89 inline Vector2& operator=(
const T*);
90 inline void set(T, T);
92 inline bool operator==(
const Vector2<T>&)
const;
93 inline bool operator!=(
const Vector2<T>&)
const;
95 inline const T& operator[](
int x)
const;
96 inline T& operator[](
int);
97 inline operator const T*()
const;
102 inline void operator*=(T);
103 inline void operator/=(T);
108 inline Vector2 operator-()
const;
109 inline Vector2 operator+()
const;
111 inline Vector2 operator*(T)
const;
112 inline Vector2 operator/(T)
const;
117 inline T length()
const;
118 inline T lengthSquared()
const;
119 inline void normalize();
128 template<
class T>
class Vector3
138 inline Vector3& operator=(
const T*);
140 inline void set(T, T, T);
142 inline bool operator==(
const Vector3<T>&)
const;
143 inline bool operator!=(
const Vector3<T>&)
const;
147 inline T& operator[](
int);
148 inline const T& operator[](
int)
const;
149 inline operator const T*()
const;
150 inline operator T*();
151 inline const T* data()
const {
return v;}
152 inline T* data() {
return v;}
156 inline void operator*=(T);
157 inline void operator/=(T);
162 inline Vector3 operator-()
const;
163 inline Vector3 operator+()
const;
165 inline Vector3 operator*(T)
const;
166 inline Vector3 operator/(T)
const;
173 inline T latitude()
const;
175 inline T longitude()
const;
179 inline T angleNormalized(
const Vector3<T>&)
const;
181 inline T length()
const;
182 inline T lengthSquared()
const;
183 inline void normalize();
185 inline void transfo4d(
const Mat4d&);
186 inline void transfo4d(
const Mat4f&);
189 inline Vec3f toVec3f()
const;
190 inline Vec3d toVec3d()
const;
194 QString toString()
const {
return QString(
"[%1, %2, %3]").arg(v[0]).arg(v[1]).arg(v[2]);}
195 QString toStringLonLat()
const {
return QString(
"[") + QString::number(longitude()*180./M_PI,
'g', 12) +
"," + QString::number(latitude()*180./M_PI,
'g', 12)+
"]";}
202 template<
class T>
class Vector4
211 inline Vector4& operator=(
const T*);
212 inline void set(T, T, T, T);
214 inline bool operator==(
const Vector4<T>&)
const;
215 inline bool operator!=(
const Vector4<T>&)
const;
217 inline T& operator[](
int);
218 inline const T& operator[](
int)
const;
219 inline operator T*();
220 inline operator const T*()
const;
224 inline void operator*=(T);
225 inline void operator/=(T);
230 inline Vector4 operator-()
const;
231 inline Vector4 operator+()
const;
233 inline Vector4 operator*(T)
const;
234 inline Vector4 operator/(T)
const;
239 inline T length()
const;
240 inline T lengthSquared()
const;
241 inline void normalize();
243 inline void transfo4d(
const Mat4d&);
251 template<
class T>
class Matrix3
259 inline Matrix3& operator=(
const T*);
260 inline void set(T,T,T,T,T,T,T,T,T);
262 inline T& operator[](
int);
263 inline operator T*();
264 inline operator const T*()
const;
277 inline void print(
void)
const;
285 template<
class T>
class Matrix4
289 Matrix4(T,T,T,T,T,T,T,T,T,T,T,T,T,T,T,T);
294 inline Matrix4& operator=(
const T*);
295 inline void set(T,T,T,T,T,T,T,T,T,T,T,T,T,T,T,T);
297 inline T& operator[](
int);
298 inline operator T*();
299 inline operator const T*()
const;
328 inline Vector4<T> getRow(
const int row)
const;
329 inline Vector4<T> getColumn(
const int column)
const;
332 inline QMatrix4x4 convertToQMatrix()
const;
334 inline void print(
void)
const;
340 template<
class T> QDataStream& operator<<(QDataStream& out, const Vector2<T>& v) {out << v[0] << v[1];
return out;}
341 template<
class T> QDataStream& operator<<(QDataStream& out, const Vector3<T>& v) {out << v[0] << v[1] << v[2];
return out;}
342 template<
class T> QDataStream& operator<<(QDataStream& out, const Vector4<T>& v) {out << v[0] << v[1] << v[2] << v[3];
return out;}
343 template<
class T> QDataStream& operator<<(QDataStream& out, const Matrix4<T>& m) {out << m[0] << m[1] << m[2] << m[3] << m[4] << m[5] << m[6] << m[7] << m[8] << m[9] << m[10] << m[11] << m[12] << m[13] << m[14] << m[15];
return out;}
344 template<
class T> QDataStream& operator<<(QDataStream& out, const Matrix3<T>& m) {out << m[0] << m[1] << m[2] << m[3] << m[4] << m[5] << m[6] << m[7] << m[8];
return out;}
346 template<
class T> QDataStream&
operator>>(QDataStream& in,
Vector2<T>& v) {in >> v[0] >> v[1];
return in;}
347 template<
class T> QDataStream&
operator>>(QDataStream& in,
Vector3<T>& v) {in >> v[0] >> v[1] >> v[2];
return in;}
348 template<
class T> QDataStream&
operator>>(QDataStream& in,
Vector4<T>& v) {in >> v[0] >> v[1] >> v[2] >> v[3];
return in;}
349 template<
class T> QDataStream&
operator>>(QDataStream& in,
Matrix4<T>& m) {in >> m[0] >> m[1] >> m[2] >> m[3] >> m[4] >> m[5] >> m[6] >> m[7] >> m[8] >> m[9] >> m[10] >> m[11] >> m[12] >> m[13] >> m[14] >> m[15];
return in;}
350 template<
class T> QDataStream&
operator>>(QDataStream& in,
Matrix3<T>& m) {in >> m[0] >> m[1] >> m[2] >> m[3] >> m[4] >> m[5] >> m[6] >> m[7] >> m[8];
return in;}
353 template <
class T>
inline bool fuzzyEquals(T a, T b, T eps = std::numeric_limits<T>::epsilon())
355 if(a == b)
return true;
356 if(((a+eps) < b) || ((a-eps) > b))
return false;
377 v[0]=a[0]; v[1]=a[1];
389 return (v[0] == a.v[0] && v[1] == a.v[1]);
394 return (v[0] != a.v[0] || v[1] != a.v[1]);
420 v[0] += a.v[0]; v[1] += a.v[1];
425 v[0] -= a.v[0]; v[1] -= a.v[1];
430 v[0] *= s; v[1] *= s;
435 v[0] /= s; v[1] /= s;
450 return Vector2<T>(v[0] + b.v[0], v[1] + b.v[1]);
455 return Vector2<T>(v[0] - b.v[0], v[1] - b.v[1]);
471 return v[0] * b.v[0] + v[1] * b.v[1];
477 return (T) std::sqrt(v[0] * v[0] + v[1] * v[1]);
482 return v[0] * v[0] + v[1] * v[1];
487 T s = (T) 1 / std::sqrt(v[0] * v[0] + v[1] * v[1]);
513 v[0]=x; v[1]=x; v[2]=x;
518 v[0]=x; v[1]=y; v[2]=z;
535 v[0]=a[0]; v[1]=a[1]; v[2]=a[2];
541 v[0]=x; v[1]=y; v[2]=z;
547 return (v[0] == a.v[0] && v[1] == a.v[1] && v[2] == a.v[2]);
552 return (v[0] != a.v[0] || v[1] != a.v[1] || v[2] != a.v[2]);
557 return ::fuzzyEquals(v[0], a.v[0], eps) && ::fuzzyEquals(v[1], a.v[1], eps) && ::fuzzyEquals(v[2], a.v[2], eps);
582 v[0] += a.v[0]; v[1] += a.v[1]; v[2] += a.v[2];
587 v[0] -= a.v[0]; v[1] -= a.v[1]; v[2] -= a.v[2];
592 v[0] *= s; v[1] *= s; v[2] *= s;
597 v[0] /= s; v[1] /= s; v[2] /= s;
612 return Vector3<T>(v[0] + b.v[0], v[1] + b.v[1], v[2] + b.v[2]);
617 return Vector3<T>(v[0] - b.v[0], v[1] - b.v[1], v[2] - b.v[2]);
622 return Vector3<T>(s * v[0], s * v[1], s * v[2]);
633 return v[0] * b.v[0] + v[1] * b.v[1] + v[2] * b.v[2];
640 return Vector3<T>(v[1] * b.v[2] - v[2] * b.v[1],
641 v[2] * b.v[0] - v[0] * b.v[2],
642 v[0] * b.v[1] - v[1] * b.v[0]);
648 const T cosAngle = dot(b)/std::sqrt(lengthSquared()*b.lengthSquared());
649 return cosAngle>=1 ? 0 : (cosAngle<=-1 ? M_PI : std::acos(cosAngle));
655 const T cosAngle = dot(b);
656 return cosAngle>=1 ? 0 : (cosAngle<=-1 ? M_PI : std::acos(cosAngle));
661 return (T) std::sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]);
666 return v[0] * v[0] + v[1] * v[1] + v[2] * v[2];
671 T s = (T) (1. / std::sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]));
681 v[0]=m.r[0]*v0 + m.r[4]*v1 + m.r[8]*v[2] + m.r[12];
682 v[1]=m.r[1]*v0 + m.r[5]*v1 + m.r[9]*v[2] + m.r[13];
683 v[2]=m.r[2]*v0 + m.r[6]*v1 + m.r[10]*v[2] + m.r[14];
690 v[0]=m.r[0]*v0 + m.r[4]*v1 + m.r[8]*v[2] + m.r[12];
691 v[1]=m.r[1]*v0 + m.r[5]*v1 + m.r[9]*v[2] + m.r[13];
692 v[2]=m.r[2]*v0 + m.r[6]*v1 + m.r[10]*v[2] + m.r[14];
697 return Vec3f(v[0],v[1],v[2]);
702 return Vec3d(v[0],v[1],v[2]);
708 return std::asin(v[2]/length());
714 return std::atan2(v[1],v[0]);
724 v[0]=a.v[0]; v[1]=a.v[1]; v[2]=a.v[2]; v[3]=1;
729 v[0]=x; v[1]=y; v[2]=z; v[3]=1;
734 v[0]=x; v[1]=y; v[2]=z; v[3]=a;
739 v[0]=a.v[0]; v[1]=a.v[1]; v[2]=a.v[2]; v[3]=1;
745 v[0]=a[0]; v[1]=a[1]; v[2]=a[2]; v[3]=a[3];
751 v[0]=x; v[1]=y; v[2]=z; v[3]=a;
756 return (v[0] == a.v[0] && v[1] == a.v[1] && v[2] == a.v[2] && v[3] == a.v[3]);
761 return (v[0] != a.v[0] || v[1] != a.v[1] || v[2] != a.v[2] || v[3] != a.v[3]);
786 v[0] += a.v[0]; v[1] += a.v[1]; v[2] += a.v[2]; v[3] += a.v[3];
791 v[0] -= a.v[0]; v[1] -= a.v[1]; v[2] -= a.v[2]; v[3] -= a.v[3];
796 v[0] *= s; v[1] *= s; v[2] *= s; v[3] *= s;
801 v[0] /= s; v[1] /= s; v[2] /= s; v[3] /= s;
806 return Vector4<T>(-v[0], -v[1], -v[2], -v[3]);
816 return Vector4<T>(v[0] + b.v[0], v[1] + b.v[1], v[2] + b.v[2], v[3] + b.v[3]);
821 return Vector4<T>(v[0] - b.v[0], v[1] - b.v[1], v[2] - b.v[2], v[3] - b.v[3]);
826 return Vector4<T>(s * v[0], s * v[1], s * v[2], s * v[3]);
831 return Vector4<T>(v[0]/s, v[1]/s, v[2]/s, v[3]/s);
836 return v[0] * b.v[0] + v[1] * b.v[1] + v[2] * b.v[2] + v[3] * b.v[3];
841 return (T) std::sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2] + v[3] * v[3]);
846 return v[0] * v[0] + v[1] * v[1] + v[2] * v[2] + v[3] * v[3];
851 T s = (T) (1. / std::sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2] + v[3] * v[3]));
875 memcpy(r,m,
sizeof(T)*9);
880 r[0] = v0.v[0]; r[3] = v1.v[0]; r[6] = v2.v[0];
881 r[1] = v0.v[1]; r[4] = v1.v[1]; r[7] = v2.v[1];
882 r[2] = v0.v[2]; r[5] = v1.v[2]; r[8] = v2.v[2];
887 r[0] = a; r[3] = d; r[6] = g;
888 r[1] = b; r[4] = e; r[7] = h;
889 r[2] = c; r[5] = f; r[8] = i;
892 template<
class T>
void Matrix3<T>::set(T a, T b, T c, T d, T e, T f, T g, T h, T i)
894 r[0] = a; r[3] = d; r[6] = g;
895 r[1] = b; r[4] = e; r[7] = h;
896 r[2] = c; r[5] = f; r[8] = i;
924 return Vector3<T>(r[0]*a.v[0] + r[3]*a.v[1] + r[6]*a.v[2],
925 r[1]*a.v[0] + r[4]*a.v[1] + r[7]*a.v[2],
926 r[2]*a.v[0] + r[5]*a.v[1] + r[8]*a.v[2]);
938 #define MATMUL(R, C) (r[R] * a.r[C] + r[R+3] * a.r[C+1] + r[R+6] * a.r[C+2])
939 return Matrix3<T>(MATMUL(0,0), MATMUL(1,0), MATMUL(2,0),
940 MATMUL(0,3), MATMUL(1,3), MATMUL(2,3),
941 MATMUL(0,6), MATMUL(1,6), MATMUL(2,6));
948 return Matrix3<T>(r[0]+a.r[0], r[1]+a.r[1], r[2]+a.r[2],
949 r[3]+a.r[3], r[4]+a.r[4], r[5]+a.r[5],
950 r[6]+a.r[6], r[7]+a.r[7], r[8]+a.r[8]);
955 return Matrix3<T>(r[0]-a.r[0], r[1]-a.r[1], r[2]-a.r[2],
956 r[3]-a.r[3], r[4]-a.r[4], r[5]-a.r[5],
957 r[6]-a.r[6], r[7]-a.r[7], r[8]-a.r[8]);
970 #define SWAP_ROWS(a, b) { T *_tmp = a; (a)=(b); (b)=_tmp; }
971 #define MAT(m,r,c) (m)[(c)*3+(r)]
977 r0 = wtmp[0], r1 = wtmp[1], r2 = wtmp[2];
979 r0[0] = MAT(m, 0, 0), r0[1] = MAT(m, 0, 1), r0[2] = MAT(m, 0, 2),
980 r0[3] = 1.0, r0[4] = r0[5] = 0.0,
981 r1[0] = MAT(m, 1, 0), r1[1] = MAT(m, 1, 1), r1[2] = MAT(m, 1, 2),
982 r1[4] = 1.0, r1[3] = r1[5] = 0.0,
983 r2[0] = MAT(m, 2, 0), r2[1] = MAT(m, 2, 1), r2[2] = MAT(m, 2, 2),
984 r2[5] = 1.0, r2[3] = r2[4] = 0.0;
987 if (fabs(r2[0]) > fabs(r1[0]))
989 if (fabs(r1[0]) > fabs(r0[0]))
1023 if (fabs(r2[1]) > fabs(r1[1]))
1030 r2[2] -= m2 * r1[2];
1054 r1[3] = s * (r1[3] - r2[3] * m1), r1[4] = s * (r1[4] - r2[4] * m1), r1[5] = s * (r1[5] - r2[5] * m1);
1056 r0[3] -= r2[3] * m0, r0[4] -= r2[4] * m0, r0[5] -= r2[5] * m0;
1060 r0[3] = s * (r0[3] - r1[3] * m0), r0[4] = s * (r0[4] - r1[4] * m0), r0[5] = s * (r0[5] - r1[5] * m0);
1062 MAT(out, 0, 0) = r0[3]; MAT(out, 0, 1) = r0[4]; MAT(out, 0, 2) = r0[5];
1063 MAT(out, 1, 0) = r1[3]; MAT(out, 1, 1) = r1[4]; MAT(out, 1, 2) = r1[5];
1064 MAT(out, 2, 0) = r2[3]; MAT(out, 2, 1) = r2[4]; MAT(out, 2, 2) = r2[5];
1074 printf(
"[%5.2lf %5.2lf %5.2lf]\n"
1075 "[%5.2lf %5.2lf %5.2lf]\n"
1076 "[%5.2lf %5.2lf %5.2lf]\n",
1088 memcpy(r,m,
sizeof(T)*16);
1115 template<
class T>
Matrix4<T>::Matrix4(T a, T b, T c, T d, T e, T f, T g, T h, T i, T j, T k, T l, T m, T n, T o, T p)
1117 r[0]=a; r[1]=b; r[2]=c; r[3]=d; r[4]=e; r[5]=f; r[6]=g; r[7]=h;
1118 r[8]=i; r[9]=j; r[10]=k; r[11]=l; r[12]=m; r[13]=n; r[14]=o; r[15]=p;
1121 template<
class T>
void Matrix4<T>::set(T a, T b, T c, T d, T e, T f, T g, T h, T i, T j, T k, T l, T m, T n, T o, T p)
1123 r[0]=a; r[1]=b; r[2]=c; r[3]=d; r[4]=e; r[5]=f; r[6]=g; r[7]=h;
1124 r[8]=i; r[9]=j; r[10]=k; r[11]=l; r[12]=m; r[13]=n; r[14]=o; r[15]=p;
1156 a.v[0], a.v[1], a.v[2], 1);
1164 const T c = (T) cos(angle);
1165 const T s = (T) sin(angle);
1167 return Matrix4<T>(a[0]*a[0]*d+c , a[1]*a[0]*d+a[2]*s, a[0]*a[2]*d-a[1]*s, 0,
1168 a[0]*a[1]*d-a[2]*s, a[1]*a[1]*d+c , a[1]*a[2]*d+a[0]*s, 0,
1169 a[0]*a[2]*d+a[1]*s, a[1]*a[2]*d-a[0]*s, a[2]*a[2]*d+c , 0,
1175 T c = (T) cos(angle);
1176 T s = (T) sin(angle);
1187 T c = (T) cos(angle);
1188 T s = (T) sin(angle);
1199 T c = (T) cos(angle);
1200 T s = (T) sin(angle);
1220 return scaling(
Vector3<T>(scale, scale, scale));
1226 return Vector3<T>(r[0]*a.v[0] + r[4]*a.v[1] + r[8]*a.v[2] + r[12],
1227 r[1]*a.v[0] + r[5]*a.v[1] + r[9]*a.v[2] + r[13],
1228 r[2]*a.v[0] + r[6]*a.v[1] + r[10]*a.v[2] + r[14]);
1233 return Vector3<T>(r[0]*a.v[0] + r[4]*a.v[1] + r[8]*a.v[2],
1234 r[1]*a.v[0] + r[5]*a.v[1] + r[9]*a.v[2],
1235 r[2]*a.v[0] + r[6]*a.v[1] + r[10]*a.v[2]);
1241 return Vector4<T>(r[0]*a.v[0] + r[4]*a.v[1] + r[8]*a.v[2] + r[12]*a.v[3],
1242 r[1]*a.v[0] + r[5]*a.v[1] + r[9]*a.v[2] + r[13]*a.v[3],
1243 r[2]*a.v[0] + r[6]*a.v[1] + r[10]*a.v[2] + r[14]*a.v[3]);
1248 a.set(r[0]*a.v[0] + r[4]*a.v[1] + r[8]*a.v[2] + r[12],
1249 r[1]*a.v[0] + r[5]*a.v[1] + r[9]*a.v[2] + r[13],
1250 r[2]*a.v[0] + r[6]*a.v[1] + r[10]*a.v[2] + r[14]);
1256 r[1], r[5], r[9], r[13],
1257 r[2], r[6], r[10], r[14],
1258 r[3], r[7], r[11], r[15]);
1263 #define MATMUL(R, C) (r[R] * a.r[C] + r[R+4] * a.r[C+1] + r[R+8] * a.r[C+2] + r[R+12] * a.r[C+3])
1264 return Matrix4<T>(MATMUL(0,0) , MATMUL(1,0) , MATMUL(2,0) , MATMUL(3,0) ,
1265 MATMUL(0,4) , MATMUL(1,4) , MATMUL(2,4) , MATMUL(3,4) ,
1266 MATMUL(0,8) , MATMUL(1,8) , MATMUL(2,8) , MATMUL(3,8) ,
1267 MATMUL(0,12), MATMUL(1,12), MATMUL(2,12), MATMUL(3,12));
1274 return Matrix4<T>(r[0]+a.r[0] , r[1]+a.r[1] , r[2]+a.r[2] , r[3]+a.r[3] ,
1275 r[4]+a.r[4] , r[5]+a.r[5] , r[6]+a.r[6] , r[7]+a.r[7] ,
1276 r[8]+a.r[8] , r[9]+a.r[9] , r[10]+a.r[10], r[11]+a.r[11],
1277 r[12]+a.r[12], r[13]+a.r[13], r[14]+a.r[14], r[15]+a.r[15]);
1282 return Matrix4<T>(r[0]-a.r[0] , r[1]-a.r[1] , r[2]-a.r[2] , r[3]-a.r[3] ,
1283 r[4]-a.r[4] , r[5]-a.r[5] , r[6]-a.r[6] , r[7]-a.r[7] ,
1284 r[8]-a.r[8] , r[9]-a.r[9] , r[10]-a.r[10], r[11]-a.r[11],
1285 r[12]-a.r[12], r[13]-a.r[13], r[14]-a.r[14], r[15]-a.r[15]);
1300 #define SWAP_ROWS(a, b) { T *_tmp = a; (a)=(b); (b)=_tmp; }
1301 #define MAT(m,r,c) (m)[(c)*4+(r)]
1304 T m0, m1, m2, m3, s;
1305 T *r0, *r1, *r2, *r3;
1307 r0 = wtmp[0], r1 = wtmp[1], r2 = wtmp[2], r3 = wtmp[3];
1309 r0[0] = MAT(m, 0, 0), r0[1] = MAT(m, 0, 1),
1310 r0[2] = MAT(m, 0, 2), r0[3] = MAT(m, 0, 3),
1311 r0[4] = 1.0, r0[5] = r0[6] = r0[7] = 0.0,
1312 r1[0] = MAT(m, 1, 0), r1[1] = MAT(m, 1, 1),
1313 r1[2] = MAT(m, 1, 2), r1[3] = MAT(m, 1, 3),
1314 r1[5] = 1.0, r1[4] = r1[6] = r1[7] = 0.0,
1315 r2[0] = MAT(m, 2, 0), r2[1] = MAT(m, 2, 1),
1316 r2[2] = MAT(m, 2, 2), r2[3] = MAT(m, 2, 3),
1317 r2[6] = 1.0, r2[4] = r2[5] = r2[7] = 0.0,
1318 r3[0] = MAT(m, 3, 0), r3[1] = MAT(m, 3, 1),
1319 r3[2] = MAT(m, 3, 2), r3[3] = MAT(m, 3, 3),
1320 r3[7] = 1.0, r3[4] = r3[5] = r3[6] = 0.0;
1323 if (fabs(r3[0]) > fabs(r2[0]))
1325 if (fabs(r2[0]) > fabs(r1[0]))
1327 if (fabs(r1[0]) > fabs(r0[0]))
1374 if (fabs(r3[1]) > fabs(r2[1]))
1376 if (fabs(r2[1]) > fabs(r1[1]))
1384 r2[2] -= m2 * r1[2];
1385 r3[2] -= m3 * r1[2];
1386 r2[3] -= m2 * r1[3];
1387 r3[3] -= m3 * r1[3];
1410 if (fabs(r3[2]) > fabs(r2[2]))
1417 r3[3] -= m3 * r2[3], r3[4] -= m3 * r2[4],
1418 r3[5] -= m3 * r2[5], r3[6] -= m3 * r2[6], r3[7] -= m3 * r2[7];
1432 r2[4] = s * (r2[4] - r3[4] * m2), r2[5] = s * (r2[5] - r3[5] * m2),
1433 r2[6] = s * (r2[6] - r3[6] * m2), r2[7] = s * (r2[7] - r3[7] * m2);
1435 r1[4] -= r3[4] * m1, r1[5] -= r3[5] * m1,
1436 r1[6] -= r3[6] * m1, r1[7] -= r3[7] * m1;
1438 r0[4] -= r3[4] * m0, r0[5] -= r3[5] * m0,
1439 r0[6] -= r3[6] * m0, r0[7] -= r3[7] * m0;
1443 r1[4] = s * (r1[4] - r2[4] * m1), r1[5] = s * (r1[5] - r2[5] * m1),
1444 r1[6] = s * (r1[6] - r2[6] * m1), r1[7] = s * (r1[7] - r2[7] * m1);
1446 r0[4] -= r2[4] * m0, r0[5] -= r2[5] * m0,
1447 r0[6] -= r2[6] * m0, r0[7] -= r2[7] * m0;
1451 r0[4] = s * (r0[4] - r1[4] * m0), r0[5] = s * (r0[5] - r1[5] * m0),
1452 r0[6] = s * (r0[6] - r1[6] * m0), r0[7] = s * (r0[7] - r1[7] * m0);
1454 MAT(out, 0, 0) = r0[4];
1455 MAT(out, 0, 1) = r0[5], MAT(out, 0, 2) = r0[6];
1456 MAT(out, 0, 3) = r0[7], MAT(out, 1, 0) = r1[4];
1457 MAT(out, 1, 1) = r1[5], MAT(out, 1, 2) = r1[6];
1458 MAT(out, 1, 3) = r1[7], MAT(out, 2, 0) = r2[4];
1459 MAT(out, 2, 1) = r2[5], MAT(out, 2, 2) = r2[6];
1460 MAT(out, 2, 3) = r2[7], MAT(out, 3, 0) = r3[4];
1461 MAT(out, 3, 1) = r3[5], MAT(out, 3, 2) = r3[6];
1462 MAT(out, 3, 3) = r3[7];
1478 return Vector4<T>(r[0 + row], r[4 + row], r[8 + row], r[12 + row]);
1483 return Vector4<T>(r[0 + column * 4], r[1 + column * 4], r[2 + column * 4], r[3 + column * 4]);
1488 return QMatrix4x4( r[0], r[4], r[8],r[12],
1489 r[1], r[5], r[9],r[13],
1490 r[2], r[6],r[10],r[14],
1491 r[3], r[7],r[11],r[15] );
1496 printf(
"[%5.2lf %5.2lf %5.2lf %17.12le]\n"
1497 "[%5.2lf %5.2lf %5.2lf %17.12le]\n"
1498 "[%5.2lf %5.2lf %5.2lf %17.12le]\n"
1499 "[%5.2lf %5.2lf %5.2lf %17.12le]\n\n",
1500 r[0],r[4],r[8],r[12],
1501 r[1],r[5],r[9],r[13],
1502 r[2],r[6],r[10],r[14],
1503 r[3],r[7],r[11],r[15]);
1507 template<
class T>
inline
1510 return a.v[0] * b.v[0] + a.v[1] * b.v[1];
1513 template<
class T>
inline
1516 return a.v[0] * b.v[0] + a.v[1] * b.v[1] + a.v[2] * b.v[2];
1519 template<
class T>
inline
1522 return a.v[0]*b.v[0] + a.v[1]*b.v[1] + a.v[2]*b.v[2] + a.v[3]*b.v[3];
1525 template<
class T>
inline
1531 template<
class T>
inline
1537 template<
class T>
inline
1540 return Vector4<T>(s*v[0],s*v[1],s*v[2],s*v[3]);
1543 Q_DECLARE_TYPEINFO(
Vec2d, Q_PRIMITIVE_TYPE);
1544 Q_DECLARE_TYPEINFO(
Vec2f, Q_PRIMITIVE_TYPE);
1545 Q_DECLARE_TYPEINFO(
Vec2i, Q_PRIMITIVE_TYPE);
1546 Q_DECLARE_TYPEINFO(
Vec3d, Q_PRIMITIVE_TYPE);
1547 Q_DECLARE_TYPEINFO(
Vec3f, Q_PRIMITIVE_TYPE);
1548 Q_DECLARE_TYPEINFO(
Vec4d, Q_PRIMITIVE_TYPE);
1549 Q_DECLARE_TYPEINFO(
Vec4f, Q_PRIMITIVE_TYPE);
1550 Q_DECLARE_TYPEINFO(
Vec4i, Q_PRIMITIVE_TYPE);
1551 Q_DECLARE_TYPEINFO(
Mat4d, Q_PRIMITIVE_TYPE);
1552 Q_DECLARE_TYPEINFO(
Mat4f, Q_PRIMITIVE_TYPE);
1553 Q_DECLARE_TYPEINFO(
Mat3d, Q_PRIMITIVE_TYPE);
1554 Q_DECLARE_TYPEINFO(
Mat3f, Q_PRIMITIVE_TYPE);
1558 inline QVector3D operator*(
const QMatrix3x3& mat,
const QVector3D& vec)
1561 x = vec.x() * mat(0,0) +
1562 vec.y() * mat(0,1) +
1564 y = vec.x() * mat(1,0) +
1565 vec.y() * mat(1,1) +
1567 z = vec.x() * mat(2,0) +
1568 vec.y() * mat(2,1) +
1570 return QVector3D(x,y,z);
1573 #endif // _VECMATH_H_
bool fuzzyEquals(const Vector3< T > &, T epsilon=std::numeric_limits< T >::epsilon()) const
allows for a fuzzy comparison using some epsilon value
A templatized column-major 3x3 matrix compatible with openGL (mostly for NormalMatrix calculation)...
A templatized 2d vector compatible with openGL.
A templatized column-major 4x4 matrix compatible with openGL.
A templatized 4d vector compatible with openGL.
QDataStream & operator>>(QDataStream &in, SphericalRegionP ®ion)
Load the SphericalRegionP from a binary blob.
A templatized 3d vector compatible with openGL.