | 86 quad[1].fY = (fromC1.fY + fromC2.fY) / 2; |
87 quad[2] = fPts[3]; | 87 quad[2] = fPts[3]; |
88 return quad; | 88 return quad; |
89 } | 89 } |
90 | 90 |
91 static bool add_simple_ts(const SkDCubic& cubic, double precision, SkTDArray<dou
ble>* ts) { | 91 static bool add_simple_ts(const SkDCubic& cubic, double precision, SkTArray<doub
le, true>* ts) { |
92 double tDiv = calc_t_div(cubic, precision, 0); | 92 double tDiv = calc_t_div(cubic, precision, 0); |
93 if (tDiv >= 1) { | 93 if (tDiv >= 1) { |
94 return true; | 94 return true; |
95 } | 95 } |
96 if (tDiv >= 0.5) { | 96 if (tDiv >= 0.5) { |
97 *ts->append() = 0.5; | 97 ts->push_back(0.5); |
98 return true; | 98 return true; |
99 } | 99 } |
100 return false; | 100 return false; |
101 } | 101 } |
102 | 102 |
103 static void addTs(const SkDCubic& cubic, double precision, double start, double
end, | 103 static void addTs(const SkDCubic& cubic, double precision, double start, double
end, |
104 SkTDArray<double>* ts) { | 104 SkTArray<double, true>* ts) { |
105 double tDiv = calc_t_div(cubic, precision, 0); | 105 double tDiv = calc_t_div(cubic, precision, 0); |
106 double parts = ceil(1.0 / tDiv); | 106 double parts = ceil(1.0 / tDiv); |
107 for (double index = 0; index < parts; ++index) { | 107 for (double index = 0; index < parts; ++index) { |
108 double newT = start + (index / parts) * (end - start); | 108 double newT = start + (index / parts) * (end - start); |
109 if (newT > 0 && newT < 1) { | 109 if (newT > 0 && newT < 1) { |
110 *ts->append() = newT; | 110 ts->push_back(newT); |
111 } | 111 } |
112 } | 112 } |
113 } | 113 } |
114 | 114 |
115 // flavor that returns T values only, deferring computing the quads until they a
re needed | 115 // flavor that returns T values only, deferring computing the quads until they a
re needed |
116 // FIXME: when called from recursive intersect 2, this could take the original c
ubic | 116 // FIXME: when called from recursive intersect 2, this could take the original c
ubic |
117 // and do a more precise job when calling chop at and sub divide by computing th
e fractional ts. | 117 // and do a more precise job when calling chop at and sub divide by computing th
e fractional ts. |
118 // it would still take the prechopped cubic for reduce order and find cubic infl
ections | 118 // it would still take the prechopped cubic for reduce order and find cubic infl
ections |
119 void SkDCubic::toQuadraticTs(double precision, SkTDArray<double>* ts) const { | 119 void SkDCubic::toQuadraticTs(double precision, SkTArray<double, true>* ts) const
{ |
120 SkReduceOrder reducer; | 120 SkReduceOrder reducer; |
121 int order = reducer.reduce(*this, SkReduceOrder::kAllow_Quadratics, SkReduce
Order::kFill_Style); | 121 int order = reducer.reduce(*this, SkReduceOrder::kAllow_Quadratics, SkReduce
Order::kFill_Style); |
122 if (order < 3) { | 122 if (order < 3) { |
123 return; | 123 return; |
124 } | 124 } |
125 double inflectT[5]; | 125 double inflectT[5]; |
126 int inflections = findInflections(inflectT); | 126 int inflections = findInflections(inflectT); |
127 SkASSERT(inflections <= 2); | 127 SkASSERT(inflections <= 2); |
128 if (!endsAreExtremaInXOrY()) { | 128 if (!endsAreExtremaInXOrY()) { |
129 inflections += findMaxCurvature(&inflectT[inflections]); | 129 inflections += findMaxCurvature(&inflectT[inflections]); |
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181 for (int idx = 0; idx < last; ++idx) { | 181 for (int idx = 0; idx < last; ++idx) { |
182 part = subDivide(inflectT[idx], inflectT[idx + 1]); | 182 part = subDivide(inflectT[idx], inflectT[idx + 1]); |
183 addTs(part, precision, inflectT[idx], inflectT[idx + 1], ts); | 183 addTs(part, precision, inflectT[idx], inflectT[idx + 1], ts); |
184 } | 184 } |
185 part = subDivide(inflectT[last], 1); | 185 part = subDivide(inflectT[last], 1); |
186 addTs(part, precision, inflectT[last], 1, ts); | 186 addTs(part, precision, inflectT[last], 1, ts); |
187 return; | 187 return; |
188 } | 188 } |
189 addTs(*this, precision, 0, 1, ts); | 189 addTs(*this, precision, 0, 1, ts); |
190 } | 190 } |
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