这是国内找不到的超好文章。(为什么大陆的4元数文章很垃圾呢?) (翻译中。。。奉献给大家~~) 70秒即懂,能使用,用四元数,4元数,阔特尼恩,Quaternion旋转 ★这个页面的对象读者 ★旋转篇: 正规地用虚数单位i,j,k的写法的话, (2)四元数之间的乘法 A = (a; U) (3)3次元的坐标的四元数表示 (4)旋转的四元数表示 那么,如要实行旋转, 请像这样三明治式地计算。这个值的虚部就是旋转之后的点的坐标值。 *未完。。。 |
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2007-04-22
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2007-04-15
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2007-04-10
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前腐后继 2007-3-7 00:52:00
/// Quaternion.cpp
/// (C) Toru Nakata, toru-nakata@aist.go.jp
/// 2004 Dec 29
#include <math.h>
#include <iostream.h>
/// Define Data type
typedef struct
{
double t; // real-component
double x; // x-component
double y; // y-component
double z; // z-component
} quaternion;
//// Kakezan
quaternion Kakezan(quaternion left, quaternion right)
{
quaternion ans;
double d1, d2, d3, d4;
d1 = left.t * right.t;
d2 = -left.x * right.x;
d3 = -left.y * right.y;
d4 = -left.z * right.z;
ans.t = d1+ d2+ d3+ d4;
d1 = left.t * right.x;
d2 = right.t * left.x;
d3 = left.y * right.z;
d4 = -left.z * right.y;
ans.x = d1+ d2+ d3+ d4;
d1 = left.t * right.y;
d2 = right.t * left.y;
d3 = left.z * right.x;
d4 = -left.x * right.z;
ans.y = d1+ d2+ d3+ d4;
d1 = left.t * right.z;
d2 = right.t * left.z;
d3 = left.x * right.y;
d4 = -left.y * right.x;
ans.z = d1+ d2+ d3+ d4;
return ans;
}
//// Make Rotational quaternion
quaternion MakeRotationalQuaternion(double radian, double AxisX, double AxisY, double AxisZ)
{
quaternion ans;
double norm;
double ccc, sss;
ans.t = ans.x = ans.y = ans.z = 0.0;
norm = AxisX * AxisX + AxisY * AxisY + AxisZ * AxisZ;
if(norm <= 0.0) return ans;
norm = 1.0 / sqrt(norm);
AxisX *= norm;
AxisY *= norm;
AxisZ *= norm;
ccc = cos(0.5 * radian);
sss = sin(0.5 * radian);
ans.t = ccc;
ans.x = sss * AxisX;
ans.y = sss * AxisY;
ans.z = sss * AxisZ;
return ans;
}
//// Put XYZ into quaternion
quaternion PutXYZToQuaternion(double PosX, double PosY, double PosZ)
{
quaternion ans;
ans.t = 0.0;
ans.x = PosX;
ans.y = PosY;
ans.z = PosZ;
return ans;
}
///// main
int main()
{
double px, py, pz;
double ax, ay, az, th;
quaternion ppp, qqq, rrr;
cout << "Point Position (x, y, z) " << endl;
cout << " x = ";
cin >> px;
cout << " y = ";
cin >> py;
cout << " z = ";
cin >> pz;
ppp = PutXYZToQuaternion(px, py, pz);
while(1) {
cout << "\nRotation Degree ? (Enter 0 to Quit) " << endl;
cout << " angle = ";
cin >> th;
if(th == 0.0) break;
cout << "Rotation Axis Direction ? (x, y, z) " << endl;
cout << " x = ";
cin >> ax;
cout << " y = ";
cin >> ay;
cout << " z = ";
cin >> az;
th *= 3.1415926535897932384626433832795 / 180.0; /// Degree -> radian;
qqq = MakeRotationalQuaternion(th, ax, ay, az);
rrr = MakeRotationalQuaternion(-th, ax, ay, az);
ppp = Kakezan(rrr, ppp);
ppp = Kakezan(ppp, qqq);
cout << "\nAnser X = " << ppp.x
<< "\n Y = " << ppp.y
<< "\n Z = " << ppp.z << endl;
}
return 0;
} -
前腐后继 2007-3-7 00:53:00
/// Quaternion.cpp
/// (C) Toru Nakata, toru-nakata@aist.go.jp
/// 2004 Dec 29
#include <math.h>
#include <iostream.h>
/// Define Data type
typedef struct
{
double t; // real-component
double x; // x-component
double y; // y-component
double z; // z-component
} quaternion;
//// Kakezan
quaternion Kakezan(quaternion left, quaternion right)
{
quaternion ans;
double d1, d2, d3, d4;
d1 = left.t * right.t;
d2 = -left.x * right.x;
d3 = -left.y * right.y;
d4 = -left.z * right.z;
ans.t = d1+ d2+ d3+ d4;
d1 = left.t * right.x;
d2 = right.t * left.x;
d3 = left.y * right.z;
d4 = -left.z * right.y;
ans.x = d1+ d2+ d3+ d4;
d1 = left.t * right.y;
d2 = right.t * left.y;
d3 = left.z * right.x;
d4 = -left.x * right.z;
ans.y = d1+ d2+ d3+ d4;
d1 = left.t * right.z;
d2 = right.t * left.z;
d3 = left.x * right.y;
d4 = -left.y * right.x;
ans.z = d1+ d2+ d3+ d4;
return ans;
}
//// Make Rotational quaternion
quaternion MakeRotationalQuaternion(double radian, double AxisX, double AxisY, double AxisZ)
{
quaternion ans;
double norm;
double ccc, sss;
ans.t = ans.x = ans.y = ans.z = 0.0;
norm = AxisX * AxisX + AxisY * AxisY + AxisZ * AxisZ;
if(norm <= 0.0) return ans;
norm = 1.0 / sqrt(norm);
AxisX *= norm;
AxisY *= norm;
AxisZ *= norm;
ccc = cos(0.5 * radian);
sss = sin(0.5 * radian);
ans.t = ccc;
ans.x = sss * AxisX;
ans.y = sss * AxisY;
ans.z = sss * AxisZ;
return ans;
}
//// Put XYZ into quaternion
quaternion PutXYZToQuaternion(double PosX, double PosY, double PosZ)
{
quaternion ans;
ans.t = 0.0;
ans.x = PosX;
ans.y = PosY;
ans.z = PosZ;
return ans;
}
///// main
int main()
{
double px, py, pz;
double ax, ay, az, th;
quaternion ppp, qqq, rrr;
cout << "Point Position (x, y, z) " << endl;
cout << " x = ";
cin >> px;
cout << " y = ";
cin >> py;
cout << " z = ";
cin >> pz;
ppp = PutXYZToQuaternion(px, py, pz);
while(1) {
cout << "\nRotation Degree ? (Enter 0 to Quit) " << endl;
cout << " angle = ";
cin >> th;
if(th == 0.0) break;
cout << "Rotation Axis Direction ? (x, y, z) " << endl;
cout << " x = ";
cin >> ax;
cout << " y = ";
cin >> ay;
cout << " z = ";
cin >> az;
th *= 3.1415926535897932384626433832795 / 180.0; /// Degree -> radian;
qqq = MakeRotationalQuaternion(th, ax, ay, az);
rrr = MakeRotationalQuaternion(-th, ax, ay, az);
ppp = Kakezan(rrr, ppp);
ppp = Kakezan(ppp, qqq);
cout << "\nAnser X = " << ppp.x
<< "\n Y = " << ppp.y
<< "\n Z = " << ppp.z << endl;
}
return 0;
}
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/// (C) Toru Nakata, toru-nakata@aist.go.jp
/// 2004 Dec 29
#include <math.h>
#include <iostream.h>
/// Define Data type
typedef struct
{
double t; // real-component
double x; // x-component
double y; // y-component
double z; // z-component
} quaternion;
//// Kakezan
quaternion Kakezan(quaternion left, quaternion right)
{
quaternion ans;
double d1, d2, d3, d4;
d1 = left.t * right.t;
d2 = -left.x * right.x;
d3 = -left.y * right.y;
d4 = -left.z * right.z;
ans.t = d1+ d2+ d3+ d4;
d1 = left.t * right.x;
d2 = right.t * left.x;
d3 = left.y * right.z;
d4 = -left.z * right.y;
ans.x = d1+ d2+ d3+ d4;
d1 = left.t * right.y;
d2 = right.t * left.y;
d3 = left.z * right.x;
d4 = -left.x * right.z;
ans.y = d1+ d2+ d3+ d4;
d1 = left.t * right.z;
d2 = right.t * left.z;
d3 = left.x * right.y;
d4 = -left.y * right.x;
ans.z = d1+ d2+ d3+ d4;
return ans;
}
//// Make Rotational quaternion
quaternion MakeRotationalQuaternion(double radian, double AxisX, double AxisY, double AxisZ)
{
quaternion ans;
double norm;
double ccc, sss;
ans.t = ans.x = ans.y = ans.z = 0.0;
norm = AxisX * AxisX + AxisY * AxisY + AxisZ * AxisZ;
if(norm <= 0.0) return ans;
norm = 1.0 / sqrt(norm);
AxisX *= norm;
AxisY *= norm;
AxisZ *= norm;
ccc = cos(0.5 * radian);
sss = sin(0.5 * radian);
ans.t = ccc;
ans.x = sss * AxisX;
ans.y = sss * AxisY;
ans.z = sss * AxisZ;
return ans;
}
//// Put XYZ into quaternion
quaternion PutXYZToQuaternion(double PosX, double PosY, double PosZ)
{
quaternion ans;
ans.t = 0.0;
ans.x = PosX;
ans.y = PosY;
ans.z = PosZ;
return ans;
}
///// main
int main()
{
double px, py, pz;
double ax, ay, az, th;
quaternion ppp, qqq, rrr;
cout << "Point Position (x, y, z) " << endl;
cout << " x = ";
cin >> px;
cout << " y = ";
cin >> py;
cout << " z = ";
cin >> pz;
ppp = PutXYZToQuaternion(px, py, pz);
while(1) {
cout << "\nRotation Degree ? (Enter 0 to Quit) " << endl;
cout << " angle = ";
cin >> th;
if(th == 0.0) break;
cout << "Rotation Axis Direction ? (x, y, z) " << endl;
cout << " x = ";
cin >> ax;
cout << " y = ";
cin >> ay;
cout << " z = ";
cin >> az;
th *= 3.1415926535897932384626433832795 / 180.0; /// Degree -> radian;
qqq = MakeRotationalQuaternion(th, ax, ay, az);
rrr = MakeRotationalQuaternion(-th, ax, ay, az);
ppp = Kakezan(rrr, ppp);
ppp = Kakezan(ppp, qqq);
cout << "\nAnser X = " << ppp.x
<< "\n Y = " << ppp.y
<< "\n Z = " << ppp.z << endl;
}
return 0;
}