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：
1 #include <windows.h>
2 #include <xnamath.h>
3 #include <iostream>
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,1.0f
38 );
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 }
