266 lines
6.8 KiB
C++
266 lines
6.8 KiB
C++
#include "quaternion.h"
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#include "math.h"
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#include "stdio.h"
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#define PI 3.141592f
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/*给定一个绕单位向量（x,y,z）绕此单位向量旋转angle角度，创建四元数*/
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Quaternion CreateQuaternion(float angle,Vector3 v)
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{
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Quaternion q;
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/*把angle转换为弧度*/
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angle = PI*angle/(180.0f);
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q.w = cos(angle/2.0f);
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q.x = v.x * sin(angle/2);
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q.y = v.y * sin(angle/2);
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q.z = v.z * sin(angle/2);
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return q;
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}
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/*计算两个四元数相乘，返回相乘的结果*/
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Quaternion QuaternionMulti(Quaternion q1,_Quaternion q2)
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{
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Quaternion q;
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float mod;
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/*按照四元数乘法计算系数*/
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q.w = q1.w * q2.w - q1.x * q2.x - q1.y * q2.y - q1.z * q2.z; //按照3D数学基础：图形与游戏开发 中四元数修改的定义
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q.x = q1.w * q2.x + q1.x * q2.w - q1.y * q2.z + q1.z * q2.y; //按照3D数学基础：图形与游戏开发 中四元数修改的定义
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q.y = q1.w * q2.y + q1.y * q2.w + q1.x * q2.z - q1.z * q2.x; //按照3D数学基础：图形与游戏开发 中四元数修改的定义
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q.z = q1.w * q2.z + q1.z * q2.w + q1.y * q2.x - q1.x * q2.y; //按照3D数学基础：图形与游戏开发 中四元数修改的定义
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// //按照四元数乘法标准计算法，实际不用
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//q.w = q1.w * q2.w - q1.x * q2.x - q1.y * q2.y - q1.z * q2.z;
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//q.x = q1.w * q2.x + q1.x * q2.w + q1.y * q2.z - q1.z * q2.y;
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//q.y = q1.w * q2.y - q1.x * q2.z + q1.y * q2.w + q1.z * q2.x;
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//q.z = q1.w * q2.z + q1.x * q2.y - q1.y * q2.x + q1.z * q2.w;
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mod = QuaternionMod(q);
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q.w = q.w/mod; q.x = q.x/mod; q.y = q.y/mod; q.z = q.z/mod;
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return q;
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}
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/*给定四元数求该四元数的共轭四元数*/
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Quaternion QuaternionConjugate(Quaternion q1)
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{
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Quaternion q;
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/*按照四元数乘法计算系数*/
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q.w = q1.w;
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q.x = -q1.x;
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q.y = -q1.y;
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q.z = -q1.z;
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return q;
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}
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/*给定四元数求该四元数的模*/
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float QuaternionMod(Quaternion q1)
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{
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float mod;
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/*按照四元数乘法计算系数*/
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mod = q1.w * q1.w + q1.x * q1.x +
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q1.y * q1.y + q1.z * q1.z;
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mod = sqrt(mod);
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return mod;
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}
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/*给定四元数求该四元数的逆*/
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Quaternion QuaternionInversion(Quaternion q1)
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{
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Quaternion q;
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/*计算四元数模的平方*/
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float mod2 = QuaternionMod(q1);
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/* 按照公式： *q^-1 = (q*)/(|q|)^2 */
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q = QuaternionConjugate(q1);
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q.w = q.w / mod2;
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q.x = q.x / mod2;
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q.y = q.y / mod2;
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q.z = q.z / mod2;
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return q;
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}
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void DisplayQuaternion(Quaternion q)
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{
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float q0,q1,q2,q3;
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q0 = q.w; q1 = q.x; q2 = q.y; q3 = q.z;
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printf("DisplayQuaternion ::w = %f x = %f y = %f z = %f\n",q.w,q.x,q.y,q.z);
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}
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/*欧拉角转四元数*/
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Quaternion EulerAnglesToQuaternion(EulerAngles e)
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{
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Quaternion q;
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e.Pitch = e.Pitch/(180.00f/3.141592f);
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e.Yaw = e.Yaw/ (180.00f/3.141592f);
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e.Roll = e.Roll/ (180.00f/3.141592f);
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// 按照Qz*Qy*Qx 产生四元数
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/*w*/
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q.w = (float)(cos(0.5*e.Roll)*cos(0.5*e.Pitch)*cos(0.5*e.Yaw) - sin(0.5*e.Roll)*sin(0.5*e.Pitch)*sin(0.5*e.Yaw));
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/*x 绕x轴旋转是pitch*/
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q.x = (float)(cos(0.5*e.Roll)*sin(0.5*e.Pitch)*cos(0.5*e.Yaw) - sin(0.5*e.Roll)*cos(0.5*e.Pitch)*sin(0.5*e.Yaw));
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/*y 绕y轴旋转是roll*/
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q.y = (float)(sin(0.5*e.Roll)*cos(0.5*e.Pitch)*cos(0.5*e.Yaw) + cos(0.5*e.Roll)*sin(0.5*e.Pitch)*sin(0.5*e.Yaw));
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/*z 绕z轴旋转是Yaw*/
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q.z = (float)(cos(0.5*e.Roll)*cos(0.5*e.Pitch)*sin(0.5*e.Yaw) + sin(0.5*e.Roll)*sin(0.5*e.Pitch)*cos(0.5*e.Yaw));
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return q;
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}
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EulerAngles QuaternionToEulerAngles(Quaternion q,bool useRefer)
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{
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EulerAngles e;
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/*Pitch 在D3D坐标系中被认为是绕x轴旋转，Roll绕z旋转，Yaw是绕y旋转*/
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float w,x,y,z;
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w = q.w; x = q.x; y = q.y; z = q.z;
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e.Pitch = asin(-2.0f*(y*z-w*x))* (180.0f /PI);
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e.Yaw = atan2(x*z + w*y,0.5f - x*x - y*y)* (180.0f /PI);
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e.Roll = atan2(x*y + w*z,0.5f - x*x - z*z)* (180.0f /PI);
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return e;
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}
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void DisplayEulerAngles(EulerAngles e)
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{
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printf("DisplayEulerAngles::Yaw=%f,Pitch=%f,Roll=%f\n",e.Yaw,e.Pitch,e.Roll);
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}
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void SetEulerAngles(EulerAngles *e,float Yaw,float Pitch,float Roll)
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{
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(*e).Pitch = Pitch; (*e).Roll = Roll;(*e).Yaw = Yaw;
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}
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EulerAngles SetEulerAngles(float Yaw,float Pitch,float Roll)
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{
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EulerAngles e;
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(e).Pitch = Pitch; (e).Roll = Roll;(e).Yaw = Yaw;
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return e;
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}
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Vector3 SetVector3(float x,float y,float z)
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{
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Vector3 v;
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v.x = x;
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v.y = y;
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v.z = z;
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return v;
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}
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bool QuaternionEqual(Quaternion q1,Quaternion q2)
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{
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if(fabsf(q1.w-q2.w)<0.0001f&&
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fabsf(q1.x-q2.x)<0.0001f&&
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fabsf(q1.y-q2.y)<0.0001f&&
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fabsf(q1.z-q2.z)<0.0001f)return true;
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return false;
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}
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Quaternion CreateQuaternionByGyro(float gx,float gy,float gz)
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{
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float qw,qx,qy,qz;
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static float q0 = 1.0f,q1 = 0.0f,q2 = 0.0f,q3 = 0.0f;
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float halfT = 1.0f;
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Quaternion q;
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qw = (-q1*gx - q2*gy - q3*gz)*halfT; /*利用一阶龙格库塔法对四元数进行更新*/
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qx = ( q0*gx + q2*gz - q3*gy)*halfT;
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qy = ( q0*gy - q1*gz + q3*gx)*halfT;
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qz = ( q0*gz + q1*gy - q2*gx)*halfT;
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q0 = q0 + qw;
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q1 = q1 + qx;
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q2 = q2 + qy;
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q3 = q3 + qz;
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q.w = q0;
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q.x = q1;
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q.y = q2;
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q.z = q3;
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float mod2 = QuaternionMod(q); /*求模*/
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q.w = q.w / mod2;
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q.x = q.x / mod2;
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q.y = q.y / mod2;
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q.z = q.z / mod2;
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return q;
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}
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/*把四元数转换为旋转矩阵*/
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Matrix3 QuaternionToMatrix(Quaternion q)
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{
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Matrix3 mMatrix;
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float w,x,y,z;
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w = q.w; x = q.x; y = q.y; z = q.z;
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mMatrix.m[0][0] = 1 - 2*y*y -2*z*z;
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mMatrix.m[0][1] = 2*x*y + 2*w*z;
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mMatrix.m[0][2] = 2*x*y - 2*w*y;
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mMatrix.m[1][0] = 2*x*y - 2*w*z;
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mMatrix.m[1][1] = 1 - 2*x*x -2*z*z;
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mMatrix.m[1][2] = 2*y*z + 2*w*x;
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mMatrix.m[2][0] = 2*x*z + 2*w*z;
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mMatrix.m[2][1] = 2*y*z - 2*w*x;
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mMatrix.m[2][2] = 1 - 2*x*x -2*y*y;
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return mMatrix;
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}
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/* 给定旋转矩阵以及向量，返回旋转后的向量*/
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MVector3 ComputeRotate(Matrix3 mMatrix,MVector3 vec)
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{
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MVector3 mResult;
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int j;
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for(j=0;j<3;j++)
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{
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mResult.v[j] = mMatrix.m[j][0]*vec.v[0] +
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mMatrix.m[j][1]*vec.v[1] +
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mMatrix.m[j][2]*vec.v[2];
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}
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return mResult;
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}
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/*************************************************************************
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* 描 述 ： 把标准笛卡尔坐标系下的四元数转换到欧拉角显示。
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这里的变换公式为物体-惯性四元数转换到欧拉角
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**************************************************************************/
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EulerAngles MathQuaternionToEulerAngles(Quaternion q)
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{
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EulerAngles e;
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/*标准笛卡尔坐标系中，我们认为绕z轴为Yaw，绕x轴为Roll，绕y轴为Pitch*/
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float w,x,y,z;
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w = q.w; x = q.x; y = q.y; z = q.z;
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e.Pitch = asin(-2.0f*(z*x-w*y))* (180.0f /PI);
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e.Yaw = atan2(y*x + w*z,0.5f - y*y - z*z)* (180.0f /PI);
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e.Roll = atan2(y*z + w*x,0.5f - y*y - x*x)* (180.0f /PI);
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return e;
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}
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/*************************************************************************
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* 描 述 ： 把D3D坐标系下的四元数转换到欧拉角显示。
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这里的变换公式为物体-惯性四元数转换到欧拉角
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**************************************************************************/
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EulerAngles D3DQuaternionToEulerAngles(Quaternion q)
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{
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EulerAngles e;
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/*Pitch 在D3D坐标系中被认为是绕x轴旋转，Roll绕z旋转，Yaw是绕y旋转*/
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double w,x,y,z;
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w = q.w; x = q.x; y = q.y; z = q.z;
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e.Pitch = asin(-2.0f*(y*z-w*x))* (180.0f /PI);
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e.Yaw = atan2(x*z + w*y,0.5f - x*x - y*y)* (180.0f /PI);
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e.Roll = atan2(x*y + w*z,0.5f - x*x - z*z)* (180.0f /PI);
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return e;
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} |