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
还记得
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
首先看下数学公式：
由上面的数学公式，我们转换的C++函数：
具体使用上面两个函数的例子：
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)：
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 D3DDeviceLPDIRECT3DDEVICE9 g_pd3dDevice = NULL; // Our rendering deviceLPDIRECT3DVERTEXBUFFER9 g_pVB = NULL; // Buffer to hold verticesID3DXMesh* 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-axisreturnMatrix->_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-axisreturnMatrix->_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-axisreturnMatrix->_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 indexassert(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 );}//-----------------------------------------// 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)
http://download.csdn.net/detail/fox64194167/4843805 (CSDN下载，免积分)
文章源地址：http://www.waitingfy.com/?p=363
