欧拉角 EulerAngles 中的旋转 Directx D3DXMatrixRotationYawPitchRoll
写在前面：正当很高兴地完成了矩阵相关的旋转后，发现如果涉及到旋转；矩阵，欧拉角(EulerAngles) ，四元数(Quaternions)这三个概念哪本书上都会提。这次先讲下欧拉角。
1.什么是欧拉角
欧拉角是由三个角组成，这三个角分别是Yaw,Pitch,Roll。很难翻译这三个单词，Yaw 表示绕y轴旋转的角度，Pitch表示绕x轴旋转的角度，Roll表示绕z轴旋转的角度。也就是说，任意的旋转角度都可以通过这三次按照先后顺序旋转得到。矩阵很难让人具体形象表示，欧拉角就容易多了。注意可能很多地方三个角的先后次序不一样，我们这里选择跟DirectX 中的D3DXMatrixRotationYawPitchRoll函数保持一致，先绕y轴旋转，在绕x轴旋转，最后绕z轴旋转。
感觉Yaw(偏航),Pitch(投掷；倾斜；坠落),Roll(转动) 介绍飞机旋转的比较多，窃了三张图来更象形地表示下：
2.欧拉角中的旋转
还记得这三个矩阵吗？绕相关轴旋转，乘以相关矩阵就行了，也就是说欧拉角最终还是转换成矩阵相乘，不过是要与三个矩阵相乘。
我们知道可以先把这三个矩阵相乘，这样可以节约计算量。就是要先计算这三个矩阵相乘，注意矩阵相乘次序是不可更改的，更改了结果就不一样了。
欧拉角的三个角，可以转变为矩阵与矩阵的相乘。
3.开始替换D3DXMatrixRotationYawPitchRoll函数
Directx 9.0中有个函数叫D3DXMatrixRotationYawPitchRoll(D3DXMATRIX *pOut, FLOAT Yaw, FLOAT Pitch, FLOAT Roll)。根据上面复杂的矩阵，我们用C++替换成下面的函数。可能这个函数还有优化空间，数学太差啊。
//-----------------------------------------------------------------------------
// Name: setupRotate()
// Desc: 绕3个角度旋转
//-----------------------------------------------------------------------------
VOID setupRotate(D3DXMATRIXA16 *returnMatrix, float yaw, float pitch, float roll)
{
float sx = sin(pitch); float sy = sin(yaw); float sz = sin(roll);
float cx = cos(pitch); float cy = cos(yaw); float cz = cos(roll);
returnMatrix->_11 = cz * cy - sx * sy * sz;
returnMatrix->_12 = cy * sz + sx * sy * cz;
returnMatrix->_13 = -sy * cx;
returnMatrix->_14 = 0.0f;
returnMatrix->_21 = -cx * sz;
returnMatrix->_22 = cx * cz;
returnMatrix->_23 = sx;
returnMatrix->_24 = 0.0f;
returnMatrix->_31 = sy * cz + sx * cy * sz;
returnMatrix->_32 = sy * sz - sx * cy * cz;
returnMatrix->_33 = cx * cy;
returnMatrix->_34 = 0.0f;
returnMatrix->_41 = 0.0f;
returnMatrix->_42 = 0.0f;
returnMatrix->_43 = 0.0f;
returnMatrix->_44 = 1.0f;
}
先看下我们使用这个函数的例子效果：跟随鼠标移动的水壶，而不是自己在那旋转个不停。
对上面这张gif图片是如何制作感兴趣？看截取视频，然后制成gif 教程
除了上面的函数之外的核心代码(需要对Windows中的消息处理熟悉)：
float g_fSpinX = 0.0f;
float g_fSpinY = 0.0f;
//鼠标最后位置
static POINT ptLastMousePosit;
//当前鼠标位置
static POINT ptCurrentMousePosit;
static bool bMousing;
switch( msg )
{
case WM_LBUTTONDOWN: // 当鼠标左键按下时，记录当前的位置(屏幕坐标),并设置按下标志
{
ptLastMousePosit.x = ptCurrentMousePosit.x = LOWORD (lParam);
ptLastMousePosit.y = ptCurrentMousePosit.y = HIWORD (lParam);
bMousing = true;
}
break;
case WM_LBUTTONUP:
{
bMousing = false;
}
break;
case WM_MOUSEMOVE: // 鼠标移动时，保存X/Y轴的移动距离
{
ptCurrentMousePosit.x = LOWORD (lParam);
ptCurrentMousePosit.y = HIWORD (lParam);
if( bMousing )
{
g_fSpinX -= (ptCurrentMousePosit.x - ptLastMousePosit.x);
g_fSpinY -= (ptCurrentMousePosit.y - ptLastMousePosit.y);
}
ptLastMousePosit.x = ptCurrentMousePosit.x;
ptLastMousePosit.y = ptCurrentMousePosit.y;
}
break;
}
//最后两个值传到我们写好的函数中即可
setupRotate(&matWorld,D3DXToRadian(g_fSpinX),D3DXToRadian(g_fSpinY),0.0f);
完整代码：如果觉得看起来太累，拉到最底部，下载整个项目来看。
//-----------------------------------------------------------------------------
// File: Lights.cpp
// Copyright (c) Microsoft Corporation & Waitingfy.com. All rights reserved.
//-----------------------------------------------------------------------------
#include <Windows.h>
#include <mmsystem.h>
#include <d3dx9.h>
#include <strsafe.h>
#include <math.h>
#include <assert.h>
//-----------------------------------------------------------------------------
// Global variables
//-----------------------------------------------------------------------------
LPDIRECT3D9 g_pD3D = NULL; // Used to create the D3DDevice
LPDIRECT3DDEVICE9 g_pd3dDevice = NULL; // Our rendering device
LPDIRECT3DVERTEXBUFFER9 g_pVB = NULL; // Buffer to hold vertices
ID3DXMesh* Objects = 0;//茶壶
float g_fSpinX = 0.0f;
float g_fSpinY = 0.0f;
// A structure for our custom vertex type. We added a normal, and omitted the
// color (which is provided by the material)
struct CUSTOMVERTEX
{
D3DXVECTOR3 position; // The 3D position for the vertex
D3DXVECTOR3 normal; // The surface normal for the vertex
};
// Our custom FVF, which describes our custom vertex structure
#define D3DFVF_CUSTOMVERTEX (D3DFVF_XYZ|D3DFVF_NORMAL)
//-----------------------------------------------------------------------------
// Name: InitD3D()
// Desc: Initializes Direct3D
//-----------------------------------------------------------------------------
HRESULT InitD3D( HWND hWnd )
{
// Create the D3D object.
if( NULL == ( g_pD3D = Direct3DCreate9( D3D_SDK_VERSION ) ) )
return E_FAIL;
// Set up the structure used to create the D3DDevice. Since we are now
// using more complex geometry, we will create a device with a zbuffer.
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;
// Create the D3DDevice
if( FAILED( g_pD3D->CreateDevice( D3DADAPTER_DEFAULT, D3DDEVTYPE_HAL, hWnd,
D3DCREATE_SOFTWARE_VERTEXPROCESSING,
&d3dpp, &g_pd3dDevice ) ) )
{
return E_FAIL;
}
// Turn off culling
g_pd3dDevice->SetRenderState( D3DRS_CULLMODE, D3DCULL_NONE );
// Turn on the zbuffer
g_pd3dDevice->SetRenderState( D3DRS_ZENABLE, TRUE );
return S_OK;
}
//-----------------------------------------------------------------------------
// Name: Cleanup()
// Desc: Releases all previously initialized objects
//-----------------------------------------------------------------------------
VOID Cleanup()
{
if( g_pVB != NULL )
g_pVB->Release();
if( g_pd3dDevice != NULL )
g_pd3dDevice->Release();
if( g_pD3D != NULL )
g_pD3D->Release();
if(Objects != NULL){
Objects->Release();
}
}
//-----------------------------------------------------------------------------
// Name: setupRotate()
// Desc: 绕3个角度旋转
//-----------------------------------------------------------------------------
VOID setupRotate(D3DXMATRIXA16 *returnMatrix, float yaw, float pitch, float roll)
{
float sx = sin(pitch); float sy = sin(yaw); float sz = sin(roll);
float cx = cos(pitch); float cy = cos(yaw); float cz = cos(roll);
returnMatrix->_11 = cz * cy - sx * sy * sz;
returnMatrix->_12 = cy * sz + sx * sy * cz;
returnMatrix->_13 = -sy * cx;
returnMatrix->_14 = 0.0f;
returnMatrix->_21 = -cx * sz;
returnMatrix->_22 = cx * cz;
returnMatrix->_23 = sx;
returnMatrix->_24 = 0.0f;
returnMatrix->_31 = sy * cz + sx * cy * sz;
returnMatrix->_32 = sy * sz - sx * cy * cz;
returnMatrix->_33 = cx * cy;
returnMatrix->_34 = 0.0f;
returnMatrix->_41 = 0.0f;
returnMatrix->_42 = 0.0f;
returnMatrix->_43 = 0.0f;
returnMatrix->_44 = 1.0f;
}
//-----------------------------------------------------------------------------
// Name: SetupMatrices()
// Desc: Sets up the world, view, and projection transform matrices.
//-----------------------------------------------------------------------------
VOID SetupMatrices()
{
// 旋转
D3DXMATRIXA16 matWorld;
D3DXMatrixIdentity( &matWorld );
//根据x轴和y轴移动距离旋转
setupRotate(&matWorld,D3DXToRadian(g_fSpinX),D3DXToRadian(g_fSpinY),0.0f);
g_pd3dDevice->SetTransform( D3DTS_WORLD, &matWorld );
// 摄像机的位置
D3DXVECTOR3 vEyePt( 0.0f, 3.0f,-5.0f );
D3DXVECTOR3 vLookatPt( 0.0f, 0.0f, 0.0f );
D3DXVECTOR3 vUpVec( 0.0f, 1.0f, 0.0f );
D3DXMATRIXA16 matView;
D3DXMatrixLookAtLH( &matView, &vEyePt, &vLookatPt, &vUpVec );
g_pd3dDevice->SetTransform( D3DTS_VIEW, &matView );
// 设置视锥体大小
D3DXMATRIXA16 matProj;
D3DXMatrixPerspectiveFovLH( &matProj, D3DX_PI/4, 1.0f, 1.0f, 100.0f );
g_pd3dDevice->SetTransform( D3DTS_PROJECTION, &matProj );
}
//-----------------------------------------------------------------------------
// Name: SetupLights()
// Desc: Sets up the Lights and materials for the scene.
//-----------------------------------------------------------------------------
VOID SetupLights()
{
// 初始化一个材料
D3DMATERIAL9 mtrl;
ZeroMemory( &mtrl, sizeof(D3DMATERIAL9) );
mtrl.Diffuse = mtrl.Ambient = D3DXCOLOR(1.0f,1.0f,0.0f,1.0f); //材质有漫射和环境光的设置，都为黄色
g_pd3dDevice->SetMaterial( &mtrl );
// 初始化一个白色的方向光
///*
D3DXVECTOR3 vecDir;
D3DLIGHT9 light;
ZeroMemory( &light, sizeof(D3DLIGHT9) );
light.Type = D3DLIGHT_DIRECTIONAL;//方向光
light.Diffuse = D3DXCOLOR(1.0f,1.0f,1.0f,1.0f);//设置光源的漫射光颜色为白色
light.Direction = D3DXVECTOR3(0.0f,0.0f,1.0f);//光的传播方向平行z轴
light.Range = 1000.0f;
g_pd3dDevice->SetLight( 0, &light );
g_pd3dDevice->LightEnable( 0, TRUE );
g_pd3dDevice->SetRenderState( D3DRS_LIGHTING, TRUE );
//*/
// Finally, turn on some ambient light.
g_pd3dDevice->SetRenderState( D3DRS_AMBIENT, 0x00202020 );
}
//-----------------------------------------------------------------------------
// Name: Render()
// Desc: Draws the scene
//-----------------------------------------------------------------------------
VOID Render()
{
// 背景为蓝色
g_pd3dDevice->Clear( 0, NULL, D3DCLEAR_TARGET|D3DCLEAR_ZBUFFER,
D3DCOLOR_XRGB(0,0,255), 1.0f, 0 );
// Begin the scene
if( SUCCEEDED( g_pd3dDevice->BeginScene() ) )
{
// 茶壶的材料颜色也定义在这个函数中
SetupLights();
// Setup the world, view, and projection matrices
SetupMatrices();
// Render the vertex buffer contents
g_pd3dDevice->SetStreamSource( 0, g_pVB, 0, sizeof(CUSTOMVERTEX) );
g_pd3dDevice->SetFVF( D3DFVF_CUSTOMVERTEX );
//创建一个茶壶
//Objects = 0;
D3DXMATRIX Worlds;
D3DXCreateTeapot(g_pd3dDevice, &Objects, 0);
Objects->DrawSubset(0);
Objects->Release();
Objects = 0;
// End the scene
g_pd3dDevice->EndScene();
}
// Present the backbuffer contents to the display
g_pd3dDevice->Present( NULL, NULL, NULL, NULL );
//Objects->Release();
}
//-----------------------------------------------------------------------------
// Name: MsgProc()
// Desc: The window's message handler
//-----------------------------------------------------------------------------
LRESULT WINAPI MsgProc( HWND hWnd, UINT msg, WPARAM wParam, LPARAM lParam )
{
static POINT ptLastMousePosit;
static POINT ptCurrentMousePosit;
static bool bMousing;
switch( msg )
{
case WM_DESTROY:
Cleanup();
PostQuitMessage( 0 );
return 0;
case WM_LBUTTONDOWN: // 当鼠标左键按下时，记录当前的位置（屏幕坐标），并设置按下标志
{
ptLastMousePosit.x = ptCurrentMousePosit.x = LOWORD (lParam);
ptLastMousePosit.y = ptCurrentMousePosit.y = HIWORD (lParam);
bMousing = true;
}
break;
case WM_LBUTTONUP:
{
bMousing = false;
}
break;
case WM_MOUSEMOVE: // 鼠标移动时，保存X/Y轴的移动距离
{
ptCurrentMousePosit.x = LOWORD (lParam);
ptCurrentMousePosit.y = HIWORD (lParam);
if( bMousing )
{
g_fSpinX -= (ptCurrentMousePosit.x - ptLastMousePosit.x);
g_fSpinY -= (ptCurrentMousePosit.y - ptLastMousePosit.y);
}
ptLastMousePosit.x = ptCurrentMousePosit.x;
ptLastMousePosit.y = ptCurrentMousePosit.y;
}
break;
}
return DefWindowProc( hWnd, msg, wParam, lParam );
}
//-----------------------------------------------------------------------------
// Name: WinMain()
// Desc: The application's entry point
//-----------------------------------------------------------------------------
INT WINAPI WinMain( HINSTANCE hInst, HINSTANCE, LPSTR, INT )
{
// Register the window class
WNDCLASSEX wc = { sizeof(WNDCLASSEX), CS_CLASSDC, MsgProc, 0L, 0L,
GetModuleHandle(NULL), NULL, NULL, NULL, NULL,
"D3D Tutorial", NULL };
RegisterClassEx( &wc );
// Create the application's window
HWND hWnd = CreateWindow( "D3D Tutorial", "D3D Tutorial 04: Lights",
WS_OVERLAPPEDWINDOW, 100, 100, 300, 300,
GetDesktopWindow(), NULL, wc.hInstance, NULL );
// Initialize Direct3D
if( SUCCEEDED( InitD3D( hWnd ) ) )
{
// Show the window
ShowWindow( hWnd, SW_SHOWDEFAULT );
UpdateWindow( hWnd );
// Enter the message loop
MSG msg;
ZeroMemory( &msg, sizeof(msg) );
while( msg.message!=WM_QUIT )
{
if( PeekMessage( &msg, NULL, 0U, 0U, PM_REMOVE ) )
{
TranslateMessage( &msg );
DispatchMessage( &msg );
}
else
Render();
}
}
UnregisterClass( "D3D Tutorial", wc.hInstance );
return 0;
}
文章源地址：http://www.waitingfy.com/?p=375
项目下载：
YawPitchRoll (本站下载)
参考资源：http://hi.baidu.com/_鈊_烦_薏乱/blog/item/bac886c46164c1d438db49e7.html