Directx11学习笔记【六】基本的数学知识----矩阵篇-白红宇

Directx11学习笔记【六】基本的数学知识----矩阵篇

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发布时间：2019-06-28

本文共 2226 字，大约阅读时间需要 7 分钟。

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

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：

1 #include 
     
       2 #include 
      
        3 #include 
       
         4 using namespace std; 5  6 ostream& operator<<(ostream &os, FXMVECTOR v) 7 { 8     XMFLOAT4 dest; 9     XMStoreFloat4(&dest, v);10     os << "(" << dest.x << "," << dest.y << "," << dest.z << ")";11     return os;12 }13 14 ostream& operator<<(ostream &os, CXMMATRIX m)15 {16     for (int i = 0; i < 4; ++i)17     {18         for (int j = 0; j < 4; ++j)19         {20             os << m(i, j) << "\t";21         }22         os << endl;23     }24     return os;25 }26 27 int main()28 {29     if (!XMVerifyCPUSupport())30     {31         cout << "xna math not supported" << endl;32         return 0;33     }34     XMMATRIX A(1.0f,0.0f,0.0f,0.0f,35                0.0f,2.0f,0.0f,0.0f,36                0.0f,0.0f,4.0f,0.0f,37                1.0f,2.0f,3.0f,1.0f38         );39     XMMATRIX B = XMMatrixIdentity();40     XMMATRIX C = A * B;41     XMMATRIX D = XMMatrixTranspose(A);42     XMVECTOR det = XMMatrixDeterminant(A);43     XMMATRIX E = XMMatrixInverse(&det,A);44     XMMATRIX F = A * E;45 46     cout << "A = " << endl << A << endl;47     cout << "B = " << endl << B << endl;48     cout << "C = A*B = " << endl << C << endl;49     cout << "D = transpose(A) = " << endl << D << endl;50     cout << "det = determinant(A) = " << det << endl << endl;51     cout << "E = inverse(A) = " << endl << E << endl;52     cout << "F = A*E = " << endl << F << endl;53 54     return 0;55 }