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Mat2.h
00001 /* 00002 File: Mat2.h 00003 00004 Function: Defines a 2 x 2 matrix. 00005 00006 Author(s): Andrew Willmott 00007 00008 Copyright: (c) 1995-2001, Andrew Willmott 00009 */ 00010 00011 #ifndef __Mat2__ 00012 #define __Mat2__ 00013 00014 #include "Vec2.h" 00015 00016 00017 // --- Mat2 Class ------------------------------------------------------------- 00018 00019 class Mat2 00020 { 00021 public: 00022 00023 // Constructors 00024 00025 Mat2(); 00026 Mat2(Real a, Real b, Real c, Real d); // Create from rows 00027 Mat2(const Mat2 &m); // Copy constructor 00028 Mat2(ZeroOrOne k); 00029 Mat2(Block k); 00030 00031 // Accessor functions 00032 00033 Int Rows() const { return(2); }; 00034 Int Cols() const { return(2); }; 00035 00036 Vec2 &operator [] (Int i); 00037 const Vec2 &operator [] (Int i) const; 00038 00039 Real *Ref() const; // Return pointer to data 00040 00041 // Assignment operators 00042 00043 Mat2 &operator = (const Mat2 &m); 00044 Mat2 &operator = (ZeroOrOne k); 00045 Mat2 &operator = (Block k); 00046 Mat2 &operator += (const Mat2 &m); 00047 Mat2 &operator -= (const Mat2 &m); 00048 Mat2 &operator *= (const Mat2 &m); 00049 Mat2 &operator *= (Real s); 00050 Mat2 &operator /= (Real s); 00051 00052 // Comparison operators 00053 00054 Bool operator == (const Mat2 &m) const; // M == N? 00055 Bool operator != (const Mat2 &m) const; // M != N? 00056 00057 // Arithmetic operators 00058 00059 Mat2 operator + (const Mat2 &m) const; // M + N 00060 Mat2 operator - (const Mat2 &m) const; // M - N 00061 Mat2 operator - () const; // -M 00062 Mat2 operator * (const Mat2 &m) const; // M * N 00063 Mat2 operator * (Real s) const; // M * s 00064 Mat2 operator / (Real s) const; // M / s 00065 00066 // Initialisers 00067 00068 Void MakeZero(); // Zero matrix 00069 Void MakeDiag(Real k = vl_one); // I 00070 Void MakeBlock(Real k = vl_one); // all elts=k 00071 00072 // Vector Transformations 00073 00074 Mat2& MakeRot(Real theta); 00075 Mat2& MakeScale(const Vec2 &s); 00076 00077 // Private... 00078 00079 protected: 00080 00081 Vec2 row[2]; // Rows of the matrix 00082 }; 00083 00084 00085 // --- Matrix operators ------------------------------------------------------- 00086 00087 inline Vec2 &operator *= (Vec2 &v, const Mat2 &m); // v *= m 00088 inline Vec2 operator * (const Mat2 &m, const Vec2 &v); // m * v 00089 inline Vec2 operator * (const Vec2 &v, const Mat2 &m); // v * m 00090 inline Mat2 operator * (Real s, const Mat2 &m); // s * m 00091 00092 inline Mat2 trans(const Mat2 &m); // Transpose 00093 inline Real trace(const Mat2 &m); // Trace 00094 inline Mat2 adj(const Mat2 &m); // Adjoint 00095 Real det(const Mat2 &m); // Determinant 00096 Mat2 inv(const Mat2 &m); // Inverse 00097 Mat2 oprod(const Vec2 &a, const Vec2 &b); 00098 // Outer product 00099 00100 // The xform functions help avoid dependence on whether row or column 00101 // vectors are used to represent points and vectors. 00102 inline Vec2 xform(const Mat2 &m, const Vec2 &v); // Transform of v by m 00103 inline Mat2 xform(const Mat2 &m, const Mat2 &n); // xform v -> m(n(v)) 00104 00105 //std::ostream &operator << (std::ostream &s, const Mat2 &m); 00106 //std::istream &operator >> (std::istream &s, Mat2 &m); 00107 00108 void printMat2(const Mat2 &m); 00109 00110 00111 // --- Inlines ---------------------------------------------------------------- 00112 00113 inline Vec2 &Mat2::operator [] (Int i) 00114 { 00115 CheckRange(i, 0, 2, "(Mat2::[i]) index out of range"); 00116 return(row[i]); 00117 } 00118 00119 inline const Vec2 &Mat2::operator [] (Int i) const 00120 { 00121 CheckRange(i, 0, 2, "(Mat2::[i]) index out of range"); 00122 return(row[i]); 00123 } 00124 00125 inline Real *Mat2::Ref() const 00126 { 00127 return((Real*) row); 00128 } 00129 00130 inline Mat2::Mat2() 00131 { 00132 } 00133 00134 inline Mat2::Mat2(Real a, Real b, Real c, Real d) 00135 { 00136 row[0][0] = a; row[0][1] = b; 00137 row[1][0] = c; row[1][1] = d; 00138 } 00139 00140 inline Mat2::Mat2(const Mat2 &m) 00141 { 00142 row[0] = m[0]; 00143 row[1] = m[1]; 00144 } 00145 00146 00147 inline Void Mat2::MakeZero() 00148 { 00149 row[0][0] = vl_zero; row[0][1] = vl_zero; 00150 row[1][0] = vl_zero; row[1][1] = vl_zero; 00151 } 00152 00153 inline Void Mat2::MakeDiag(Real k) 00154 { 00155 row[0][0] = k; row[0][1] = vl_zero; 00156 row[1][0] = vl_zero; row[1][1] = k; 00157 } 00158 00159 inline Void Mat2::MakeBlock(Real k) 00160 { 00161 row[0][0] = k; row[0][1] = k; 00162 row[1][0] = k; row[1][1] = k; 00163 } 00164 00165 inline Mat2::Mat2(ZeroOrOne k) 00166 { 00167 MakeDiag(k); 00168 } 00169 00170 inline Mat2::Mat2(Block k) 00171 { 00172 MakeBlock((ZeroOrOne) k); 00173 } 00174 00175 inline Mat2 &Mat2::operator = (ZeroOrOne k) 00176 { 00177 MakeDiag(k); 00178 00179 return(SELF); 00180 } 00181 00182 inline Mat2 &Mat2::operator = (Block k) 00183 { 00184 MakeBlock((ZeroOrOne) k); 00185 00186 return(SELF); 00187 } 00188 00189 inline Mat2 &Mat2::operator = (const Mat2 &m) 00190 { 00191 row[0] = m[0]; 00192 row[1] = m[1]; 00193 00194 return(SELF); 00195 } 00196 00197 inline Mat2 &Mat2::operator += (const Mat2 &m) 00198 { 00199 row[0] += m[0]; 00200 row[1] += m[1]; 00201 00202 return(SELF); 00203 } 00204 00205 inline Mat2 &Mat2::operator -= (const Mat2 &m) 00206 { 00207 row[0] -= m[0]; 00208 row[1] -= m[1]; 00209 00210 return(SELF); 00211 } 00212 00213 inline Mat2 &Mat2::operator *= (const Mat2 &m) 00214 { 00215 SELF = SELF * m; 00216 00217 return(SELF); 00218 } 00219 00220 inline Mat2 &Mat2::operator *= (Real s) 00221 { 00222 row[0] *= s; 00223 row[1] *= s; 00224 00225 return(SELF); 00226 } 00227 00228 inline Mat2 &Mat2::operator /= (Real s) 00229 { 00230 row[0] /= s; 00231 row[1] /= s; 00232 00233 return(SELF); 00234 } 00235 00236 00237 inline Mat2 Mat2::operator + (const Mat2 &m) const 00238 { 00239 Mat2 result; 00240 00241 result[0] = row[0] + m[0]; 00242 result[1] = row[1] + m[1]; 00243 00244 return(result); 00245 } 00246 00247 inline Mat2 Mat2::operator - (const Mat2 &m) const 00248 { 00249 Mat2 result; 00250 00251 result[0] = row[0] - m[0]; 00252 result[1] = row[1] - m[1]; 00253 00254 return(result); 00255 } 00256 00257 inline Mat2 Mat2::operator - () const 00258 { 00259 Mat2 result; 00260 00261 result[0] = -row[0]; 00262 result[1] = -row[1]; 00263 00264 return(result); 00265 } 00266 00267 inline Mat2 Mat2::operator * (const Mat2 &m) const 00268 { 00269 #define N(x,y) row[x][y] 00270 #define M(x,y) m.row[x][y] 00271 #define R(x,y) result[x][y] 00272 00273 Mat2 result; 00274 00275 R(0,0) = N(0,0) * M(0,0) + N(0,1) * M(1,0); 00276 R(0,1) = N(0,0) * M(0,1) + N(0,1) * M(1,1); 00277 R(1,0) = N(1,0) * M(0,0) + N(1,1) * M(1,0); 00278 R(1,1) = N(1,0) * M(0,1) + N(1,1) * M(1,1); 00279 00280 return(result); 00281 00282 #undef N 00283 #undef M 00284 #undef R 00285 } 00286 00287 inline Mat2 Mat2::operator * (Real s) const 00288 { 00289 Mat2 result; 00290 00291 result[0] = row[0] * s; 00292 result[1] = row[1] * s; 00293 00294 return(result); 00295 } 00296 00297 inline Mat2 Mat2::operator / (Real s) const 00298 { 00299 Mat2 result; 00300 00301 result[0] = row[0] / s; 00302 result[1] = row[1] / s; 00303 00304 return(result); 00305 } 00306 00307 inline Mat2 operator * (Real s, const Mat2 &m) 00308 { 00309 return(m * s); 00310 } 00311 00312 inline Vec2 operator * (const Mat2 &m, const Vec2 &v) 00313 { 00314 Vec2 result; 00315 00316 result[0] = m[0][0] * v[0] + m[0][1] * v[1]; 00317 result[1] = m[1][0] * v[0] + m[1][1] * v[1]; 00318 00319 return(result); 00320 } 00321 00322 inline Vec2 operator * (const Vec2 &v, const Mat2 &m) 00323 { 00324 Vec2 result; 00325 00326 result[0] = v[0] * m[0][0] + v[1] * m[1][0]; 00327 result[1] = v[0] * m[0][1] + v[1] * m[1][1]; 00328 00329 return(result); 00330 } 00331 00332 inline Vec2 &operator *= (Vec2 &v, const Mat2 &m) 00333 { 00334 Real t; 00335 00336 t = v[0] * m[0][0] + v[1] * m[1][0]; 00337 v[1] = v[0] * m[0][1] + v[1] * m[1][1]; 00338 v[0] = t; 00339 00340 return(v); 00341 } 00342 00343 00344 inline Mat2 trans(const Mat2 &m) 00345 { 00346 Mat2 result; 00347 00348 result[0][0] = m[0][0]; result[0][1] = m[1][0]; 00349 result[1][0] = m[0][1]; result[1][1] = m[1][1]; 00350 00351 return(result); 00352 } 00353 00354 inline Real trace(const Mat2 &m) 00355 { 00356 return(m[0][0] + m[1][1]); 00357 } 00358 00359 inline Mat2 adj(const Mat2 &m) 00360 { 00361 Mat2 result; 00362 00363 result[0] = cross(m[1]); 00364 result[1] = -cross(m[0]); 00365 00366 return(result); 00367 } 00368 00369 #ifdef VL_ROW_ORIENT 00370 inline Vec2 xform(const Mat2 &m, const Vec2 &v) 00371 { return(v * m); } 00372 inline Mat2 xform(const Mat2 &m, const Mat2 &n) 00373 { return(n * m); } 00374 #else 00375 inline Vec2 xform(const Mat2 &m, const Vec2 &v) 00376 { return(m * v); } 00377 inline Mat2 xform(const Mat2 &m, const Mat2 &n) 00378 { return(m * n); } 00379 #endif 00380 00381 #endif
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