首先來看看向量，向量的坐標表示對于DirectX游戲開發來說是必須的，在世界坐標系或投影坐標系下的三角形面的法線，光線的方向和觀察者的方向等都是通過向量的坐標形式來準確給出的。
DirectX的頭文件D3DX9Math.h給出了兩個結構體來支持向量的計算：
typedef struct _D3DVECTOR {
float x;
float y;
float z;
} D3DVECTOR;
typedef struct D3DXVECTOR3 : public D3DVECTOR
{
public:
D3DXVECTOR3() {};
D3DXVECTOR3( CONST FLOAT * );
D3DXVECTOR3( CONST D3DVECTOR& );
D3DXVECTOR3( CONST D3DXFLOAT16 * );
D3DXVECTOR3( FLOAT x, FLOAT y, FLOAT z );
// casting
operator FLOAT* ();
operator CONST FLOAT* () const;
// assignment operators
D3DXVECTOR3& operator += ( CONST D3DXVECTOR3& );
D3DXVECTOR3& operator -= ( CONST D3DXVECTOR3& );
D3DXVECTOR3& operator *= ( FLOAT );
D3DXVECTOR3& operator /= ( FLOAT );
// unary operators
D3DXVECTOR3 operator + () const;
D3DXVECTOR3 operator - () const;
// binary operators
D3DXVECTOR3 operator + ( CONST D3DXVECTOR3& ) const;
D3DXVECTOR3 operator - ( CONST D3DXVECTOR3& ) const;
D3DXVECTOR3 operator * ( FLOAT ) const;
D3DXVECTOR3 operator / ( FLOAT ) const;
friend D3DXVECTOR3 operator * ( FLOAT, CONST struct D3DXVECTOR3& );
BOOL operator == ( CONST D3DXVECTOR3& ) const;
BOOL operator != ( CONST D3DXVECTOR3& ) const;
} D3DXVECTOR3, *LPD3DXVECTOR3;
以下整理出DirextX 9的一些向量函數，由于本人也只是初學DirectX 9，所以文章中可能蘊含著一些錯誤，也可能不完整，敬請指出，以后會陸續補充。
要正確運行以下的示例程序，需要在工程中包含d3dx9.lib，或者在main函數前加入
#pragma comment(lib, "d3dx9.lib")
以指示編譯器鏈接d3dx9.lib。
向量相加： 重載的運算符 +
向量相減： 重載的運算符－函數原型：
D3DXVECTOR3 operator + ( CONST D3DXVECTOR3& ) const;
D3DXVECTOR3 operator － ( CONST D3DXVECTOR3& ) const;
代碼示例:
#include <stdio.h>
#include <D3DX9Math.h>
#pragma warning(disable : 4305)
int main()
{
// calculate for 2 dimension vector
D3DXVECTOR2 A2(6.0, 3.0);
D3DXVECTOR2 B2(4.0, 2.0);
D3DXVECTOR2 C2 = A2 + B2;
printf("\nC2 = (%.2f, %.2f) + (%.2f, %.2f) = (%.2f, %.2f)\n", A2.x, A2.y, B2.x, B2.y, C2.x, C2.y);
// calculate for 3 dimension vector
D3DXVECTOR3 A3(5.0, 2.6, 10);
D3DXVECTOR3 B3(2.0, 3.4, 3.0);
D3DXVECTOR3 C3 = A3 + B3;
printf("\nC3 = (%.2f, %.2f, %.2f) + (%.2f, %.2f, %.2f) = (%.2f, %.2f, %.2f)\n",
A3.x, A3.y, A3.z, B3.x, B3.y, B3.z, C3.x, C3.y, C3.z);
D3DXVECTOR3 D3 = A3 - B3;
printf("\nD3 = (%.2f, %.2f, %.2f) - (%.2f, %.2f, %.2f) = (%.2f, %.2f, %.2f)\n",
A3.x, A3.y, A3.z, B3.x, B3.y, B3.z, D3.x, D3.y, D3.z);
return 0;
}
輸出：
C2 = (6.00, 3.00) + (4.00, 2.00) = (10.00, 5.00)
C3 = (5.00, 2.60, 10.00) + (2.00, 3.40, 3.00) = (7.00, 6.00, 13.00)
D3 = (5.00, 2.60, 10.00) - (2.00, 3.40, 3.00) = (3.00, -0.80, 7.00)
向量的標量乘法： 重載的運算符 *
函數原型：
friend D3DXVECTOR3 operator * ( FLOAT, CONST struct D3DXVECTOR3& );
代碼示例：
#include <stdio.h>
#include <D3DX9Math.h>
#pragma warning(disable : 4305)
int main()
{
// calculate for 2 dimension multiply
D3DXVECTOR2 A(6.0, 3.0);
float m = 5.0;
D3DXVECTOR2 B = m * A;
printf("\nB = %.2f * (%.2f, %.2f) = (%.2f, %.2f)\n", m, A.x, A.y, B.x, B.y);
// calculate for 3 dimension multiply
D3DXVECTOR3 C(1.0, 2.0, 3.0);
D3DXVECTOR3 D = m * C;
printf("\nD = %.2f * (%.2f, %.2f, %.2f) = (%.2f, %.2f, %.2f)\n\n",
m, C.x, C.y, C.z, D.x, D.y, D.z);
return 0;
}
輸出：
B = 5.00 * (6.00, 3.00) = (30.00, 15.00)
D = 5.00 * (1.00, 2.00, 3.00) = (5.00, 10.00, 15.00)
向量長度的計算： D3DXVec3Length
函數原型：
FLOAT D3DXVec3Length ( CONST D3DXVECTOR3 *pV );
代碼示例：
#include <stdio.h>
#include <D3DX9Math.h>
#pragma warning(disable : 4305)
int main()
{
// calculate vector length for 2 dimension
D3DXVECTOR2 A(3.0, 5.0);
float A_len = D3DXVec2Length(&A);
printf("\nvector A(%.2f, %.2f) length = %f\n", A.x, A.y, A_len);
// calculate vector length for 3 dimension
D3DXVECTOR3 B(23.0, 3.8, -12.3);
float B_len = D3DXVec3Length(&B);
printf("\nvector B(%.2f, %.2f, %.2f) length = %f\n", B.x, B.y, B.z, B_len);
return 0;
}
輸出：
vector A(3.00, 5.00) length = 5.830952
vector B(23.00, 3.80, -12.30) length = 26.357731
向量的單位化： D3DXVec2Normalize, D3DXVec3Normalize
函數原型：
D3DXVECTOR2* WINAPI D3DXVec2Normalize( D3DXVECTOR2 *pOut, CONST D3DXVECTOR2 *pV );
D3DXVECTOR3* WINAPI D3DXVec3Normalize( D3DXVECTOR3 *pOut, CONST D3DXVECTOR3 *pV );
代碼示例：
#include <stdio.h>
#include <D3DX9Math.h>
#pragma warning(disable : 4305)
int main()
{
// vector normalize for 2D dimension
D3DXVECTOR2 A(3.0, 6.0);
D3DXVECTOR2 A_normal;
D3DXVec2Normalize(&A_normal, &A);
printf("vector A(%.2f, %.2f) normal = (%f, %f)\n\n", A.x, A.y, A_normal.x, A_normal.y);
// vector normalize for 3D dimension
D3DXVECTOR3 B(2.5, 10.0, 8.0);
D3DXVECTOR3 B_normal;
D3DXVec3Normalize(&B_normal, &B);
printf("vector B(%.2f, %.2f, %.2f) normal = (%f, %f, %f)\n\n", B.x, B.y, B.z, B_normal.x, B_normal.y, B_normal.z);
return 0;
}
輸出：
vector A(3.00, 6.00) normal = (0.447214, 0.894427)
vector B(2.50, 10.00, 8.00) normal = (0.191600, 0.766402, 0.613121)
向量的點積： D3DXVec3Dot
函數原型：
FLOAT D3DXVec3Dot ( CONST D3DXVECTOR3 *pV1, CONST D3DXVECTOR3 *pV2 )；
代碼示例：
#include <stdio.h>
#include <D3DX9Math.h>
#pragma warning(disable : 4305)
int main()
{
D3DXVECTOR3 u(2.0, 3.0, 4.0);
D3DXVECTOR3 v(11.0, 5.0, 7.0);
float dot_value = D3DXVec3Dot(&u, &v);
if(dot_value < 0)
printf("The angle between u and v is > 90");
else if(dot_value == 0)
printf("The angle between u and v is = 90");
else
printf("The angle between u and v is < 90");
printf("\n\n");
return 0;
}
輸出：
The angle between u and v is < 90
向量的叉積：D3DXVec3Cross
函數原型：
D3DXVECTOR3* D3DXVec3Cross
( D3DXVECTOR3 *pOut, CONST D3DXVECTOR3 *pV1, CONST D3DXVECTOR3 *pV2 )；
代碼示例：
#include <stdio.h>
#include <D3DX9Math.h>
#pragma warning(disable : 4305)
int main()
{
D3DXVECTOR3 i(1.0, 0.0, 0.0);
D3DXVECTOR3 j(0.0, 1.0, 0.0);
D3DXVECTOR3 k(0.0, 0.0, 1.0);
D3DXVECTOR3 cross_vector;
D3DXVec3Cross(&cross_vector, &i, &j);
printf("ixj = (%f, %f, %f)\n\n", cross_vector.x, cross_vector.y, cross_vector.z);
D3DXVec3Cross(&cross_vector, &j, &k);
printf("jxk = (%f, %f, %f)\n\n", cross_vector.x, cross_vector.y, cross_vector.z);
D3DXVec3Cross(&cross_vector, &k, &i);
printf("kxi = (%f, %f, %f)\n\n", cross_vector.x, cross_vector.y, cross_vector.z);
return 0;
}
輸出：
ixj = (0.000000, 0.000000, 1.000000)
jxk = (1.000000, 0.000000, 0.000000)
kxi = (0.000000, 1.000000, 0.000000)