40 #include "FGMatrix33.h"
41 #include "FGColumnVector3.h"
42 #include "FGQuaternion.h"
58 FGMatrix33::FGMatrix33(
void)
60 data[0] = data[1] = data[2] = data[3] = data[4] = data[5] =
61 data[6] = data[7] = data[8] = 0.0;
66 string FGMatrix33::Dump(
const string& delimiter)
const
69 buffer << setw(12) << setprecision(10) << data[0] << delimiter;
70 buffer << setw(12) << setprecision(10) << data[3] << delimiter;
71 buffer << setw(12) << setprecision(10) << data[6] << delimiter;
72 buffer << setw(12) << setprecision(10) << data[1] << delimiter;
73 buffer << setw(12) << setprecision(10) << data[4] << delimiter;
74 buffer << setw(12) << setprecision(10) << data[7] << delimiter;
75 buffer << setw(12) << setprecision(10) << data[2] << delimiter;
76 buffer << setw(12) << setprecision(10) << data[5] << delimiter;
77 buffer << setw(12) << setprecision(10) << data[8];
83 string FGMatrix33::Dump(
const string& delimiter,
const string& prefix)
const
87 buffer << prefix << right << fixed << setw(9) << setprecision(6) << data[0] << delimiter;
88 buffer << right << fixed << setw(9) << setprecision(6) << data[3] << delimiter;
89 buffer << right << fixed << setw(9) << setprecision(6) << data[6] << endl;
91 buffer << prefix << right << fixed << setw(9) << setprecision(6) << data[1] << delimiter;
92 buffer << right << fixed << setw(9) << setprecision(6) << data[4] << delimiter;
93 buffer << right << fixed << setw(9) << setprecision(6) << data[7] << endl;
95 buffer << prefix << right << fixed << setw(9) << setprecision(6) << data[2] << delimiter;
96 buffer << right << fixed << setw(9) << setprecision(6) << data[5] << delimiter;
97 buffer << right << fixed << setw(9) << setprecision(6) << data[8];
99 buffer << setw(0) << left;
113 tempQ[0] = 1.0 + data[0] + data[4] + data[8];
114 tempQ[1] = 1.0 + data[0] - data[4] - data[8];
115 tempQ[2] = 1.0 - data[0] + data[4] - data[8];
116 tempQ[3] = 1.0 - data[0] - data[4] + data[8];
120 for (
int i=1; i<4; i++)
if (tempQ[i] > tempQ[idx]) idx = i;
124 Q(1) = 0.50*sqrt(tempQ[0]);
125 Q(2) = 0.25*(data[7] - data[5])/Q(1);
126 Q(3) = 0.25*(data[2] - data[6])/Q(1);
127 Q(4) = 0.25*(data[3] - data[1])/Q(1);
130 Q(2) = 0.50*sqrt(tempQ[1]);
131 Q(1) = 0.25*(data[7] - data[5])/Q(2);
132 Q(3) = 0.25*(data[3] + data[1])/Q(2);
133 Q(4) = 0.25*(data[2] + data[6])/Q(2);
136 Q(3) = 0.50*sqrt(tempQ[2]);
137 Q(1) = 0.25*(data[2] - data[6])/Q(3);
138 Q(2) = 0.25*(data[3] + data[1])/Q(3);
139 Q(4) = 0.25*(data[7] + data[5])/Q(3);
142 Q(4) = 0.50*sqrt(tempQ[3]);
143 Q(1) = 0.25*(data[3] - data[1])/Q(4);
144 Q(2) = 0.25*(data[6] + data[2])/Q(4);
145 Q(3) = 0.25*(data[7] + data[5])/Q(4);
162 bool GimbalLock =
false;
164 if (data[6] <= -1.0) {
165 mEulerAngles(2) = 0.5*M_PI;
168 else if (1.0 <= data[6]) {
169 mEulerAngles(2) = -0.5*M_PI;
173 mEulerAngles(2) = asin(-data[6]);
176 mEulerAngles(1) = atan2(-data[5], data[4]);
178 mEulerAngles(1) = atan2(data[7], data[8]);
181 mEulerAngles(3) = 0.0;
183 double psi = atan2(data[3], data[0]);
186 mEulerAngles(3) = psi;
194 ostream& operator<<(ostream& os,
const FGMatrix33& M)
196 for (
unsigned int i=1; i<=M.
Rows(); i++) {
197 for (
unsigned int j=1; j<=M.
Cols(); j++) {
201 os << M(i,j) <<
", ";
209 istream& operator>>(istream& is, FGMatrix33& M)
211 for (
unsigned int i=1; i<=M.Rows(); i++) {
212 for (
unsigned int j=1; j<=M.Cols(); j++) {
221 double FGMatrix33::Determinant(
void)
const {
222 return data[0]*data[4]*data[8] + data[3]*data[7]*data[2]
223 + data[6]*data[1]*data[5] - data[6]*data[4]*data[2]
224 - data[3]*data[1]*data[8] - data[7]*data[5]*data[0];
234 if (Determinant() != 0.0) {
235 double rdet = 1.0/Determinant();
237 double i11 = rdet*(data[4]*data[8]-data[7]*data[5]);
238 double i21 = rdet*(data[7]*data[2]-data[1]*data[8]);
239 double i31 = rdet*(data[1]*data[5]-data[4]*data[2]);
240 double i12 = rdet*(data[6]*data[5]-data[3]*data[8]);
241 double i22 = rdet*(data[0]*data[8]-data[6]*data[2]);
242 double i32 = rdet*(data[3]*data[2]-data[0]*data[5]);
243 double i13 = rdet*(data[3]*data[7]-data[6]*data[4]);
244 double i23 = rdet*(data[6]*data[1]-data[0]*data[7]);
245 double i33 = rdet*(data[0]*data[4]-data[3]*data[1]);
259 void FGMatrix33::InitMatrix(
void)
261 data[0] = data[1] = data[2] = data[3] = data[4] = data[5] =
262 data[6] = data[7] = data[8] = 0.0;
279 data[8] - M.data[8] );
286 data[0] -= M.data[0];
287 data[1] -= M.data[1];
288 data[2] -= M.data[2];
289 data[3] -= M.data[3];
290 data[4] -= M.data[4];
291 data[5] -= M.data[5];
292 data[6] -= M.data[6];
293 data[7] -= M.data[7];
294 data[8] -= M.data[8];
311 data[8] + M.data[8] );
318 data[0] += M.data[0];
319 data[3] += M.data[3];
320 data[6] += M.data[6];
321 data[1] += M.data[1];
322 data[4] += M.data[4];
323 data[7] += M.data[7];
324 data[2] += M.data[2];
325 data[5] += M.data[5];
326 data[8] += M.data[8];
384 Product.data[0] = data[0]*M.data[0] + data[3]*M.data[1] + data[6]*M.data[2];
385 Product.data[3] = data[0]*M.data[3] + data[3]*M.data[4] + data[6]*M.data[5];
386 Product.data[6] = data[0]*M.data[6] + data[3]*M.data[7] + data[6]*M.data[8];
387 Product.data[1] = data[1]*M.data[0] + data[4]*M.data[1] + data[7]*M.data[2];
388 Product.data[4] = data[1]*M.data[3] + data[4]*M.data[4] + data[7]*M.data[5];
389 Product.data[7] = data[1]*M.data[6] + data[4]*M.data[7] + data[7]*M.data[8];
390 Product.data[2] = data[2]*M.data[0] + data[5]*M.data[1] + data[8]*M.data[2];
391 Product.data[5] = data[2]*M.data[3] + data[5]*M.data[4] + data[8]*M.data[5];
392 Product.data[8] = data[2]*M.data[6] + data[5]*M.data[7] + data[8]*M.data[8];
404 a = data[0]; b=data[3]; c=data[6];
405 data[0] = a*M.data[0] + b*M.data[1] + c*M.data[2];
406 data[3] = a*M.data[3] + b*M.data[4] + c*M.data[5];
407 data[6] = a*M.data[6] + b*M.data[7] + c*M.data[8];
409 a = data[1]; b=data[4]; c=data[7];
410 data[1] = a*M.data[0] + b*M.data[1] + c*M.data[2];
411 data[4] = a*M.data[3] + b*M.data[4] + c*M.data[5];
412 data[7] = a*M.data[6] + b*M.data[7] + c*M.data[8];
414 a = data[2]; b=data[5]; c=data[8];
415 data[2] = a*M.data[0] + b*M.data[1] + c*M.data[2];
416 data[5] = a*M.data[3] + b*M.data[4] + c*M.data[5];
417 data[8] = a*M.data[6] + b*M.data[7] + c*M.data[8];
428 double tmp = 1.0/scalar;
429 Quot.data[0] = data[0] * tmp;
430 Quot.data[3] = data[3] * tmp;
431 Quot.data[6] = data[6] * tmp;
432 Quot.data[1] = data[1] * tmp;
433 Quot.data[4] = data[4] * tmp;
434 Quot.data[7] = data[7] * tmp;
435 Quot.data[2] = data[2] * tmp;
436 Quot.data[5] = data[5] * tmp;
437 Quot.data[8] = data[8] * tmp;
446 double tmp = 1.0/scalar;
462 void FGMatrix33::T(
void)
487 double tmp1 = v1*data[0];
488 double tmp2 = v1*data[1];
489 double tmp3 = v1*data[2];
This class implements a 3 element column vector.
Handles matrix math operations.
unsigned int Cols(void) const
Number of cloumns in the matrix.
unsigned int Rows(void) const
Number of rows in the matrix.
Models the Quaternion representation of rotations.