Directx11学习笔记【六】 基本的数学知识----矩阵篇

参考dx11龙书 Chapter2 matrix algebra(矩阵代数)

关于矩阵的一些基本概念定理（例如矩阵加减乘法，逆矩阵，伴随矩阵，转置矩阵等）可以参考维基百科

https://zh.wikipedia.org/wiki/

XNA MATRICES

Matrix Types

在xna math中代表一个4*4的矩阵，我们使用XMMATRIX

当在类中存储数据时使用XMFLOAT4X4

用XMMatrixSet创建，原型为

XMMATRIX XMMatrixSet(FLOAT m00,FLOAT m01,FLOAT m02,FLOAT m03,

　　　　　　　　　　　  FLOAT m10,FLOAT m11,FLOAT m12,FLOAT m13,

　　　　　　　　　　　　  FLOAT m20,FLOAT m21,FLOAT m22,FLOAT m23,

　　　　　　　　　　　  FLOAT m30,FLOAT m31,FLOAT m32,FLOAT m33,

　　　　　　　　　　　　);

下面是一些Matrix Functions

XMMATRIX XMMatrixIdentity();//单位矩阵

BOOL XMMatrixIsIdentity(CXMMATRIX M);//判断是否是单位矩阵

XMMATRIX XMMatrixMultiply(CXMMATRIX A,CXMMATRIX B);//矩阵相乘

XMMATRIX XMMatrixTranspose(CXMMATRIX M);//转置矩阵

XMVECTOR XMMatrixDeterminiant(CXMMATRIX M);//矩阵的行列式

XMMATRIX XMMatrixInverse(XMVECTOR *pDeteminiant,CXMMATRIX M);//逆矩阵

下面是dx11龙书给出的测试代码：

 #include <windows.h>
 #include <xnamath.h>
 #include <iostream>
 using namespace std;

 ostream& operator<<(ostream &os, FXMVECTOR v)
 {
     XMFLOAT4 dest;
     XMStoreFloat4(&dest, v);
     os << "(" << dest.x << "," << dest.y << "," << dest.z << ")";
     return os;
 }

 ostream& operator<<(ostream &os, CXMMATRIX m)
 {
     for (int i = ; i < ; ++i)
     {
         for (int j = ; j < ; ++j)
         {
             os << m(i, j) << "\t";
         }
         os << endl;
     }
     return os;
 }

 int main()
 {
     if (!XMVerifyCPUSupport())
     {
         cout << "xna math not supported" << endl;
         return ;
     }
     XMMATRIX A(1.0f,0.0f,0.0f,0.0f,
                0.0f,2.0f,0.0f,0.0f,
                0.0f,0.0f,4.0f,0.0f,
                1.0f,2.0f,3.0f,1.0f
         );
     XMMATRIX B = XMMatrixIdentity();
     XMMATRIX C = A * B;
     XMMATRIX D = XMMatrixTranspose(A);
     XMVECTOR det = XMMatrixDeterminant(A);
     XMMATRIX E = XMMatrixInverse(&det,A);
     XMMATRIX F = A * E;

     cout << "A = " << endl << A << endl;
     cout << "B = " << endl << B << endl;
     cout << "C = A*B = " << endl << C << endl;
     cout << "D = transpose(A) = " << endl << D << endl;
     cout << "det = determinant(A) = " << det << endl << endl;
     cout << "E = inverse(A) = " << endl << E << endl;
     cout << "F = A*E = " << endl << F << endl;

     return ;
 }