在三維圖形程序中的一個模型對應空間中的一個物體，在現實世界中要完全定位一個物體需要6個參數，物體位置坐標的3個分量（x,
y, z）和3個歐拉角（偏航角yaw，俯仰角pitch，側傾角roll）。
3個歐拉角的定義為：
（1）偏航角：物體繞自身y軸（即上向量up）旋轉的角度。
（2）俯仰角：物體繞自身x軸（即右向量right）旋轉的角度。
（3）側傾角：物體繞自身z軸（即前向量look）旋轉的角度。
通過矩陣實現模型旋轉
在三維圖形程序中模型在世界空間中的位置和姿態都是通過通過其世界矩陣來表示的，所以要在程序中確定一個模型的位置和姿態，就是將控制其狀態的6個參數應用到其世界矩陣中。
通過物體的位置和物體的3個自身坐標軸朝向（3個向量）同樣也可以完全定位模型，實際上在Direct3D程序中，模型的世界矩陣本身包含了模型的位置向量和3個方向向量，這些向量在世界矩陣中存儲的順序是：第一行是right向量，第二行是up向量，第三行是look向量，第四行是位置向量pos。通過函數D3DXMatrixIdentity()將矩陣設置為單位矩陣，同時也將4個向量都設置為默認值，因此right向量為(1.0f,
0.0f, 0.0f)，up向量為(0.0, 1.0f,
0.0f)，look向量為(0.0f, 0.0f,
1.0f)，pos向量為(0.0f, 0.0f,
0.0f)。這時模型位于世界坐標系原點，并且朝向和世界坐標系的3個坐標軸方向相同。
要改變模型的狀態，就是移動物體到指定位置，旋轉物體改變其朝向。旋轉一個物體實質上就是將look、up、right向量中的兩個繞另一個作旋轉。比如要橫滾物體，就需要將up和right向量繞look向量旋轉；要使物體產生俯仰，必須將up和look向量繞right向量旋轉；要使物體產生偏航，必須將look和right向量繞up向量旋轉。
向量的旋轉需要分別借助偏航、俯仰和橫滾矩陣來完成，這些矩陣可借助于D3DXMatrixRotationAxis()函數產生，該函數的聲明如下：
Builds a matrix that rotates around an arbitrary axis.
D3DXMATRIX * D3DXMatrixRotationAxis(
D3DXMATRIX * pOut,
CONST D3DXVECTOR3 * pV,
FLOAT Angle
);
Parameters
- pOut
- [in, out] Pointer to the D3DXMATRIX structure that
is the result of the operation.
- pV
- [in] Pointer to the arbitrary axis. See
D3DXVECTOR3.
- Angle
- [in] Angle of rotation in radians. Angles are
measured clockwise when looking along the rotation axis toward the origin.
Return Values
Pointer to a D3DXMATRIX structure rotated around
the specified axis.
Remarks
The return value for this function is the same value
returned in the pOut parameter. In this way, the D3DXMatrixRotationAxis
function can be used as a parameter for another function.
有了偏航、俯仰和橫滾矩陣，就可以使用函數D3DXVec3TransformCoord()完成這種向量旋轉的計算，該函數的聲明如下：
Transforms a 3D vector by a given matrix, projecting
the result back into w = 1.
D3DXVECTOR3 * D3DXVec3TransformCoord(
D3DXVECTOR3 * pOut,
CONST D3DXVECTOR3 * pV,
CONST D3DXMATRIX * pM
);
Parameters
- pOut
- [in, out] Pointer to the D3DXVECTOR3 structure
that is the result of the operation.
- pV
- [in] Pointer to the source D3DXVECTOR3
structure.
- pM
- [in] Pointer to the source D3DXMATRIX structure.
Return Values
Pointer to a D3DXVECTOR3 structure that is the
transformed vector.
Remarks
This function transforms the vector, pV (x, y, z, 1),
by the matrix, pM, projecting the result back into w=1.
The return value for this function is the same value
returned in the pOut parameter. In this way, the D3DXVec3TransformCoord
function can be used as a parameter for another function.
以下代碼具體說明了實現這種旋轉的核心內容：
static D3DXMATRIX mat_around_right, mat_around_up, mat_around_look;
D3DXMatrixRotationAxis(&mat_around_up, &up, angle_around_up);
D3DXVec3TransformCoord(&look, &look, &mat_around_up);
D3DXVec3TransformCoord(&right, &right, &mat_around_up);
D3DXMatrixRotationAxis(&mat_around_look, &look, angle_around_look);
D3DXVec3TransformCoord(&right, &right, &mat_around_look);
D3DXVec3TransformCoord(&up, &up, &mat_around_look);
D3DXMatrixRotationAxis(&mat_around_right, &right, angle_around_right);
D3DXVec3TransformCoord(&look, &look, &mat_around_right);
D3DXVec3TransformCoord(&up, &up, &mat_around_right);
由于計算機對浮點數的處理存在精度問題，所以在向量旋轉計算過程中會帶來稍許的累加誤差。在經過幾次旋轉之后，這些舍入誤差將使3個向量不再相互垂直。以下代碼用于歸一化所有向量并使其互相垂直。
D3DXVec3Normalize(&look, &look);
D3DXVec3Cross(&right, &up, &look);
D3DXVec3Normalize(&right, &right);
D3DXVec3Cross(&up, &look, &right);
D3DXVec3Normalize(&up, &up);
示例程序演示了使用矩陣旋轉一個飛機模型，程序運行時按下"D"和"A"鍵，可使飛機模型繞look向量旋轉；按下"S"和"W"鍵，可使飛機模型繞right向量旋轉；按下"Q"和"E"鍵，可使飛機模型繞up向量旋轉；按下"F"和"V"鍵，可使飛機模型向前和向后運動。
源程序：
#include <d3dx9.h>
#pragma warning(disable : 4127)
#define CLASS_NAME "GameApp"
#define release_com(p) do { if(p) { (p)->Release(); (p) = NULL; } } while(0)
IDirect3D9* g_d3d;
IDirect3DDevice9* g_device;
ID3DXMesh* g_mesh;
D3DMATERIAL9* g_mesh_materials;
IDirect3DTexture9** g_mesh_textures;
DWORD g_num_materials;
BYTE g_keys[256];
D3DXMATRIX g_mat_world;
void setup_world_matrix()
{
static long previous_time = 0;
static float elapsed_time = 0.0f;
elapsed_time = (timeGetTime() - previous_time) / 1000.0f;
previous_time = timeGetTime();
float angle_around_right = 0.0f, angle_around_up = 0.0f, angle_around_look = 0.0f;
if(g_keys['D']) angle_around_look -= 3 * elapsed_time;
if(g_keys['A']) angle_around_look += 3 * elapsed_time;
if(g_keys['S']) angle_around_right -= 3 * elapsed_time;
if(g_keys['W']) angle_around_right += 3 * elapsed_time;
if(g_keys['Q']) angle_around_up -= 3 * elapsed_time;
if(g_keys['E']) angle_around_up += 3 * elapsed_time;
static D3DXVECTOR3 right, up, look, pos;
// save old model pos
right.x = g_mat_world._11;
right.y = g_mat_world._12;
right.z = g_mat_world._13;
up.x = g_mat_world._21;
up.y = g_mat_world._22;
up.z = g_mat_world._23;
look.x = g_mat_world._31;
look.y = g_mat_world._32;
look.z = g_mat_world._33;
pos.x = g_mat_world._41;
pos.y = g_mat_world._42;
pos.z = g_mat_world._43;
// now, calculate ratation matrix.
static D3DXMATRIX mat_around_right, mat_around_up, mat_around_look;
D3DXMatrixRotationAxis(&mat_around_up, &up, angle_around_up);
D3DXVec3TransformCoord(&look, &look, &mat_around_up);
D3DXVec3TransformCoord(&right, &right, &mat_around_up);
D3DXMatrixRotationAxis(&mat_around_look, &look, angle_around_look);
D3DXVec3TransformCoord(&right, &right, &mat_around_look);
D3DXVec3TransformCoord(&up, &up, &mat_around_look);
D3DXMatrixRotationAxis(&mat_around_right, &right, angle_around_right);
D3DXVec3TransformCoord(&look, &look, &mat_around_right);
D3DXVec3TransformCoord(&up, &up, &mat_around_right);
// normalize look, right, up to avoid float calculation error
D3DXVec3Normalize(&look, &look);
D3DXVec3Cross(&right, &up, &look);
D3DXVec3Normalize(&right, &right);
D3DXVec3Cross(&up, &look, &right);
D3DXVec3Normalize(&up, &up);
// update model pos
g_mat_world._11 = right.x;
g_mat_world._12 = right.y;
g_mat_world._13 = right.z;
g_mat_world._21 = up.x;
g_mat_world._22 = up.y;
g_mat_world._23 = up.z;
g_mat_world._31 = look.x;
g_mat_world._32 = look.y;
g_mat_world._33 = look.z;
// move model forward or backward
if(g_keys['F'])
{
g_mat_world._41 += 30 * elapsed_time * look.x;
g_mat_world._42 += 30 * elapsed_time * look.y;
g_mat_world._43 += 30 * elapsed_time * look.z;
}
if(g_keys['V'])
{
g_mat_world._41 -= 30 * elapsed_time * look.x;
g_mat_world._42 -= 30 * elapsed_time * look.y;
g_mat_world._43 -= 30 * elapsed_time * look.z;
}
g_device->SetTransform(D3DTS_WORLD, &g_mat_world);
}
void setup_view_proj_matrix()
{
// setup view matrix
D3DXVECTOR3 eye(0.0f, 10.0f, -20.0f);
D3DXVECTOR3 at(0.0f, 0.0f, 0.0f);
D3DXVECTOR3 up(0.0f, 1.0f, 0.0f);
D3DXMATRIX mat_view;
D3DXMatrixLookAtLH(&mat_view, &eye, &at, &up);
g_device->SetTransform(D3DTS_VIEW, &mat_view);
// setup projection matrix
D3DXMATRIX mat_proj;
D3DXMatrixPerspectiveFovLH(&mat_proj, D3DX_PI/4, 1.0f, 1.0f, 500.0f);
g_device->SetTransform(D3DTS_PROJECTION, &mat_proj);
}
bool init_geometry()
{
ID3DXBuffer* material_buffer;
/*
D3DXLoadMeshFromXA(
LPCSTR pFilename,
DWORD Options,
LPDIRECT3DDEVICE9 pD3DDevice,
LPD3DXBUFFER *ppAdjacency,
LPD3DXBUFFER *ppMaterials,
LPD3DXBUFFER *ppEffectInstances,
DWORD *pNumMaterials,
LPD3DXMESH *ppMesh);
*/
if(FAILED(D3DXLoadMeshFromX("airplane.x", D3DXMESH_MANAGED, g_device, NULL, &material_buffer, NULL,
&g_num_materials, &g_mesh)))
{
MessageBox(NULL, "Could not find airplane.x", "ERROR", MB_OK);
return false;
}
D3DXMATERIAL* xmaterials = (D3DXMATERIAL*) material_buffer->GetBufferPointer();
g_mesh_materials = new D3DMATERIAL9[g_num_materials];
g_mesh_textures = new IDirect3DTexture9*[g_num_materials];
for(DWORD i = 0; i < g_num_materials; i++)
{
g_mesh_materials[i] = xmaterials[i].MatD3D;
// set ambient reflected coefficient, because .x file do not set it.
g_mesh_materials[i].Ambient = g_mesh_materials[i].Diffuse;
g_mesh_textures[i] = NULL;
if(xmaterials[i].pTextureFilename != NULL && strlen(xmaterials[i].pTextureFilename) > 0)
D3DXCreateTextureFromFile(g_device, xmaterials[i].pTextureFilename, &g_mesh_textures[i]);
}
material_buffer->Release();
return true;
}
bool init_d3d(HWND hwnd)
{
g_d3d = Direct3DCreate9(D3D_SDK_VERSION);
if(g_d3d == NULL)
return false;
D3DPRESENT_PARAMETERS d3dpp;
ZeroMemory(&d3dpp, sizeof(d3dpp));
d3dpp.Windowed = TRUE;
d3dpp.SwapEffect = D3DSWAPEFFECT_DISCARD;
d3dpp.BackBufferFormat = D3DFMT_UNKNOWN;
d3dpp.EnableAutoDepthStencil = TRUE;
d3dpp.AutoDepthStencilFormat = D3DFMT_D16;
if(FAILED(g_d3d->CreateDevice(D3DADAPTER_DEFAULT, D3DDEVTYPE_HAL, hwnd, D3DCREATE_SOFTWARE_VERTEXPROCESSING,
&d3dpp, &g_device)))
{
return false;
}
if(! init_geometry())
return false;
D3DXMatrixIdentity(&g_mat_world);
setup_view_proj_matrix();
g_device->SetTextureStageState(0, D3DTSS_COLORARG1, D3DTA_TEXTURE);
g_device->SetTextureStageState(0, D3DTSS_COLOROP, D3DTOP_SELECTARG1);
return true;
}
void cleanup()
{
delete[] g_mesh_materials;
if(g_mesh_textures)
{
for(DWORD i = 0; i < g_num_materials; i++)
release_com(g_mesh_textures[i]);
delete[] g_mesh_textures;
}
release_com(g_mesh);
release_com(g_device);
release_com(g_d3d);
}
void render()
{
g_device->Clear(0, NULL, D3DCLEAR_TARGET | D3DCLEAR_ZBUFFER, D3DCOLOR_XRGB(5, 5, 5), 1.0f, 0);
g_device->BeginScene();
setup_world_matrix();
for(DWORD i = 0; i < g_num_materials; i++)
{
g_device->SetMaterial(&g_mesh_materials[i]);
g_device->SetTexture(0, g_mesh_textures[i]);
g_mesh->DrawSubset(i);
}
g_device->EndScene();
g_device->Present(NULL, NULL, NULL, NULL);
}
LRESULT WINAPI WinProc(HWND hwnd, UINT msg, WPARAM wParam, LPARAM lParam)
{
switch(msg)
{
case WM_KEYDOWN:
g_keys[wParam] = 1;
if(wParam == VK_ESCAPE)
DestroyWindow(hwnd);
break;
case WM_KEYUP:
g_keys[wParam] = 0;
break;
case WM_DESTROY:
PostQuitMessage(0);
return 0;
}
return DefWindowProc(hwnd, msg, wParam, lParam);
}
int WINAPI WinMain(HINSTANCE inst, HINSTANCE, LPSTR, INT)
{
WNDCLASSEX wc;
wc.cbSize = sizeof(WNDCLASSEX);
wc.style = CS_CLASSDC;
wc.lpfnWndProc = WinProc;
wc.cbClsExtra = 0;
wc.cbWndExtra = 0;
wc.hInstance = inst;
wc.hIcon = NULL;
wc.hCursor = NULL;
wc.hbrBackground = NULL;
wc.lpszMenuName = NULL;
wc.lpszClassName = CLASS_NAME;
wc.hIconSm = NULL;
if(! RegisterClassEx(&wc))
return -1;
HWND hwnd = CreateWindow(CLASS_NAME, "Direct3D App", WS_OVERLAPPEDWINDOW, 200, 100, 640, 480,
NULL, NULL, wc.hInstance, NULL);
if(hwnd == NULL)
return -1;
if(init_d3d(hwnd))
{
ShowWindow(hwnd, SW_SHOWDEFAULT);
UpdateWindow(hwnd);
MSG msg;
ZeroMemory(&msg, sizeof(msg));
while(msg.message != WM_QUIT)
{
if(PeekMessage(&msg, NULL, 0, 0, PM_REMOVE))
{
TranslateMessage(&msg);
DispatchMessage(&msg);
}
render();
}
}
cleanup();
UnregisterClass(CLASS_NAME, wc.hInstance);
return 0;
}
下載示例工程