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<h1>mathdefs.h</h1><div class="fragment"><pre class="fragment"><a name="l00001"></a>00001 <span class="comment">/*</span>
<a name="l00002"></a>00002 <span class="comment"> * GearBox Project: Peer-Reviewed Open-Source Libraries for Robotics</span>
<a name="l00003"></a>00003 <span class="comment"> * http://gearbox.sf.net/</span>
<a name="l00004"></a>00004 <span class="comment"> * Copyright (c) 2004-2008 Alex Brooks, Alexei Makarenko, Tobias Kaupp</span>
<a name="l00005"></a>00005 <span class="comment"> *</span>
<a name="l00006"></a>00006 <span class="comment"> * This distribution is licensed to you under the terms described in</span>
<a name="l00007"></a>00007 <span class="comment"> * the LICENSE file included in this distribution.</span>
<a name="l00008"></a>00008 <span class="comment"> *</span>
<a name="l00009"></a>00009 <span class="comment"> */</span>
<a name="l00010"></a>00010
<a name="l00011"></a>00011 <span class="comment">/*dox</span>
<a name="l00012"></a>00012 <span class="comment"> @file </span>
<a name="l00013"></a>00013 <span class="comment"> @brief Mathematical macros</span>
<a name="l00014"></a>00014 <span class="comment"> @ingroup orca_library_orcaiceutil </span>
<a name="l00015"></a>00015 <span class="comment"> */</span>
<a name="l00016"></a>00016
<a name="l00017"></a>00017 <span class="preprocessor">#ifndef GBXUTILACFR_MATH_DEFINITIONS_H</span>
<a name="l00018"></a>00018 <span class="preprocessor"></span><span class="preprocessor">#define GBXUTILACFR_MATH_DEFINITIONS_H </span>
<a name="l00019"></a>00019 <span class="preprocessor"></span>
<a name="l00020"></a>00020 <span class="preprocessor">#if defined (WIN32)</span>
<a name="l00021"></a>00021 <span class="preprocessor"></span><span class="preprocessor"> #if defined (GBXUTILACFR_STATIC)</span>
<a name="l00022"></a>00022 <span class="preprocessor"></span><span class="preprocessor"> #define GBXUTILACFR_EXPORT</span>
<a name="l00023"></a>00023 <span class="preprocessor"></span><span class="preprocessor"> #elif defined (GBXUTILACFR_EXPORTS)</span>
<a name="l00024"></a>00024 <span class="preprocessor"></span><span class="preprocessor"> #define GBXUTILACFR_EXPORT __declspec (dllexport)</span>
<a name="l00025"></a>00025 <span class="preprocessor"></span><span class="preprocessor"> #else</span>
<a name="l00026"></a>00026 <span class="preprocessor"></span><span class="preprocessor"> #define GBXUTILACFR_EXPORT __declspec (dllimport)</span>
<a name="l00027"></a>00027 <span class="preprocessor"></span><span class="preprocessor"> #endif</span>
<a name="l00028"></a>00028 <span class="preprocessor"></span><span class="preprocessor">#else</span>
<a name="l00029"></a>00029 <span class="preprocessor"></span><span class="preprocessor"> #define GBXUTILACFR_EXPORT</span>
<a name="l00030"></a>00030 <span class="preprocessor"></span><span class="preprocessor">#endif</span>
<a name="l00031"></a>00031 <span class="preprocessor"></span>
<a name="l00032"></a>00032 <span class="preprocessor">#include <assert.h></span>
<a name="l00033"></a>00033
<a name="l00034"></a>00034 <span class="comment">/*****************************************************************************</span>
<a name="l00035"></a>00035 <span class="comment"> * INCLUDE THE RELEVANT MATHS LIBRARIES</span>
<a name="l00036"></a>00036 <span class="comment"> *****************************************************************************/</span>
<a name="l00037"></a>00037
<a name="l00038"></a>00038 <span class="comment">// MSVC compiler requires this symbol before exposing the (apparently) </span>
<a name="l00039"></a>00039 <span class="comment">// non-standard symbols M_PI, etc...</span>
<a name="l00040"></a>00040 <span class="preprocessor">#ifdef WIN32</span>
<a name="l00041"></a>00041 <span class="preprocessor"></span><span class="preprocessor">#define _USE_MATH_DEFINES</span>
<a name="l00042"></a>00042 <span class="preprocessor"></span><span class="preprocessor">#endif</span>
<a name="l00043"></a>00043 <span class="preprocessor"></span>
<a name="l00044"></a>00044 <span class="preprocessor">#include <cmath></span>
<a name="l00045"></a>00045
<a name="l00046"></a>00046 <span class="comment">/*****************************************************************************</span>
<a name="l00047"></a>00047 <span class="comment"> * CONSTANTS</span>
<a name="l00048"></a>00048 <span class="comment"> *****************************************************************************/</span>
<a name="l00049"></a>00049 <span class="comment">// M_PI is not defined after including cmath for the MS visual studio compiler?</span>
<a name="l00050"></a>00050 <span class="preprocessor">#ifndef M_PI</span>
<a name="l00051"></a>00051 <span class="preprocessor"></span><span class="comment">//dox Defines number Pi</span>
<a name="l00052"></a>00052 <span class="preprocessor">#define M_PI 3.14159265358979323846</span>
<a name="l00053"></a>00053 <span class="preprocessor"></span><span class="preprocessor">#endif</span>
<a name="l00054"></a>00054 <span class="preprocessor"></span>
<a name="l00055"></a>00055 <span class="preprocessor">#ifndef NAN</span>
<a name="l00056"></a>00056 <span class="preprocessor"></span><span class="comment">//dox Defines not-a-number</span>
<a name="l00057"></a>00057 <span class="preprocessor">#define NAN (__builtin_nanf(""))</span>
<a name="l00058"></a>00058 <span class="preprocessor"></span><span class="preprocessor">#endif</span>
<a name="l00059"></a>00059 <span class="preprocessor"></span>
<a name="l00060"></a>00060 <span class="preprocessor">#ifndef INF</span>
<a name="l00061"></a>00061 <span class="preprocessor"></span><span class="comment">//dox Defines infinity</span>
<a name="l00062"></a>00062 <span class="preprocessor">#define INF (__builtin_inff())</span>
<a name="l00063"></a>00063 <span class="preprocessor"></span><span class="preprocessor">#endif</span>
<a name="l00064"></a>00064 <span class="preprocessor"></span>
<a name="l00065"></a>00065 <span class="comment">/*****************************************************************************</span>
<a name="l00066"></a>00066 <span class="comment"> * CONVERSION MACROS</span>
<a name="l00067"></a>00067 <span class="comment"> *****************************************************************************/</span>
<a name="l00068"></a>00068 <span class="preprocessor">#ifndef DEG2RAD_RATIO</span>
<a name="l00069"></a>00069 <span class="preprocessor"></span><span class="comment">//dox Convertion factor from degrees to radians.</span>
<a name="l00070"></a>00070 <span class="preprocessor">#define DEG2RAD_RATIO (M_PI/180.0)</span>
<a name="l00071"></a>00071 <span class="preprocessor"></span><span class="preprocessor">#endif</span>
<a name="l00072"></a>00072 <span class="preprocessor"></span>
<a name="l00073"></a>00073 <span class="comment">//dox Converts from degrees to radians.</span>
<a name="l00074"></a>00074 <span class="preprocessor">#define DEG2RAD(deg) ((deg)*DEG2RAD_RATIO)</span>
<a name="l00075"></a>00075 <span class="preprocessor"></span><span class="comment">//dox Converts from radians to degrees.</span>
<a name="l00076"></a>00076 <span class="preprocessor">#define RAD2DEG(rad) ((rad)/DEG2RAD_RATIO)</span>
<a name="l00077"></a>00077 <span class="preprocessor"></span>
<a name="l00078"></a>00078 <span class="comment">//dox Normalises the angle [rad] to the range [-pi,pi)</span>
<a name="l00079"></a>00079 <span class="comment">//dox Don't return the normalised angle, because it's easy to make the</span>
<a name="l00080"></a>00080 <span class="comment">//dox mistake of doing: 'NORMALISE_ANGLE( myAngle )', ignoring the return value.</span>
<a name="l00081"></a>00081 GBXUTILACFR_EXPORT <span class="keyword">inline</span> <span class="keywordtype">void</span> NORMALISE_ANGLE( <span class="keywordtype">double</span> &theta )
<a name="l00082"></a>00082 {
<a name="l00083"></a>00083 <span class="keywordtype">double</span> multiplier;
<a name="l00084"></a>00084
<a name="l00085"></a>00085 <span class="keywordflow">if</span> (theta >= -M_PI && theta < M_PI)
<a name="l00086"></a>00086 <span class="keywordflow">return</span>;
<a name="l00087"></a>00087
<a name="l00088"></a>00088 multiplier = std::floor(theta / (2*M_PI));
<a name="l00089"></a>00089 theta -= multiplier*2*M_PI;
<a name="l00090"></a>00090 <span class="keywordflow">if</span> (theta >= M_PI)
<a name="l00091"></a>00091 theta -= 2*M_PI;
<a name="l00092"></a>00092 <span class="keywordflow">else</span> <span class="keywordflow">if</span> (theta < -M_PI)
<a name="l00093"></a>00093 theta += 2*M_PI;
<a name="l00094"></a>00094 }
<a name="l00095"></a>00095
<a name="l00096"></a>00096 <span class="comment">//dox Normalises the angle [rad] to the range [-pi,pi)</span>
<a name="l00097"></a>00097 <span class="comment">//dox Don't return the normalised angle, because it's easy to make the</span>
<a name="l00098"></a>00098 <span class="comment">//dox mistake of doing: 'NORMALISE_ANGLE( myAngle )', ignoring the return value.</span>
<a name="l00099"></a>00099 GBXUTILACFR_EXPORT <span class="keyword">inline</span> <span class="keywordtype">void</span> NORMALISE_ANGLE( <span class="keywordtype">float</span> &theta )
<a name="l00100"></a>00100 {
<a name="l00101"></a>00101 <span class="keywordtype">double</span> thDouble = theta;
<a name="l00102"></a>00102 NORMALISE_ANGLE( thDouble );
<a name="l00103"></a>00103 theta = (float)thDouble;
<a name="l00104"></a>00104 }
<a name="l00105"></a>00105
<a name="l00106"></a>00106 <span class="comment">/*****************************************************************************</span>
<a name="l00107"></a>00107 <span class="comment"> * MATH MACROS</span>
<a name="l00108"></a>00108 <span class="comment"> *****************************************************************************/</span>
<a name="l00109"></a>00109 <span class="comment">// for compatability retain this old one</span>
<a name="l00110"></a>00110 <span class="comment">//#ifndef ABS</span>
<a name="l00111"></a>00111 <span class="comment">//#define ABS(x) (std::abs(x))</span>
<a name="l00112"></a>00112 <span class="comment">//#endif</span>
<a name="l00113"></a>00113 <span class="preprocessor">#ifndef MIN</span>
<a name="l00114"></a>00114 <span class="preprocessor"></span><span class="comment">//dox Minimum of two numbers</span>
<a name="l00115"></a>00115 <span class="preprocessor">#define MIN(x, y) (((x) < (y)) ? (x) : (y))</span>
<a name="l00116"></a>00116 <span class="preprocessor"></span><span class="preprocessor">#endif</span>
<a name="l00117"></a>00117 <span class="preprocessor"></span><span class="preprocessor">#ifndef MAX</span>
<a name="l00118"></a>00118 <span class="preprocessor"></span><span class="comment">//dox Maximum of two numbers</span>
<a name="l00119"></a>00119 <span class="preprocessor">#define MAX(x, y) (((x) > (y)) ? (x) : (y))</span>
<a name="l00120"></a>00120 <span class="preprocessor"></span><span class="preprocessor">#endif</span>
<a name="l00121"></a>00121 <span class="preprocessor"></span><span class="preprocessor">#ifndef APPLY_LIMITS</span>
<a name="l00122"></a>00122 <span class="preprocessor"></span><span class="comment">//dox Limits x to an interval between min_x and max_x.</span>
<a name="l00123"></a>00123 <span class="comment">//dox x must be a variable which can be assigned a value;</span>
<a name="l00124"></a>00124 <span class="comment">//dox Compares using less_than and greater_than.</span>
<a name="l00125"></a>00125 <span class="preprocessor">#define APPLY_LIMITS(max_x, x, min_x) \</span>
<a name="l00126"></a>00126 <span class="preprocessor"> if((x)>(max_x)) x=(max_x); if((x)<(min_x)) x=(min_x);</span>
<a name="l00127"></a>00127 <span class="preprocessor"></span><span class="preprocessor">#endif</span>
<a name="l00128"></a>00128 <span class="preprocessor"></span><span class="preprocessor">#ifndef NORM2</span>
<a name="l00129"></a>00129 <span class="preprocessor"></span><span class="comment">//dox Norm of a 2D vector</span>
<a name="l00130"></a>00130 <span class="preprocessor">#define NORM2(x, y) (sqrt((x)*(x)+(y)*(y)))</span>
<a name="l00131"></a>00131 <span class="preprocessor"></span><span class="preprocessor">#endif</span>
<a name="l00132"></a>00132 <span class="preprocessor"></span><span class="preprocessor">#ifndef NORM3</span>
<a name="l00133"></a>00133 <span class="preprocessor"></span><span class="comment">//dox Norm of a 3D vector</span>
<a name="l00134"></a>00134 <span class="preprocessor">#define NORM3(x, y, z) (sqrt((x)*(x)+(y)*(y)+(z)*(z)))</span>
<a name="l00135"></a>00135 <span class="preprocessor"></span><span class="preprocessor">#endif</span>
<a name="l00136"></a>00136 <span class="preprocessor"></span><span class="preprocessor">#ifndef ROUND</span>
<a name="l00137"></a>00137 <span class="preprocessor"></span><span class="comment">//dox Rounds double or float to the nearest integer.</span>
<a name="l00138"></a>00138 <span class="preprocessor">#define ROUND(x) ((int)(x+0.5))</span>
<a name="l00139"></a>00139 <span class="preprocessor"></span><span class="preprocessor">#endif</span>
<a name="l00140"></a>00140 <span class="preprocessor"></span><span class="preprocessor">#ifndef ROUND_TO</span>
<a name="l00141"></a>00141 <span class="preprocessor"></span><span class="comment">//dox Rounds @c n to the nearest whole number of multiples of @c d.</span>
<a name="l00142"></a>00142 <span class="comment">//dox For example, ROUND_TO(8,5) and ROUND_TO(12,5) will both result in 10.</span>
<a name="l00143"></a>00143 <span class="preprocessor">#define ROUND_TO(n,d) (d*rint(n/d))</span>
<a name="l00144"></a>00144 <span class="preprocessor"></span><span class="preprocessor">#endif</span>
<a name="l00145"></a>00145 <span class="preprocessor"></span><span class="preprocessor">#ifndef SIGN</span>
<a name="l00146"></a>00146 <span class="preprocessor"></span><span class="comment">//dox Sign of a number.</span>
<a name="l00147"></a>00147 <span class="preprocessor">#define SIGN(A) ((A)<0?(-1):(1))</span>
<a name="l00148"></a>00148 <span class="preprocessor"></span><span class="preprocessor">#endif</span>
<a name="l00149"></a>00149 <span class="preprocessor"></span><span class="preprocessor">#ifndef COS_LAW</span>
<a name="l00150"></a>00150 <span class="preprocessor"></span><span class="comment">//dox Law of cosines.</span>
<a name="l00151"></a>00151 <span class="preprocessor">#define COS_LAW(side1, side2, theta) \</span>
<a name="l00152"></a>00152 <span class="preprocessor"> (sqrt(SQR(side1)+SQR(side2)-2.0*(side1)*(side2)*cos(theta)))</span>
<a name="l00153"></a>00153 <span class="preprocessor"></span><span class="preprocessor">#endif</span>
<a name="l00154"></a>00154 <span class="preprocessor"></span><span class="preprocessor">#ifndef INV_COS_LAW</span>
<a name="l00155"></a>00155 <span class="preprocessor"></span><span class="comment">//dox Inverse law of cosines..</span>
<a name="l00156"></a>00156 <span class="preprocessor">#define INV_COS_LAW(oppSide, side1, side2) \</span>
<a name="l00157"></a>00157 <span class="preprocessor"> (acos((SQR(side1)+SQR(side2)-SQR(oppSide))/(2.0*(side1)*(side2))))</span>
<a name="l00158"></a>00158 <span class="preprocessor"></span><span class="preprocessor">#endif</span>
<a name="l00159"></a>00159 <span class="preprocessor"></span>
<a name="l00160"></a>00160 <span class="comment">// isinf not defined on all systems (eg Solaris)</span>
<a name="l00161"></a>00161 <span class="preprocessor">#if defined (__SVR4) && defined (__sun)</span>
<a name="l00162"></a>00162 <span class="preprocessor"></span><span class="preprocessor">#define isfinite(x) \</span>
<a name="l00163"></a>00163 <span class="preprocessor"> __extension__ ({ __typeof (x) __x_f = (x); \</span>
<a name="l00164"></a>00164 <span class="preprocessor"> __builtin_expect(!isnan(__x_f - __x_f), 1); })</span>
<a name="l00165"></a>00165 <span class="preprocessor"></span>
<a name="l00166"></a>00166 <span class="preprocessor">#define isinf(x) \</span>
<a name="l00167"></a>00167 <span class="preprocessor"> __extension__ ({ __typeof (x) __x_i = (x); \</span>
<a name="l00168"></a>00168 <span class="preprocessor"> __builtin_expect(!isnan(__x_i) && !isfinite(__x_i), 0); })</span>
<a name="l00169"></a>00169 <span class="preprocessor"></span><span class="preprocessor">#endif</span>
<a name="l00170"></a>00170 <span class="preprocessor"></span>
<a name="l00171"></a>00171
<a name="l00172"></a>00172 <span class="comment">/*****************************************************************************</span>
<a name="l00173"></a>00173 <span class="comment"> * COMPARISON MACROS</span>
<a name="l00174"></a>00174 <span class="comment"> *****************************************************************************/</span>
<a name="l00175"></a>00175 <span class="preprocessor">#ifndef NEAR</span>
<a name="l00176"></a>00176 <span class="preprocessor"></span><span class="comment">//dox Check that two numbers are sufficiently close.</span>
<a name="l00177"></a>00177 <span class="comment">//dox Compares using less_than and greater_than.</span>
<a name="l00178"></a>00178 <span class="preprocessor">#define NEAR(x,y,epsilon) (((x) > (y)-(epsilon)) && ((x) < (y)+(epsilon))) </span>
<a name="l00179"></a>00179 <span class="preprocessor"></span><span class="preprocessor">#endif</span>
<a name="l00180"></a>00180 <span class="preprocessor"></span>
<a name="l00181"></a>00181 <span class="comment">//dox Modifies x to lie within [x_min,x_max]</span>
<a name="l00182"></a>00182 <span class="comment">//dox</span>
<a name="l00183"></a>00183 <span class="keyword">template</span><<span class="keyword">typename</span> T>
<a name="l00184"></a>00184 GBXUTILACFR_EXPORT <span class="keywordtype">void</span>
<a name="l00185"></a>00185 CLIP_TO_LIMITS( <span class="keyword">const</span> T &min_x, T &x, <span class="keyword">const</span> T &max_x )
<a name="l00186"></a>00186 {
<a name="l00187"></a>00187 assert( min_x <= max_x );
<a name="l00188"></a>00188 <span class="keywordflow">if</span> ( x > max_x )
<a name="l00189"></a>00189 x = max_x;
<a name="l00190"></a>00190 <span class="keywordflow">else</span> <span class="keywordflow">if</span> ( x < min_x )
<a name="l00191"></a>00191 x = min_x;
<a name="l00192"></a>00192 }
<a name="l00193"></a>00193
<a name="l00194"></a>00194 <span class="preprocessor">#endif</span>
</pre></div></div>
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