矩阵中的数学旋转公式 转换到 C++中函数 替换DirectX 9.0中D3DXMatrixRotationAxis函数
2013-01-19 13:08
501 查看
还记得DirectX 9.0 C++ 教程 光照中这个旋转的水壶吗?当时我们用的是官方函数D3DXMatrixRotationY(D3DXMATRIX *pOut, FLOAT Angle)。刚刚我们已经学习了线性代数中的一些基础知识,Matrix
矩阵,单位矩阵,Transposition,矩阵与矩阵相乘,矩阵中的旋转(Rotation),我已经迫不及待想用自己写的旋转函数替换官方旋转函数了,来更好的记住数学知识,你呢?
![](http://img.my.csdn.net/uploads/201210/10/1349861557_5323.gif)
对上面这张gif图片是如何***感兴趣?看截取视频,然后制成gif 教程
首先看下数学公式:
![](http://img.my.csdn.net/uploads/201212/03/1354503052_5268.jpg)
由上面的数学公式,我们转换的C++函数:
可能会有人对上面函数中的D3DXMATRIXA16和D3DXVECTOR3不理解,他们其实是Direct3D中表示4维矩阵和3维向量的结构体,可是我们数学公式里涉及到的是3维矩阵,可以看下下面的转换,因为要设计到矩阵相乘,故只能4维矩阵跟4维矩阵相乘,故把3维的转换成4维的了。
![](http://img.my.csdn.net/uploads/201212/03/1354503448_6275.jpg)
具体使用上面两个函数的例子:
旋转效果:
![](http://img.my.csdn.net/uploads/201212/03/1354505256_2661.gif)
我稍微修改了下自定义旋转的轴,改成一个非单位向量,(1.0f, 1.0f, 0.0f),旋转效果(变形的飞起,哈哈):
![](http://img.my.csdn.net/uploads/201212/03/1354504749_8524.gif)
完整代码(看的麻烦的同学,可以拉到底下载整个项目来看):
项目下载:
RotationArbitrary (本站下载)
文章源地址:http://www.waitingfy.com/?p=363
矩阵,单位矩阵,Transposition,矩阵与矩阵相乘,矩阵中的旋转(Rotation),我已经迫不及待想用自己写的旋转函数替换官方旋转函数了,来更好的记住数学知识,你呢?
![](http://img.my.csdn.net/uploads/201210/10/1349861557_5323.gif)
对上面这张gif图片是如何***感兴趣?看截取视频,然后制成gif 教程
首先看下数学公式:
![](http://img.my.csdn.net/uploads/201212/03/1354503052_5268.jpg)
由上面的数学公式,我们转换的C++函数:
//----------------------------------------------------------------------------- // Name: setupRotate() // Desc: 绕x,y,z轴旋转,axis:1表示绕x轴,2表示y轴,3表示z轴 //----------------------------------------------------------------------------- VOID setupRotate(D3DXMATRIXA16 *returnMatrix,int axis, float theta) { float s, c; s = sin(theta),c=cos(theta); switch (axis) { case 1: // Rotate about the x-axis returnMatrix->_11 = 1.0f; returnMatrix->_12 = 0.0f; returnMatrix->_13 = 0.0f; returnMatrix->_14 = 0.0f; returnMatrix->_21 = 0.0f; returnMatrix->_22 = c; returnMatrix->_23 = s; returnMatrix->_24 = 0.0f; returnMatrix->_31 = 0.0f; returnMatrix->_32 = -s; returnMatrix->_33 = c; returnMatrix->_34 = 0.0f; returnMatrix->_41 = 0.0f; returnMatrix->_42 = 0.0f; returnMatrix->_43 = 0.0f; returnMatrix->_44 = 1.0f; break; case 2: // Rotate about the y-axis returnMatrix->_11 = c; returnMatrix->_12 = 0.0f; returnMatrix->_13 = -s; returnMatrix->_14 = 0.0f; returnMatrix->_21 = 0.0f; returnMatrix->_22 = 1.0f; returnMatrix->_23 = 0.0f; returnMatrix->_24 = 0.0f; returnMatrix->_31 = s; returnMatrix->_32 = 0.0f; returnMatrix->_33 = c; returnMatrix->_34 = 0.0f; returnMatrix->_41 = 0.0f; returnMatrix->_42 = 0.0f; returnMatrix->_43 = 0.0f; returnMatrix->_44 = 1.0f; break; case 3: // Rotate about the z-axis returnMatrix->_11 = c; returnMatrix->_12 = s; returnMatrix->_13 = 0.0f; returnMatrix->_14 = 0.0f; returnMatrix->_21 = -s; returnMatrix->_22 = c; returnMatrix->_23 = 0.0f; returnMatrix->_24 = 0.0f; returnMatrix->_31 = 0.0f; returnMatrix->_32 = 0.0f; returnMatrix->_33 = 1.0f; returnMatrix->_34 = 0.0f; returnMatrix->_41 = 0.0f; returnMatrix->_42 = 0.0f; returnMatrix->_43 = 0.0f; returnMatrix->_44 = 1.0f; break; default: // bogus axis index assert(false); } } //----------------------------------------------------------------------------- // Name: setupRotate() // Desc: 绕自定义轴旋转 //----------------------------------------------------------------------------- VOID setupRotate(const D3DXVECTOR3 &axis, D3DXMATRIXA16 *returnMatrix, float theta) { //要旋转的向量轴必须是单位向量,不然物体会变形 //assert(fabs(axis*axis - 1.0f) < .01f); float s, c; s = sin(theta),c=cos(theta); // 计算出一些重复利用的子表达式。 float a = 1.0f - c; float ax = a * axis.x; float ay = a * axis.y; float az = a * axis.z; returnMatrix->_11 = ax*axis.x + c; returnMatrix->_12 = ax*axis.y + axis.z*s; returnMatrix->_13 = ax*axis.z - axis.y*s; returnMatrix->_14 = 0.0f; returnMatrix->_21 = ay*axis.x - axis.z*s; returnMatrix->_22 = ay*axis.y + c; returnMatrix->_23 = ay*axis.z + axis.x*s; returnMatrix->_24 = 0.0f; returnMatrix->_31 = az*axis.x + axis.y*s; returnMatrix->_32 = az*axis.y - axis.x*s; returnMatrix->_33 = az*axis.z + c; returnMatrix->_34 = 0.0f; returnMatrix->_41 = 0.0f; returnMatrix->_42 = 0.0f; returnMatrix->_43 = 0.0f; returnMatrix->_44 = 1.0f; }
可能会有人对上面函数中的D3DXMATRIXA16和D3DXVECTOR3不理解,他们其实是Direct3D中表示4维矩阵和3维向量的结构体,可是我们数学公式里涉及到的是3维矩阵,可以看下下面的转换,因为要设计到矩阵相乘,故只能4维矩阵跟4维矩阵相乘,故把3维的转换成4维的了。
![](http://img.my.csdn.net/uploads/201212/03/1354503448_6275.jpg)
具体使用上面两个函数的例子:
// 旋转 D3DXMATRIXA16 matWorld; //自定义旋转的轴 D3DXVECTOR3 axis(1.0f/sqrt(3), 1.0f/sqrt(3), 1.0f/sqrt(3)); D3DXMatrixIdentity( &matWorld ); /*DirectX 官方API*/ //D3DXMatrixRotationY( &matWorld, timeGetTime()/500.0f ); /*使用自定义旋转函数1*/ //setupRotate(&matWorld,2,timeGetTime()/500.0f); /*使用自定义旋转函数2*/ setupRotate(axis,&matWorld,timeGetTime()/500.0f); g_pd3dDevice->SetTransform( D3DTS_WORLD, &matWorld );
旋转效果:
![](http://img.my.csdn.net/uploads/201212/03/1354505256_2661.gif)
我稍微修改了下自定义旋转的轴,改成一个非单位向量,(1.0f, 1.0f, 0.0f),旋转效果(变形的飞起,哈哈):
![](http://img.my.csdn.net/uploads/201212/03/1354504749_8524.gif)
完整代码(看的麻烦的同学,可以拉到底下载整个项目来看):
//----------------------------------------------------------------------------- // 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;//茶壶 // 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x,y,z轴旋转,axis:1表示绕x轴,2表示y轴,3表示z轴 //----------------------------------------------------------------------------- VOID setupRotate(D3DXMATRIXA16 *returnMatrix,int axis, float theta) { float s, c; s = sin(theta),c=cos(theta); switch (axis) { case 1: // Rotate about the x-axis returnMatrix->_11 = 1.0f; returnMatrix->_12 = 0.0f; returnMatrix->_13 = 0.0f; returnMatrix->_14 = 0.0f; returnMatrix->_21 = 0.0f; returnMatrix->_22 = c; returnMatrix->_23 = s; returnMatrix->_24 = 0.0f; returnMatrix->_31 = 0.0f; returnMatrix->_32 = -s; returnMatrix->_33 = c; returnMatrix->_34 = 0.0f; returnMatrix->_41 = 0.0f; returnMatrix->_42 = 0.0f; returnMatrix->_43 = 0.0f; returnMatrix->_44 = 1.0f; break; case 2: // Rotate about the y-axis returnMatrix->_11 = c; returnMatrix->_12 = 0.0f; returnMatrix->_13 = -s; returnMatrix->_14 = 0.0f; returnMatrix->_21 = 0.0f; returnMatrix->_22 = 1.0f; returnMatrix->_23 = 0.0f; returnMatrix->_24 = 0.0f; returnMatrix->_31 = s; returnMatrix->_32 = 0.0f; returnMatrix->_33 = c; returnMatrix->_34 = 0.0f; returnMatrix->_41 = 0.0f; returnMatrix->_42 = 0.0f; returnMatrix->_43 = 0.0f; returnMatrix->_44 = 1.0f; break; case 3: // Rotate about the z-axis returnMatrix->_11 = c; returnMatrix->_12 = s; returnMatrix->_13 = 0.0f; returnMatrix->_14 = 0.0f; returnMatrix->_21 = -s; returnMatrix->_22 = c; returnMatrix->_23 = 0.0f; returnMatrix->_24 = 0.0f; returnMatrix->_31 = 0.0f; returnMatrix->_32 = 0.0f; returnMatrix->_33 = 1.0f; returnMatrix->_34 = 0.0f; returnMatrix->_41 = 0.0f; returnMatrix->_42 = 0.0f; returnMatrix->_43 = 0.0f; returnMatrix->_44 = 1.0f; break; default: // bogus axis index assert(false); } } //----------------------------------------------------------------------------- // Name: setupRotate() // Desc: 绕自定义轴旋转,类似DirectX中的函数D3DXMatrixRotationAxis //----------------------------------------------------------------------------- VOID setupRotate(const D3DXVECTOR3 &axis, D3DXMATRIXA16 *returnMatrix, float theta) { //要旋转的向量轴必须是单位向量,不然物体会变形 //assert(fabs(axis*axis - 1.0f) < .01f); float s, c; s = sin(theta),c=cos(theta); // 计算出一些重复利用的子表达式。 float a = 1.0f - c; float ax = a * axis.x; float ay = a * axis.y; float az = a * axis.z; returnMatrix->_11 = ax*axis.x + c; returnMatrix->_12 = ax*axis.y + axis.z*s; returnMatrix->_13 = ax*axis.z - axis.y*s; returnMatrix->_14 = 0.0f; returnMatrix->_21 = ay*axis.x - axis.z*s; returnMatrix->_22 = ay*axis.y + c; returnMatrix->_23 = ay*axis.z + axis.x*s; returnMatrix->_24 = 0.0f; returnMatrix->_31 = az*axis.x + axis.y*s; returnMatrix->_32 = az*axis.y - axis.x*s; returnMatrix->_33 = az*axis.z + c; 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; //自定义旋转的轴 //D3DXVECTOR3 axis(1.0f/sqrt(3), 1.0f/sqrt(3), 1.0f/sqrt(3)); D3DXVECTOR3 axis(1.0f, 1.0f, 0.0f); D3DXMatrixIdentity( &matWorld ); /*DirectX 官方API*/ //D3DXMatrixRotationY( &matWorld, timeGetTime()/500.0f ); /*使用自定义旋转函数1*/ //setupRotate(&matWorld,2,timeGetTime()/500.0f); /*使用自定义旋转函数2*/ setupRotate(axis,&matWorld,timeGetTime()/500.0f); 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*** 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 ); } //----------------------------------------------------------------------------- // Name: MsgProc() // Desc: The window's message handler //----------------------------------------------------------------------------- LRESULT WINAPI MsgProc( HWND hWnd, UINT msg, WPARAM wParam, LPARAM lParam ) { switch( msg ) { case WM_DESTROY: Cleanup(); PostQuitMessage( 0 ); return 0; } 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; }
项目下载:
RotationArbitrary (本站下载)
文章源地址:http://www.waitingfy.com/?p=363
相关文章推荐
- 3d数学基础-欧拉角转换与旋转矩阵或旋转矩阵转换成欧拉角-用C++代码实现
- [C/C++]_[初级]_[标准库之几种算法库函数的运用,如字符串查找(字符个数查找)、分隔、删除、替换、排序、字符交换位置、大小写转换等等]
- 简化以下程序,将函数对象 divide_by 转换为一个函数,并将 for 循环替换为用一个标准的 C++ 算法来输出数据
- 四元数、欧拉角、旋转矩阵之间互相转换C++源码
- 四元数、欧拉角、旋转矩阵之间互相转换C++源码
- 3D数学基础公式------>矩阵,欧拉角,四元数,之间转换<2>
- DirectX 9.0 C++ 教程 关于Perspective projection,Matrices,摄像头,旋转
- c++ 成员函数和全局函数的转换
- 向量坐标转换、旋转矩阵以及视图转换
- C++中将字符或整型转换为二进制的类函数
- C++中的数学函数汇总
- 3D 视角旋转矩阵 yaw pitch roll (pan, tilt)的数学计算
- 旋转矩阵、欧拉角、四元数理论及其转换关系
- DirectX 9的一些数学计算函数:平面
- 旋转矩阵到欧拉角的转换
- DirectX 9.0 (2) 矩阵
- C++之全局函数和成员函数的转换
- java 获取数学函数公式中的参数集
- 旋转矩阵、欧拉角、四元数、轴/角之间的转换
- c++中处理相关数学函数