首先來看看向量，向量的坐標(biāo)表示對(duì)于DirectX游戲開發(fā)來說是必須的，在世界坐標(biāo)系或投影坐標(biāo)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(biāo)形式來準(zhǔn)確給出的。
DirectX的頭文件D3DX9Math.h給出了兩個(gè)結(jié)構(gòu)體來支持向量的計(jì)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(shù)，由于本人也只是初學(xué)DirectX 9，所以文章中可能蘊(yùn)含著一些錯(cuò)誤，也可能不完整，敬請(qǐng)指出，以后會(huì)陸續(xù)補(bǔ)充。
要正確運(yùn)行以下的示例程序，需要在工程中包含d3dx9.lib，或者在main函數(shù)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(yùn)算符 +
向量相減： 重載的運(yùn)算符－函數(shù)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(biāo)量乘法： 重載的運(yùn)算符 *
函數(shù)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(jì)算： D3DXVec3Length
函數(shù)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(shù)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(diǎn)積： D3DXVec3Dot
函數(shù)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(shù)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)