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<h1>qwt_spline.cpp</h1><div class="fragment"><pre class="fragment"><a name="l00001"></a>00001 <span class="comment">/* -*- mode: C++ ; c-file-style: "stroustrup" -*- *****************************</span>
21
<a name="l00002"></a>00002 <span class="comment"> * Qwt Widget Library</span>
22
<a name="l00003"></a>00003 <span class="comment"> * Copyright (C) 1997 Josef Wilgen</span>
23
<a name="l00004"></a>00004 <span class="comment"> * Copyright (C) 2002 Uwe Rathmann</span>
24
<a name="l00005"></a>00005 <span class="comment"> * </span>
25
<a name="l00006"></a>00006 <span class="comment"> * This library is free software; you can redistribute it and/or</span>
26
<a name="l00007"></a>00007 <span class="comment"> * modify it under the terms of the Qwt License, Version 1.0</span>
27
<a name="l00008"></a>00008 <span class="comment"> *****************************************************************************/</span>
28
<a name="l00009"></a>00009
29
<a name="l00010"></a>00010 <span class="preprocessor">#include "qwt_spline.h"</span>
30
<a name="l00011"></a>00011 <span class="preprocessor">#include "qwt_math.h"</span>
31
<a name="l00012"></a>00012 <span class="preprocessor">#include "qwt_array.h"</span>
32
<a name="l00013"></a>00013
33
<a name="l00014"></a>00014 <span class="keyword">class </span>QwtSpline::PrivateData
34
<a name="l00015"></a>00015 {
35
<a name="l00016"></a>00016 <span class="keyword">public</span>:
36
<a name="l00017"></a>00017 PrivateData():
37
<a name="l00018"></a>00018 <a class="code" href="class_qwt_spline.html#1ba958ef9d8ea93db822fde1a1176f51">splineType</a>(<a class="code" href="class_qwt_spline.html">QwtSpline</a>::Natural)
38
<a name="l00019"></a>00019 {
39
<a name="l00020"></a>00020 }
40
<a name="l00021"></a>00021
41
<a name="l00022"></a>00022 <a class="code" href="class_qwt_spline.html#2bd2bda128f82acd596348eb8d64231c">QwtSpline::SplineType</a> <a class="code" href="class_qwt_spline.html#1ba958ef9d8ea93db822fde1a1176f51">splineType</a>;
42
<a name="l00023"></a>00023
43
<a name="l00024"></a>00024 <span class="comment">// coefficient vectors</span>
44
<a name="l00025"></a>00025 QwtArray<double> a;
45
<a name="l00026"></a>00026 QwtArray<double> b;
46
<a name="l00027"></a>00027 QwtArray<double> c;
47
<a name="l00028"></a>00028
48
<a name="l00029"></a>00029 <span class="comment">// control points</span>
49
<a name="l00030"></a>00030 <span class="preprocessor">#if QT_VERSION < 0x040000</span>
50
<a name="l00031"></a>00031 <span class="preprocessor"></span> QwtArray<QwtDoublePoint> <a class="code" href="class_qwt_spline.html#5137512588444236e2a2ab1cab207f41">points</a>;
51
<a name="l00032"></a>00032 <span class="preprocessor">#else</span>
52
<a name="l00033"></a>00033 <span class="preprocessor"></span> QPolygonF <a class="code" href="class_qwt_spline.html#5137512588444236e2a2ab1cab207f41">points</a>;
53
<a name="l00034"></a>00034 <span class="preprocessor">#endif</span>
54
<a name="l00035"></a>00035 <span class="preprocessor"></span>};
55
<a name="l00036"></a>00036
56
<a name="l00037"></a>00037 <span class="preprocessor">#if QT_VERSION < 0x040000</span>
57
<a name="l00038"></a>00038 <span class="preprocessor"></span><span class="keyword">static</span> <span class="keywordtype">int</span> lookup(<span class="keywordtype">double</span> x, <span class="keyword">const</span> QwtArray<QwtDoublePoint> &values)
58
<a name="l00039"></a>00039 <span class="preprocessor">#else</span>
59
<a name="l00040"></a>00040 <span class="preprocessor"></span><span class="keyword">static</span> <span class="keywordtype">int</span> lookup(<span class="keywordtype">double</span> x, <span class="keyword">const</span> QPolygonF &values)
60
<a name="l00041"></a>00041 <span class="preprocessor">#endif</span>
61
<a name="l00042"></a>00042 <span class="preprocessor"></span>{
62
<a name="l00043"></a>00043 <span class="preprocessor">#if 0</span>
63
<a name="l00044"></a>00044 <span class="preprocessor"></span><span class="comment">//qLowerBiund/qHigherBound ???</span>
64
<a name="l00045"></a>00045 <span class="preprocessor">#endif</span>
65
<a name="l00046"></a>00046 <span class="preprocessor"></span> <span class="keywordtype">int</span> i1;
66
<a name="l00047"></a>00047 <span class="keyword">const</span> <span class="keywordtype">int</span> size = (int)values.size();
67
<a name="l00048"></a>00048
68
<a name="l00049"></a>00049 <span class="keywordflow">if</span> (x <= values[0].x())
69
<a name="l00050"></a>00050 i1 = 0;
70
<a name="l00051"></a>00051 <span class="keywordflow">else</span> <span class="keywordflow">if</span> (x >= values[size - 2].x())
71
<a name="l00052"></a>00052 i1 = size - 2;
72
<a name="l00053"></a>00053 <span class="keywordflow">else</span>
73
<a name="l00054"></a>00054 {
74
<a name="l00055"></a>00055 i1 = 0;
75
<a name="l00056"></a>00056 <span class="keywordtype">int</span> i2 = size - 2;
76
<a name="l00057"></a>00057 <span class="keywordtype">int</span> i3 = 0;
77
<a name="l00058"></a>00058
78
<a name="l00059"></a>00059 <span class="keywordflow">while</span> ( i2 - i1 > 1 )
79
<a name="l00060"></a>00060 {
80
<a name="l00061"></a>00061 i3 = i1 + ((i2 - i1) >> 1);
81
<a name="l00062"></a>00062
82
<a name="l00063"></a>00063 <span class="keywordflow">if</span> (values[i3].x() > x)
83
<a name="l00064"></a>00064 i2 = i3;
84
<a name="l00065"></a>00065 <span class="keywordflow">else</span>
85
<a name="l00066"></a>00066 i1 = i3;
86
<a name="l00067"></a>00067 }
87
<a name="l00068"></a>00068 }
88
<a name="l00069"></a>00069 <span class="keywordflow">return</span> i1;
89
<a name="l00070"></a>00070 }
90
<a name="l00071"></a>00071
91
<a name="l00073"></a><a class="code" href="class_qwt_spline.html#5d1e0ba35c637a88c66d9e4cbaf36e93">00073</a> <a class="code" href="class_qwt_spline.html#5d1e0ba35c637a88c66d9e4cbaf36e93">QwtSpline::QwtSpline</a>()
92
<a name="l00074"></a>00074 {
93
<a name="l00075"></a>00075 <a class="code" href="class_qwt_spline.html#784545391f14c014684f391c6d92fd27">d_data</a> = <span class="keyword">new</span> PrivateData;
94
<a name="l00076"></a>00076 }
95
<a name="l00077"></a>00077
96
<a name="l00078"></a><a class="code" href="class_qwt_spline.html#2e42391f76d0b3091bf7754239f3ff0d">00078</a> <a class="code" href="class_qwt_spline.html#5d1e0ba35c637a88c66d9e4cbaf36e93">QwtSpline::QwtSpline</a>(<span class="keyword">const</span> <a class="code" href="class_qwt_spline.html">QwtSpline</a>& other)
97
<a name="l00079"></a>00079 {
98
<a name="l00080"></a>00080 <a class="code" href="class_qwt_spline.html#784545391f14c014684f391c6d92fd27">d_data</a> = <span class="keyword">new</span> PrivateData(*other.<a class="code" href="class_qwt_spline.html#784545391f14c014684f391c6d92fd27">d_data</a>);
99
<a name="l00081"></a>00081 }
100
<a name="l00082"></a>00082
101
<a name="l00083"></a><a class="code" href="class_qwt_spline.html#8a597c34477dd4b5298db2d445b4e596">00083</a> <a class="code" href="class_qwt_spline.html">QwtSpline</a> &<a class="code" href="class_qwt_spline.html#8a597c34477dd4b5298db2d445b4e596">QwtSpline::operator=</a>( <span class="keyword">const</span> <a class="code" href="class_qwt_spline.html">QwtSpline</a> &other)
102
<a name="l00084"></a>00084 {
103
<a name="l00085"></a>00085 *<a class="code" href="class_qwt_spline.html#784545391f14c014684f391c6d92fd27">d_data</a> = *other.<a class="code" href="class_qwt_spline.html#784545391f14c014684f391c6d92fd27">d_data</a>;
104
<a name="l00086"></a>00086 <span class="keywordflow">return</span> *<span class="keyword">this</span>;
105
<a name="l00087"></a>00087 }
106
<a name="l00088"></a>00088
107
<a name="l00090"></a><a class="code" href="class_qwt_spline.html#90805882826469c94fdc871f18261bb6">00090</a> <a class="code" href="class_qwt_spline.html#90805882826469c94fdc871f18261bb6">QwtSpline::~QwtSpline</a>()
108
<a name="l00091"></a>00091 {
109
<a name="l00092"></a>00092 <span class="keyword">delete</span> <a class="code" href="class_qwt_spline.html#784545391f14c014684f391c6d92fd27">d_data</a>;
110
<a name="l00093"></a>00093 }
111
<a name="l00094"></a>00094
112
<a name="l00095"></a><a class="code" href="class_qwt_spline.html#222953661f01658a16042d587196aff8">00095</a> <span class="keywordtype">void</span> <a class="code" href="class_qwt_spline.html#222953661f01658a16042d587196aff8">QwtSpline::setSplineType</a>(<a class="code" href="class_qwt_spline.html#2bd2bda128f82acd596348eb8d64231c">SplineType</a> splineType)
113
<a name="l00096"></a>00096 {
114
<a name="l00097"></a>00097 <a class="code" href="class_qwt_spline.html#784545391f14c014684f391c6d92fd27">d_data</a>->splineType = splineType;
115
<a name="l00098"></a>00098 }
116
<a name="l00099"></a>00099
117
<a name="l00100"></a><a class="code" href="class_qwt_spline.html#1ba958ef9d8ea93db822fde1a1176f51">00100</a> <a class="code" href="class_qwt_spline.html#2bd2bda128f82acd596348eb8d64231c">QwtSpline::SplineType</a> <a class="code" href="class_qwt_spline.html#1ba958ef9d8ea93db822fde1a1176f51">QwtSpline::splineType</a>()<span class="keyword"> const</span>
118
<a name="l00101"></a>00101 <span class="keyword"></span>{
119
<a name="l00102"></a>00102 <span class="keywordflow">return</span> <a class="code" href="class_qwt_spline.html#784545391f14c014684f391c6d92fd27">d_data</a>->splineType;
120
<a name="l00103"></a>00103 }
121
<a name="l00104"></a>00104
122
<a name="l00106"></a>00106
123
<a name="l00123"></a>00123 <span class="preprocessor">#if QT_VERSION < 0x040000</span>
124
<a name="l00124"></a>00124 <span class="preprocessor"></span><span class="keywordtype">bool</span> <a class="code" href="class_qwt_spline.html#6ed13410b1d5f6b33ba0e3c2b07932cf">QwtSpline::setPoints</a>(<span class="keyword">const</span> QwtArray<QwtDoublePoint>& points)
125
<a name="l00125"></a>00125 <span class="preprocessor">#else</span>
126
<a name="l00126"></a><a class="code" href="class_qwt_spline.html#6ed13410b1d5f6b33ba0e3c2b07932cf">00126</a> <span class="preprocessor"></span><span class="keywordtype">bool</span> <a class="code" href="class_qwt_spline.html#6ed13410b1d5f6b33ba0e3c2b07932cf">QwtSpline::setPoints</a>(<span class="keyword">const</span> QPolygonF& points)
127
<a name="l00127"></a>00127 <span class="preprocessor">#endif</span>
128
<a name="l00128"></a>00128 <span class="preprocessor"></span>{
129
<a name="l00129"></a>00129 <span class="keyword">const</span> <span class="keywordtype">int</span> size = points.size();
130
<a name="l00130"></a>00130 <span class="keywordflow">if</span> (size <= 2)
131
<a name="l00131"></a>00131 {
132
<a name="l00132"></a>00132 reset();
133
<a name="l00133"></a>00133 <span class="keywordflow">return</span> <span class="keyword">false</span>;
134
<a name="l00134"></a>00134 }
135
<a name="l00135"></a>00135
136
<a name="l00136"></a>00136 <span class="preprocessor">#if QT_VERSION < 0x040000</span>
137
<a name="l00137"></a>00137 <span class="preprocessor"></span> d_data->points = points.copy(); <span class="comment">// Qt3: deep copy</span>
138
<a name="l00138"></a>00138 <span class="preprocessor">#else</span>
139
<a name="l00139"></a>00139 <span class="preprocessor"></span> d_data->points = points;
140
<a name="l00140"></a>00140 <span class="preprocessor">#endif</span>
141
<a name="l00141"></a>00141 <span class="preprocessor"></span>
142
<a name="l00142"></a>00142 d_data->a.resize(size-1);
143
<a name="l00143"></a>00143 d_data->b.resize(size-1);
144
<a name="l00144"></a>00144 d_data->c.resize(size-1);
145
<a name="l00145"></a>00145
146
<a name="l00146"></a>00146 <span class="keywordtype">bool</span> ok;
147
<a name="l00147"></a>00147 <span class="keywordflow">if</span> ( d_data->splineType == Periodic )
148
<a name="l00148"></a>00148 ok = buildPeriodicSpline(points);
149
<a name="l00149"></a>00149 <span class="keywordflow">else</span>
150
<a name="l00150"></a>00150 ok = buildNaturalSpline(points);
151
<a name="l00151"></a>00151
152
<a name="l00152"></a>00152 <span class="keywordflow">if</span> (!ok)
153
<a name="l00153"></a>00153 reset();
154
<a name="l00154"></a>00154
155
<a name="l00155"></a>00155 <span class="keywordflow">return</span> ok;
156
<a name="l00156"></a>00156 }
157
<a name="l00157"></a>00157
158
<a name="l00161"></a>00161 <span class="preprocessor">#if QT_VERSION < 0x040000</span>
159
<a name="l00162"></a>00162 <span class="preprocessor"></span>QwtArray<QwtDoublePoint> <a class="code" href="class_qwt_spline.html#5137512588444236e2a2ab1cab207f41">QwtSpline::points</a>() const
160
<a name="l00163"></a>00163 <span class="preprocessor">#else</span>
161
<a name="l00164"></a><a class="code" href="class_qwt_spline.html#5137512588444236e2a2ab1cab207f41">00164</a> <span class="preprocessor"></span>QPolygonF <a class="code" href="class_qwt_spline.html#5137512588444236e2a2ab1cab207f41">QwtSpline::points</a>() const
162
<a name="l00165"></a>00165 <span class="preprocessor">#endif</span>
163
<a name="l00166"></a>00166 <span class="preprocessor"></span>{
164
<a name="l00167"></a>00167 <span class="keywordflow">return</span> d_data->points;
165
<a name="l00168"></a>00168 }
166
<a name="l00169"></a>00169
167
<a name="l00170"></a>00170
168
<a name="l00172"></a><a class="code" href="class_qwt_spline.html#fc52fd49e7f00d57a0336059fae299c0">00172</a> <span class="keywordtype">void</span> <a class="code" href="class_qwt_spline.html#fc52fd49e7f00d57a0336059fae299c0">QwtSpline::reset</a>()
169
<a name="l00173"></a>00173 {
170
<a name="l00174"></a>00174 <a class="code" href="class_qwt_spline.html#784545391f14c014684f391c6d92fd27">d_data</a>->a.resize(0);
171
<a name="l00175"></a>00175 <a class="code" href="class_qwt_spline.html#784545391f14c014684f391c6d92fd27">d_data</a>->b.resize(0);
172
<a name="l00176"></a>00176 <a class="code" href="class_qwt_spline.html#784545391f14c014684f391c6d92fd27">d_data</a>->c.resize(0);
173
<a name="l00177"></a>00177 <a class="code" href="class_qwt_spline.html#784545391f14c014684f391c6d92fd27">d_data</a>->points.resize(0);
174
<a name="l00178"></a>00178 }
175
<a name="l00179"></a>00179
176
<a name="l00181"></a><a class="code" href="class_qwt_spline.html#50298a899c2199373b0d73fb50bc406d">00181</a> <span class="keywordtype">bool</span> <a class="code" href="class_qwt_spline.html#50298a899c2199373b0d73fb50bc406d">QwtSpline::isValid</a>()<span class="keyword"> const</span>
177
<a name="l00182"></a>00182 <span class="keyword"></span>{
178
<a name="l00183"></a>00183 <span class="keywordflow">return</span> <a class="code" href="class_qwt_spline.html#784545391f14c014684f391c6d92fd27">d_data</a>->a.size() > 0;
179
<a name="l00184"></a>00184 }
180
<a name="l00185"></a>00185
181
<a name="l00190"></a><a class="code" href="class_qwt_spline.html#7c7af79ee4d77dd8e0ff08a6fd234e4f">00190</a> <span class="keywordtype">double</span> <a class="code" href="class_qwt_spline.html#7c7af79ee4d77dd8e0ff08a6fd234e4f">QwtSpline::value</a>(<span class="keywordtype">double</span> x)<span class="keyword"> const</span>
182
<a name="l00191"></a>00191 <span class="keyword"></span>{
183
<a name="l00192"></a>00192 <span class="keywordflow">if</span> (<a class="code" href="class_qwt_spline.html#784545391f14c014684f391c6d92fd27">d_data</a>->a.size() == 0)
184
<a name="l00193"></a>00193 <span class="keywordflow">return</span> 0.0;
185
<a name="l00194"></a>00194
186
<a name="l00195"></a>00195 <span class="keyword">const</span> <span class="keywordtype">int</span> i = lookup(x, <a class="code" href="class_qwt_spline.html#784545391f14c014684f391c6d92fd27">d_data</a>->points);
187
<a name="l00196"></a>00196
188
<a name="l00197"></a>00197 <span class="keyword">const</span> <span class="keywordtype">double</span> delta = x - <a class="code" href="class_qwt_spline.html#784545391f14c014684f391c6d92fd27">d_data</a>->points[i].x();
189
<a name="l00198"></a>00198 <span class="keywordflow">return</span>( ( ( ( <a class="code" href="class_qwt_spline.html#784545391f14c014684f391c6d92fd27">d_data</a>->a[i] * delta) + <a class="code" href="class_qwt_spline.html#784545391f14c014684f391c6d92fd27">d_data</a>->b[i] )
190
<a name="l00199"></a>00199 * delta + <a class="code" href="class_qwt_spline.html#784545391f14c014684f391c6d92fd27">d_data</a>->c[i] ) * delta + <a class="code" href="class_qwt_spline.html#784545391f14c014684f391c6d92fd27">d_data</a>->points[i].y() );
191
<a name="l00200"></a>00200 }
192
<a name="l00201"></a>00201
193
<a name="l00206"></a>00206 <span class="preprocessor">#if QT_VERSION < 0x040000</span>
194
<a name="l00207"></a>00207 <span class="preprocessor"></span><span class="keywordtype">bool</span> <a class="code" href="class_qwt_spline.html#1cdf09e841dd6a721eb788914273c484">QwtSpline::buildNaturalSpline</a>(<span class="keyword">const</span> QwtArray<QwtDoublePoint> &points)
195
<a name="l00208"></a>00208 <span class="preprocessor">#else</span>
196
<a name="l00209"></a><a class="code" href="class_qwt_spline.html#1cdf09e841dd6a721eb788914273c484">00209</a> <span class="preprocessor"></span><span class="keywordtype">bool</span> <a class="code" href="class_qwt_spline.html#1cdf09e841dd6a721eb788914273c484">QwtSpline::buildNaturalSpline</a>(<span class="keyword">const</span> QPolygonF &points)
197
<a name="l00210"></a>00210 <span class="preprocessor">#endif</span>
198
<a name="l00211"></a>00211 <span class="preprocessor"></span>{
199
<a name="l00212"></a>00212 <span class="keywordtype">int</span> i;
200
<a name="l00213"></a>00213
201
<a name="l00214"></a>00214 <span class="preprocessor">#if QT_VERSION < 0x040000</span>
202
<a name="l00215"></a>00215 <span class="preprocessor"></span> <span class="keyword">const</span> <a class="code" href="qwt__double__rect_8h.html#5fdf5abc59b6e6cee5c11d355906927a">QwtDoublePoint</a> *p = points.data();
203
<a name="l00216"></a>00216 <span class="preprocessor">#else</span>
204
<a name="l00217"></a>00217 <span class="preprocessor"></span> <span class="keyword">const</span> QPointF *p = points.data();
205
<a name="l00218"></a>00218 <span class="preprocessor">#endif</span>
206
<a name="l00219"></a>00219 <span class="preprocessor"></span> <span class="keyword">const</span> <span class="keywordtype">int</span> size = points.size();
207
<a name="l00220"></a>00220
208
<a name="l00221"></a>00221 <span class="keywordtype">double</span> *a = d_data->a.data();
209
<a name="l00222"></a>00222 <span class="keywordtype">double</span> *b = d_data->b.data();
210
<a name="l00223"></a>00223 <span class="keywordtype">double</span> *c = d_data->c.data();
211
<a name="l00224"></a>00224
212
<a name="l00225"></a>00225 <span class="comment">// set up tridiagonal equation system; use coefficient</span>
213
<a name="l00226"></a>00226 <span class="comment">// vectors as temporary buffers</span>
214
<a name="l00227"></a>00227 QwtArray<double> h(size-1);
215
<a name="l00228"></a>00228 <span class="keywordflow">for</span> (i = 0; i < size - 1; i++)
216
<a name="l00229"></a>00229 {
217
<a name="l00230"></a>00230 h[i] = p[i+1].x() - p[i].x();
218
<a name="l00231"></a>00231 <span class="keywordflow">if</span> (h[i] <= 0)
219
<a name="l00232"></a>00232 <span class="keywordflow">return</span> <span class="keyword">false</span>;
220
<a name="l00233"></a>00233 }
221
<a name="l00234"></a>00234
222
<a name="l00235"></a>00235 QwtArray<double> d(size-1);
223
<a name="l00236"></a>00236 <span class="keywordtype">double</span> dy1 = (p[1].y() - p[0].y()) / h[0];
224
<a name="l00237"></a>00237 <span class="keywordflow">for</span> (i = 1; i < size - 1; i++)
225
<a name="l00238"></a>00238 {
226
<a name="l00239"></a>00239 b[i] = c[i] = h[i];
227
<a name="l00240"></a>00240 a[i] = 2.0 * (h[i-1] + h[i]);
228
<a name="l00241"></a>00241
229
<a name="l00242"></a>00242 <span class="keyword">const</span> <span class="keywordtype">double</span> dy2 = (p[i+1].y() - p[i].y()) / h[i];
230
<a name="l00243"></a>00243 d[i] = 6.0 * ( dy1 - dy2);
231
<a name="l00244"></a>00244 dy1 = dy2;
232
<a name="l00245"></a>00245 }
233
<a name="l00246"></a>00246
234
<a name="l00247"></a>00247 <span class="comment">//</span>
235
<a name="l00248"></a>00248 <span class="comment">// solve it</span>
236
<a name="l00249"></a>00249 <span class="comment">//</span>
237
<a name="l00250"></a>00250
238
<a name="l00251"></a>00251 <span class="comment">// L-U Factorization</span>
239
<a name="l00252"></a>00252 <span class="keywordflow">for</span>(i = 1; i < size - 2;i++)
240
<a name="l00253"></a>00253 {
241
<a name="l00254"></a>00254 c[i] /= a[i];
242
<a name="l00255"></a>00255 a[i+1] -= b[i] * c[i];
243
<a name="l00256"></a>00256 }
244
<a name="l00257"></a>00257
245
<a name="l00258"></a>00258 <span class="comment">// forward elimination</span>
246
<a name="l00259"></a>00259 QwtArray<double> s(size);
247
<a name="l00260"></a>00260 s[1] = d[1];
248
<a name="l00261"></a>00261 <span class="keywordflow">for</span> ( i = 2; i < size - 1; i++)
249
<a name="l00262"></a>00262 s[i] = d[i] - c[i-1] * s[i-1];
250
<a name="l00263"></a>00263
251
<a name="l00264"></a>00264 <span class="comment">// backward elimination</span>
252
<a name="l00265"></a>00265 s[size - 2] = - s[size - 2] / a[size - 2];
253
<a name="l00266"></a>00266 <span class="keywordflow">for</span> (i = size -3; i > 0; i--)
254
<a name="l00267"></a>00267 s[i] = - (s[i] + b[i] * s[i+1]) / a[i];
255
<a name="l00268"></a>00268 s[size - 1] = s[0] = 0.0;
256
<a name="l00269"></a>00269
257
<a name="l00270"></a>00270 <span class="comment">//</span>
258
<a name="l00271"></a>00271 <span class="comment">// Finally, determine the spline coefficients</span>
259
<a name="l00272"></a>00272 <span class="comment">//</span>
260
<a name="l00273"></a>00273 <span class="keywordflow">for</span> (i = 0; i < size - 1; i++)
261
<a name="l00274"></a>00274 {
262
<a name="l00275"></a>00275 a[i] = ( s[i+1] - s[i] ) / ( 6.0 * h[i]);
263
<a name="l00276"></a>00276 b[i] = 0.5 * s[i];
264
<a name="l00277"></a>00277 c[i] = ( p[i+1].y() - p[i].y() ) / h[i]
265
<a name="l00278"></a>00278 - (s[i+1] + 2.0 * s[i] ) * h[i] / 6.0;
266
<a name="l00279"></a>00279 }
267
<a name="l00280"></a>00280
268
<a name="l00281"></a>00281 <span class="keywordflow">return</span> <span class="keyword">true</span>;
269
<a name="l00282"></a>00282 }
270
<a name="l00283"></a>00283
271
<a name="l00288"></a>00288 <span class="preprocessor">#if QT_VERSION < 0x040000</span>
272
<a name="l00289"></a>00289 <span class="preprocessor"></span><span class="keywordtype">bool</span> <a class="code" href="class_qwt_spline.html#8184717f8c018e69fabd1e33ac68ef19">QwtSpline::buildPeriodicSpline</a>(
273
<a name="l00290"></a>00290 <span class="keyword">const</span> QwtArray<QwtDoublePoint> &points)
274
<a name="l00291"></a>00291 <span class="preprocessor">#else</span>
275
<a name="l00292"></a><a class="code" href="class_qwt_spline.html#8184717f8c018e69fabd1e33ac68ef19">00292</a> <span class="preprocessor"></span><span class="keywordtype">bool</span> <a class="code" href="class_qwt_spline.html#8184717f8c018e69fabd1e33ac68ef19">QwtSpline::buildPeriodicSpline</a>(<span class="keyword">const</span> QPolygonF &points)
276
<a name="l00293"></a>00293 <span class="preprocessor">#endif</span>
277
<a name="l00294"></a>00294 <span class="preprocessor"></span>{
278
<a name="l00295"></a>00295 <span class="keywordtype">int</span> i;
279
<a name="l00296"></a>00296
280
<a name="l00297"></a>00297 <span class="preprocessor">#if QT_VERSION < 0x040000</span>
281
<a name="l00298"></a>00298 <span class="preprocessor"></span> <span class="keyword">const</span> <a class="code" href="qwt__double__rect_8h.html#5fdf5abc59b6e6cee5c11d355906927a">QwtDoublePoint</a> *p = points.data();
282
<a name="l00299"></a>00299 <span class="preprocessor">#else</span>
283
<a name="l00300"></a>00300 <span class="preprocessor"></span> <span class="keyword">const</span> QPointF *p = points.data();
284
<a name="l00301"></a>00301 <span class="preprocessor">#endif</span>
285
<a name="l00302"></a>00302 <span class="preprocessor"></span> <span class="keyword">const</span> <span class="keywordtype">int</span> size = points.size();
286
<a name="l00303"></a>00303
287
<a name="l00304"></a>00304 <span class="keywordtype">double</span> *a = d_data->a.data();
288
<a name="l00305"></a>00305 <span class="keywordtype">double</span> *b = d_data->b.data();
289
<a name="l00306"></a>00306 <span class="keywordtype">double</span> *c = d_data->c.data();
290
<a name="l00307"></a>00307
291
<a name="l00308"></a>00308 QwtArray<double> d(size-1);
292
<a name="l00309"></a>00309 QwtArray<double> h(size-1);
293
<a name="l00310"></a>00310 QwtArray<double> s(size);
294
<a name="l00311"></a>00311
295
<a name="l00312"></a>00312 <span class="comment">//</span>
296
<a name="l00313"></a>00313 <span class="comment">// setup equation system; use coefficient</span>
297
<a name="l00314"></a>00314 <span class="comment">// vectors as temporary buffers</span>
298
<a name="l00315"></a>00315 <span class="comment">//</span>
299
<a name="l00316"></a>00316 <span class="keywordflow">for</span> (i = 0; i < size - 1; i++)
300
<a name="l00317"></a>00317 {
301
<a name="l00318"></a>00318 h[i] = p[i+1].x() - p[i].x();
302
<a name="l00319"></a>00319 <span class="keywordflow">if</span> (h[i] <= 0.0)
303
<a name="l00320"></a>00320 <span class="keywordflow">return</span> <span class="keyword">false</span>;
304
<a name="l00321"></a>00321 }
305
<a name="l00322"></a>00322
306
<a name="l00323"></a>00323 <span class="keyword">const</span> <span class="keywordtype">int</span> imax = size - 2;
307
<a name="l00324"></a>00324 <span class="keywordtype">double</span> htmp = h[imax];
308
<a name="l00325"></a>00325 <span class="keywordtype">double</span> dy1 = (p[0].y() - p[imax].y()) / htmp;
309
<a name="l00326"></a>00326 <span class="keywordflow">for</span> (i = 0; i <= imax; i++)
310
<a name="l00327"></a>00327 {
311
<a name="l00328"></a>00328 b[i] = c[i] = h[i];
312
<a name="l00329"></a>00329 a[i] = 2.0 * (htmp + h[i]);
313
<a name="l00330"></a>00330 <span class="keyword">const</span> <span class="keywordtype">double</span> dy2 = (p[i+1].y() - p[i].y()) / h[i];
314
<a name="l00331"></a>00331 d[i] = 6.0 * ( dy1 - dy2);
315
<a name="l00332"></a>00332 dy1 = dy2;
316
<a name="l00333"></a>00333 htmp = h[i];
317
<a name="l00334"></a>00334 }
318
<a name="l00335"></a>00335
319
<a name="l00336"></a>00336 <span class="comment">//</span>
320
<a name="l00337"></a>00337 <span class="comment">// solve it</span>
321
<a name="l00338"></a>00338 <span class="comment">//</span>
322
<a name="l00339"></a>00339
323
<a name="l00340"></a>00340 <span class="comment">// L-U Factorization</span>
324
<a name="l00341"></a>00341 a[0] = sqrt(a[0]);
325
<a name="l00342"></a>00342 c[0] = h[imax] / a[0];
326
<a name="l00343"></a>00343 <span class="keywordtype">double</span> sum = 0;
327
<a name="l00344"></a>00344
328
<a name="l00345"></a>00345 <span class="keywordflow">for</span>( i = 0; i < imax - 1; i++)
329
<a name="l00346"></a>00346 {
330
<a name="l00347"></a>00347 b[i] /= a[i];
331
<a name="l00348"></a>00348 <span class="keywordflow">if</span> (i > 0)
332
<a name="l00349"></a>00349 c[i] = - c[i-1] * b[i-1] / a[i];
333
<a name="l00350"></a>00350 a[i+1] = sqrt( a[i+1] - qwtSqr(b[i]));
334
<a name="l00351"></a>00351 sum += qwtSqr(c[i]);
335
<a name="l00352"></a>00352 }
336
<a name="l00353"></a>00353 b[imax-1] = (b[imax-1] - c[imax-2] * b[imax-2]) / a[imax-1];
337
<a name="l00354"></a>00354 a[imax] = sqrt(a[imax] - qwtSqr(b[imax-1]) - sum);
338
<a name="l00355"></a>00355
339
<a name="l00356"></a>00356
340
<a name="l00357"></a>00357 <span class="comment">// forward elimination</span>
341
<a name="l00358"></a>00358 s[0] = d[0] / a[0];
342
<a name="l00359"></a>00359 sum = 0;
343
<a name="l00360"></a>00360 <span class="keywordflow">for</span>( i = 1; i < imax; i++)
344
<a name="l00361"></a>00361 {
345
<a name="l00362"></a>00362 s[i] = (d[i] - b[i-1] * s[i-1]) / a[i];
346
<a name="l00363"></a>00363 sum += c[i-1] * s[i-1];
347
<a name="l00364"></a>00364 }
348
<a name="l00365"></a>00365 s[imax] = (d[imax] - b[imax-1] * s[imax-1] - sum) / a[imax];
349
<a name="l00366"></a>00366
350
<a name="l00367"></a>00367
351
<a name="l00368"></a>00368 <span class="comment">// backward elimination</span>
352
<a name="l00369"></a>00369 s[imax] = - s[imax] / a[imax];
353
<a name="l00370"></a>00370 s[imax-1] = -(s[imax-1] + b[imax-1] * s[imax]) / a[imax-1];
354
<a name="l00371"></a>00371 <span class="keywordflow">for</span> (i= imax - 2; i >= 0; i--)
355
<a name="l00372"></a>00372 s[i] = - (s[i] + b[i] * s[i+1] + c[i] * s[imax]) / a[i];
356
<a name="l00373"></a>00373
357
<a name="l00374"></a>00374 <span class="comment">//</span>
358
<a name="l00375"></a>00375 <span class="comment">// Finally, determine the spline coefficients</span>
359
<a name="l00376"></a>00376 <span class="comment">//</span>
360
<a name="l00377"></a>00377 s[size-1] = s[0];
361
<a name="l00378"></a>00378 <span class="keywordflow">for</span> ( i=0; i < size-1; i++)
362
<a name="l00379"></a>00379 {
363
<a name="l00380"></a>00380 a[i] = ( s[i+1] - s[i] ) / ( 6.0 * h[i]);
364
<a name="l00381"></a>00381 b[i] = 0.5 * s[i];
365
<a name="l00382"></a>00382 c[i] = ( p[i+1].y() - p[i].y() )
366
<a name="l00383"></a>00383 / h[i] - (s[i+1] + 2.0 * s[i] ) * h[i] / 6.0;
367
<a name="l00384"></a>00384 }
368
<a name="l00385"></a>00385
369
<a name="l00386"></a>00386 <span class="keywordflow">return</span> <span class="keyword">true</span>;
370
<a name="l00387"></a>00387 }
371
</pre></div><hr size="1"><address style="align: right;"><small>Generated on Thu May 1 15:44:09 2008 for Qwt User's Guide by
372
<a href="http://www.doxygen.org/index.html">
373
<img src="doxygen.png" alt="doxygen" align="middle" border="0"></a> 1.5.0 </small></address>
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qwt-5.1.0/doc/html/qwt__spline_8cpp-source.html
