渐变（tweening）网格模型是Direct3D中实现模型动画最简单的方式和途径，它的原理也非常简单。例如对于场景内的某个网格模型，最初只记录t0时刻和t1时刻该网格模型的状态（即这两个时刻网格模型中所有顶点的位置），对于t0到t1这段时间内的任意时刻t_current，根据该时刻距离t0和t1时刻的远近，实时地分配给这两个网格模型不同的权重，然后按照这两个网格模型中顶点的不同位置和它们各自的权重进行插值，计算出t_current时刻整个网格模型中所有顶点的位置，从而实现动画效果。

通常将t0时刻的网格模型称为源网格模型，将t1时刻的网格模型称为目标网格模型，将最后拟合得到的网格模型称为结果网格模型。当然初始条件还可以是3个或更多时刻网格模型的状态，再根据时间的推移对这些网格模型进行插值而实时得到当前时刻网格模型的状态。

事实上，渐变网格模型就是对一系列已知的网格模型进行插值得到最终的网格模型。

首先，我们需要从.x文件加载源网格模型和目标网格模型:

V_RETURN(D3DXLoadMeshFromXW(L"source.x", D3DXMESH_MANAGED, pd3dDevice, NULL, NULL, NULL, &g_num_materials, &g_source_mesh));

V_RETURN(D3DXLoadMeshFromXW(L"target.x", D3DXMESH_MANAGED, pd3dDevice, NULL, NULL, NULL, &g_num_materials, &g_target_mesh));

由于我们仅对两个网格模型中的顶点位置坐标和法向量进行插值，所以在创建好源网格模型和目标网格模型后，需要按照指定的顶点格式克隆源网格模型、目标网格模型和结果网格模型，使这时的源网格模型、目标网格模型和结果网格模型仅包含顶点位置和法向量：

ID3DXMesh* cloned_mesh;

// clone source mesh with specified vertex format
g_source_mesh->CloneMeshFVF(g_source_mesh->GetOptions(), CUSTOM_VERTEX_FVF, pd3dDevice, &cloned_mesh);
release_com(g_source_mesh);
g_source_mesh = cloned_mesh;

// clone target mesh with specified vertex format
g_target_mesh->CloneMeshFVF(g_target_mesh->GetOptions(), CUSTOM_VERTEX_FVF, pd3dDevice, &cloned_mesh);
release_com(g_target_mesh);
g_target_mesh = cloned_mesh;

// clone result mesh with specified vertex format from target mesh
g_target_mesh->CloneMeshFVF(g_target_mesh->GetOptions(), CUSTOM_VERTEX_FVF, pd3dDevice, &g_result_mesh);

g_source_mesh->GetVertexBuffer(&g_source_vb);
g_target_mesh->GetVertexBuffer(&g_target_vb);
g_result_mesh->GetVertexBuffer(&g_result_vb);

其中源网格模型的状态如下图所示：

目标网格模型的状态如下图所示：

最后我们根据程序当前运行时间，分别计算源网格模型和目标网格模型的权重，利用计算出的权重对源网格模型和目标网格模型的顶点坐标和法向量进行插值，得到当前时刻的结果网格模型：

sVertex* source_vertices;
sVertex* target_vertices;
sVertex* result_vertices;

g_source_vb->Lock(0, 0, (void**) &source_vertices, 0);
g_target_vb->Lock(0, 0, (void**) &target_vertices, 0);
g_result_vb->Lock(0, 0, (void**) &result_vertices, 0);

float time_factor = (float)(timeGetTime() % 2000) / 1000.0f;
float scalar      = (time_factor <= 1.0f) ? time_factor : (2.0f - time_factor);

for(DWORD i = 0; i < g_result_mesh->GetNumVertices(); i++)
{result_vertices[i].x = source_vertices[i].x * (1.0f - scalar) + target_vertices[i].x * scalar;result_vertices[i].y = source_vertices[i].y * (1.0f - scalar) + target_vertices[i].y * scalar;result_vertices[i].z = source_vertices[i].z * (1.0f - scalar) + target_vertices[i].z * scalar;

   result_vertices[i].nx = source_vertices[i].nx * (1.0f - scalar) + target_vertices[i].nx * scalar;result_vertices[i].ny = source_vertices[i].ny * (1.0f - scalar) + target_vertices[i].ny * scalar;result_vertices[i].nz = source_vertices[i].nz * (1.0f - scalar) + target_vertices[i].nz * scalar;
}

g_source_vb->Unlock();
g_target_vb->Unlock();
g_result_vb->Unlock();

为了让海豚动起来，我们还必须修改世界坐标矩阵：

// move dolphin around circle

float kick_freq = float(2.0f * fTime);
float phas       = float(fTime) / 3.0f;

D3DXMATRIX mat_dolphin, mat_trans, mat_rot_y, mat_rot_z;

D3DXMatrixScaling(&mat_dolphin, 0.01f, 0.01f, 0.01f);
D3DXMatrixRotationZ(&mat_rot_z, -cosf(kick_freq) / 6);
D3DXMatrixRotationY(&mat_rot_y, phase);
D3DXMatrixTranslation(&mat_trans, -5 * sinf(phase), sinf(kick_freq)/2, 10 - 10 * cosf(phase));

mat_dolphin = mat_dolphin * mat_rot_z * mat_rot_y * mat_trans;;

pd3dDevice->SetTransform(D3DTS_WORLD, &mat_dolphin);

运行效果图：

主程序：

#include "dxstdafx.h"
#include "resource.h"

#pragma warning(disable : 4127 4995)

#define IDC_TOGGLE_FULLSCREEN 1
#define IDC_TOGGLE_REF 2
#define IDC_CHANGE_DEVICE        3

struct sVertex
{
    float x, y, z;
    float nx, ny, nz;
};

const DWORD CUSTOM_VERTEX_FVF = D3DFVF_XYZ | D3DFVF_NORMAL;

#define release_com(p)    do { if(p) { (p)->Release(); (p) = NULL; } } while(0)

ID3DXFont*                    g_font;
ID3DXSprite*                g_text_sprite;
bool                        g_show_help;

CDXUTDialogResourceManager    g_dlg_resource_manager;
CD3DSettingsDlg                g_settings_dlg;
CDXUTDialog                    g_button_dlg;

ID3DXMesh*                    g_source_mesh;
ID3DXMesh*                    g_target_mesh;
ID3DXMesh*                    g_result_mesh;

IDirect3DVertexBuffer9*        g_source_vb;
IDirect3DVertexBuffer9*        g_target_vb;
IDirect3DVertexBuffer9*        g_result_vb;

DWORD                        g_num_materials;

//--------------------------------------------------------------------------------------
// Rejects any devices that aren't acceptable by returning false
//--------------------------------------------------------------------------------------
bool CALLBACK IsDeviceAcceptable( D3DCAPS9* pCaps, D3DFORMAT AdapterFormat,
                                  D3DFORMAT BackBufferFormat, bool bWindowed, void* pUserContext )
{
    // Typically want to skip backbuffer formats that don't support alpha blending

IDirect3D9* pD3D = DXUTGetD3DObject();

if( FAILED( pD3D->CheckDeviceFormat( pCaps->AdapterOrdinal, pCaps->DeviceType, AdapterFormat,
                    D3DUSAGE_QUERY_POSTPIXELSHADER_BLENDING, D3DRTYPE_TEXTURE, BackBufferFormat ) ) )
        return false;

return true;
}

//--------------------------------------------------------------------------------------
// Before a device is created, modify the device settings as needed.
//--------------------------------------------------------------------------------------
bool CALLBACK ModifyDeviceSettings( DXUTDeviceSettings* pDeviceSettings, const D3DCAPS9* pCaps, void* pUserContext )
{
    // If video card does not support hardware vertex processing, then uses sofaware vertex processing.
    if((pCaps->DevCaps & D3DDEVCAPS_HWTRANSFORMANDLIGHT) == 0)
        pDeviceSettings->BehaviorFlags = D3DCREATE_SOFTWARE_VERTEXPROCESSING;

static bool is_first_time = true;

if(is_first_time)
    {
        is_first_time = false;

// if using reference device, then pop a warning message box.
        if(pDeviceSettings->DeviceType == D3DDEVTYPE_REF)
            DXUTDisplaySwitchingToREFWarning();
    }

return true;
}

//--------------------------------------------------------------------------------------
// Remove path from fullname, and convert filename from multibyte to wchar.
//--------------------------------------------------------------------------------------
void RemovePathFromFileName(LPSTR fullname, LPWSTR wfilename)
{
    WCHAR wbuf[MAX_PATH]  = {0};
    MultiByteToWideChar(CP_ACP, 0, fullname, -1, wbuf, MAX_PATH);

LPWSTR w_last_back_slash = wcsrchr(wbuf, '\\');

if(w_last_back_slash)
        lstrcpy(wfilename, ++w_last_back_slash);
    else
        lstrcpy(wfilename, wbuf);
}

//--------------------------------------------------------------------------------------
// Create any D3DPOOL_MANAGED resources here
//--------------------------------------------------------------------------------------
HRESULT CALLBACK OnCreateDevice( IDirect3DDevice9* pd3dDevice,
                                 const D3DSURFACE_DESC* pBackBufferSurfaceDesc,
                                 void* pUserContext )
{
    HRESULT    hr;

V_RETURN(g_dlg_resource_manager.OnCreateDevice(pd3dDevice));
    V_RETURN(g_settings_dlg.OnCreateDevice(pd3dDevice));

D3DXCreateFont(pd3dDevice, 18, 0, FW_BOLD, 1, FALSE, DEFAULT_CHARSET, OUT_DEFAULT_PRECIS, DEFAULT_QUALITY,
                   DEFAULT_PITCH | FF_DONTCARE, L"Arial", &g_font);

V_RETURN(D3DXLoadMeshFromXW(L"source.x", D3DXMESH_MANAGED, pd3dDevice, NULL, NULL, NULL, &g_num_materials,
                                &g_source_mesh));

V_RETURN(D3DXLoadMeshFromXW(L"target.x", D3DXMESH_MANAGED, pd3dDevice, NULL, NULL, NULL, &g_num_materials,
                                &g_target_mesh));

ID3DXMesh* cloned_mesh;

// clone source mesh with specified vertex format
    g_source_mesh->CloneMeshFVF(g_source_mesh->GetOptions(), CUSTOM_VERTEX_FVF, pd3dDevice, &cloned_mesh);
    release_com(g_source_mesh);
    g_source_mesh = cloned_mesh;

// clone target mesh with specified vertex format
    g_target_mesh->CloneMeshFVF(g_target_mesh->GetOptions(), CUSTOM_VERTEX_FVF, pd3dDevice, &cloned_mesh);
    release_com(g_target_mesh);
    g_target_mesh = cloned_mesh;

// clone result mesh with specified vertex format from target mesh
    g_target_mesh->CloneMeshFVF(g_target_mesh->GetOptions(), CUSTOM_VERTEX_FVF, pd3dDevice, &g_result_mesh);

g_source_mesh->GetVertexBuffer(&g_source_vb);
    g_target_mesh->GetVertexBuffer(&g_target_vb);
    g_result_mesh->GetVertexBuffer(&g_result_vb);

return S_OK;
}

//--------------------------------------------------------------------------------------
// Create any D3DPOOL_DEFAULT resources here
//--------------------------------------------------------------------------------------
HRESULT CALLBACK OnResetDevice( IDirect3DDevice9* pd3dDevice,
                                const D3DSURFACE_DESC* pBackBufferSurfaceDesc,
                                void* pUserContext )
{
    HRESULT hr;

V_RETURN(g_dlg_resource_manager.OnResetDevice());
    V_RETURN(g_settings_dlg.OnResetDevice());
    V_RETURN(g_font->OnResetDevice());
    V_RETURN(D3DXCreateSprite(pd3dDevice, &g_text_sprite));

// set dialog position and size

g_button_dlg.SetLocation(pBackBufferSurfaceDesc->Width - 170, 0);
    g_button_dlg.SetSize(170, 170);

// setup view matrix

D3DXMATRIX mat_view;
    D3DXVECTOR3 eye(0.0f, 0.0f,  -8.0f);
    D3DXVECTOR3  at(0.0f, 0.0f,  0.0f);
    D3DXVECTOR3  up(0.0f, 1.0f,  0.0f);

D3DXMatrixLookAtLH(&mat_view, &eye, &at, &up);
    pd3dDevice->SetTransform(D3DTS_VIEW, &mat_view);

// set projection matrix
    D3DXMATRIX mat_proj;
    float aspect = (float)pBackBufferSurfaceDesc->Width / pBackBufferSurfaceDesc->Height;
    D3DXMatrixPerspectiveFovLH(&mat_proj, D3DX_PI/4, aspect, 1.0f, 100.0f);
    pd3dDevice->SetTransform(D3DTS_PROJECTION, &mat_proj);

// setup material

D3DMATERIAL9 material;
    ZeroMemory(&material, sizeof(D3DMATERIAL9));

material.Diffuse.r = 0.5f;
    material.Diffuse.g = 0.5f;
    material.Diffuse.b = 0.8f;
    material.Diffuse.a = 1.0f;

material.Ambient.r = 0.5f;
    material.Ambient.g = 0.5f;
    material.Ambient.b = 0.8f;
    material.Ambient.a = 1.0f;

pd3dDevice->SetMaterial(&material);

// setup light

D3DLIGHT9 light;
    ZeroMemory(&light, sizeof(D3DLIGHT9));

light.Type       = D3DLIGHT_DIRECTIONAL;

light.Diffuse.r  = 0.1f;
    light.Diffuse.g  = 0.1f;
    light.Diffuse.b  = 0.3f;
    light.Diffuse.a  = 1.0f;

light.Ambient.r  = 0.1f;
    light.Ambient.g  = 0.1f;
    light.Ambient.b  = 0.3f;
    light.Ambient.a  = 1.0f;

D3DXVECTOR3 light_dir = D3DXVECTOR3(-1, -1, 1);
    D3DXVec3Normalize((D3DXVECTOR3*) &light.Direction, &light_dir);
    pd3dDevice->SetLight(0, &light);
    pd3dDevice->LightEnable(0, TRUE);
    pd3dDevice->SetRenderState(D3DRS_LIGHTING, TRUE);

return S_OK;
}

//--------------------------------------------------------------------------------------
// Release resources created in the OnResetDevice callback here
//--------------------------------------------------------------------------------------
void CALLBACK OnLostDevice( void* pUserContext )
{
    g_dlg_resource_manager.OnLostDevice();
    g_settings_dlg.OnLostDevice();
    g_font->OnLostDevice();

release_com(g_text_sprite);
}

//--------------------------------------------------------------------------------------
// Release resources created in the OnCreateDevice callback here
//--------------------------------------------------------------------------------------
void CALLBACK OnDestroyDevice( void* pUserContext )
{
    g_dlg_resource_manager.OnDestroyDevice();
    g_settings_dlg.OnDestroyDevice();

release_com(g_font);

release_com(g_source_mesh);
    release_com(g_target_mesh);   
    release_com(g_result_mesh);

release_com(g_source_vb);
    release_com(g_target_vb);
    release_com(g_result_vb);
}

//--------------------------------------------------------------------------------------
// Handle updates to the scene
//--------------------------------------------------------------------------------------
void CALLBACK OnFrameMove( IDirect3DDevice9* pd3dDevice, double fTime, float fElapsedTime, void* pUserContext )
{
    sVertex* source_vertices;
    sVertex* target_vertices;
    sVertex* result_vertices;

g_source_vb->Lock(0, 0, (void**) &source_vertices, 0);
    g_target_vb->Lock(0, 0, (void**) &target_vertices, 0);
    g_result_vb->Lock(0, 0, (void**) &result_vertices, 0);

float time_factor = (float)(timeGetTime() % 2000) / 1000.0f;
    float scalar      = (time_factor <= 1.0f) ? time_factor : (2.0f - time_factor);

for(DWORD i = 0; i < g_result_mesh->GetNumVertices(); i++)
    {
        result_vertices[i].x = source_vertices[i].x * (1.0f - scalar) + target_vertices[i].x * scalar;
        result_vertices[i].y = source_vertices[i].y * (1.0f - scalar) + target_vertices[i].y * scalar;
        result_vertices[i].z = source_vertices[i].z * (1.0f - scalar) + target_vertices[i].z * scalar;

result_vertices[i].nx = source_vertices[i].nx * (1.0f - scalar) + target_vertices[i].nx * scalar;
        result_vertices[i].ny = source_vertices[i].ny * (1.0f - scalar) + target_vertices[i].ny * scalar;
        result_vertices[i].nz = source_vertices[i].nz * (1.0f - scalar) + target_vertices[i].nz * scalar;
    }

g_source_vb->Unlock();
    g_target_vb->Unlock();
    g_result_vb->Unlock();

// move dolphin around circle

float kick_freq = float(2.0f * fTime);
    float phase        = float(fTime) / 3.0f;

D3DXMATRIX mat_dolphin, mat_trans, mat_rot_y, mat_rot_z;

D3DXMatrixScaling(&mat_dolphin, 0.01f, 0.01f, 0.01f);
    D3DXMatrixRotationZ(&mat_rot_z, -cosf(kick_freq) / 6);
    D3DXMatrixRotationY(&mat_rot_y, phase);
    D3DXMatrixTranslation(&mat_trans, -5 * sinf(phase), sinf(kick_freq)/2, 10 - 10 * cosf(phase));

mat_dolphin = mat_dolphin * mat_rot_z * mat_rot_y * mat_trans;;

pd3dDevice->SetTransform(D3DTS_WORLD, &mat_dolphin);
}

//--------------------------------------------------------------------------------------
// Render the helper information
//--------------------------------------------------------------------------------------
void RenderText()
{
    CDXUTTextHelper text_helper(g_font, g_text_sprite, 20);
   
    text_helper.Begin();

// show frame and device states
    text_helper.SetInsertionPos(5, 5);
    text_helper.SetForegroundColor( D3DXCOLOR(1.0f, 0.475f, 0.0f, 1.0f) );
    text_helper.DrawTextLine( DXUTGetFrameStats(true) );
    text_helper.DrawTextLine( DXUTGetDeviceStats() );

// show helper information
   
    const D3DSURFACE_DESC* surface_desc = DXUTGetBackBufferSurfaceDesc();

if(g_show_help)
    {
        text_helper.SetInsertionPos(10, surface_desc->Height - 15 * 6);
        text_helper.SetForegroundColor( D3DXCOLOR(1.0f, 0.475f, 0.0f, 1.0f) );
        text_helper.DrawTextLine(L"Controls (F1 to hide):");
       
        text_helper.SetInsertionPos(40, surface_desc->Height - 15 * 4);
        text_helper.DrawTextLine(L"Quit: ESC");
    }
    else
    {
        text_helper.SetInsertionPos(10, surface_desc->Height - 15 * 4);
        text_helper.SetForegroundColor( D3DXCOLOR(1.0f, 1.0f, 1.0f, 1.0f) );
        text_helper.DrawTextLine(L"Press F1 for help");
    }

text_helper.End();
}

//--------------------------------------------------------------------------------------
// Render the scene
//--------------------------------------------------------------------------------------
void CALLBACK OnFrameRender( IDirect3DDevice9* pd3dDevice, double fTime, float fElapsedTime, void* pUserContext )
{
    HRESULT hr;

if(g_settings_dlg.IsActive())
    {
        g_settings_dlg.OnRender(fElapsedTime);
        return;
    }

// Clear the render target and the zbuffer
    V( pd3dDevice->Clear(0, NULL, D3DCLEAR_TARGET | D3DCLEAR_ZBUFFER, D3DCOLOR_ARGB(0, 32, 64, 128), 1.0f, 0) );

// Render the scene
    if( SUCCEEDED( pd3dDevice->BeginScene() ) )
    {
        for(DWORD i = 0; i < g_num_materials; i++)
            g_result_mesh->DrawSubset(i);

RenderText();
        V(g_button_dlg.OnRender(fElapsedTime));

V( pd3dDevice->EndScene() );
    }
}

//--------------------------------------------------------------------------------------
// Handle messages to the application
//--------------------------------------------------------------------------------------
LRESULT CALLBACK MsgProc( HWND hWnd, UINT uMsg, WPARAM wParam, LPARAM lParam,
                          bool* pbNoFurtherProcessing, void* pUserContext )
{
    *pbNoFurtherProcessing = g_dlg_resource_manager.MsgProc(hWnd, uMsg, wParam, lParam);
    if(*pbNoFurtherProcessing)
        return 0;

if(g_settings_dlg.IsActive())
    {
        g_settings_dlg.MsgProc(hWnd, uMsg, wParam, lParam);
        return 0;
    }

*pbNoFurtherProcessing = g_button_dlg.MsgProc(hWnd, uMsg, wParam, lParam);
    if(*pbNoFurtherProcessing)
        return 0;
   
    return 0;
}

//--------------------------------------------------------------------------------------
// Handle keybaord event
//--------------------------------------------------------------------------------------
void CALLBACK OnKeyboardProc(UINT charater, bool is_key_down, bool is_alt_down, void* user_context)
{
    if(is_key_down)
    {
        switch(charater)
        {
        case VK_F1:
            g_show_help = !g_show_help;
            break;
        }
    }
}

//--------------------------------------------------------------------------------------
// Handle events for controls
//--------------------------------------------------------------------------------------
void CALLBACK OnGUIEvent(UINT event, int control_id, CDXUTControl* control, void* user_context)
{
    switch(control_id)
    {
    case IDC_TOGGLE_FULLSCREEN:
        DXUTToggleFullScreen();
        break;

case IDC_TOGGLE_REF:
        DXUTToggleREF();
        break;

case IDC_CHANGE_DEVICE:
        g_settings_dlg.SetActive(true);
        break;
    }
}

//--------------------------------------------------------------------------------------
// Initialize dialogs
//--------------------------------------------------------------------------------------
void InitDialogs()
{
    g_settings_dlg.Init(&g_dlg_resource_manager);
    g_button_dlg.Init(&g_dlg_resource_manager);

g_button_dlg.SetCallback(OnGUIEvent);

int x = 35, y = 10, width = 125, height = 22;

g_button_dlg.AddButton(IDC_TOGGLE_FULLSCREEN, L"Toggle full screen", x, y,         width, height);
    g_button_dlg.AddButton(IDC_TOGGLE_REF,          L"Toggle REF (F3)",     x, y += 24, width, height);
    g_button_dlg.AddButton(IDC_CHANGE_DEVICE,      L"Change device (F2)", x, y += 24, width, height, VK_F2);
}

//--------------------------------------------------------------------------------------
// Initialize everything and go into a render loop
//--------------------------------------------------------------------------------------
INT WINAPI WinMain( HINSTANCE, HINSTANCE, LPSTR, int )
{
    // Enable run-time memory check for debug builds.
#if defined(DEBUG) | defined(_DEBUG)
    _CrtSetDbgFlag( _CRTDBG_ALLOC_MEM_DF | _CRTDBG_LEAK_CHECK_DF );
#endif

// Set the callback functions
    DXUTSetCallbackDeviceCreated( OnCreateDevice );
    DXUTSetCallbackDeviceReset( OnResetDevice );
    DXUTSetCallbackDeviceLost( OnLostDevice );
    DXUTSetCallbackDeviceDestroyed( OnDestroyDevice );
    DXUTSetCallbackMsgProc( MsgProc );
    DXUTSetCallbackFrameRender( OnFrameRender );
    DXUTSetCallbackFrameMove( OnFrameMove );
    DXUTSetCallbackKeyboard(OnKeyboardProc);
  
    // TODO: Perform any application-level initialization here
    InitDialogs();

// Initialize DXUT and create the desired Win32 window and Direct3D device for the application
    DXUTInit( true, true, true ); // Parse the command line, handle the default hotkeys, and show msgboxes
    DXUTSetCursorSettings( true, true ); // Show the cursor and clip it when in full screen
    DXUTCreateWindow( L"Tweening" );
    DXUTCreateDevice( D3DADAPTER_DEFAULT, true, 640, 480, IsDeviceAcceptable, ModifyDeviceSettings );

// Start the render loop
    DXUTMainLoop();

// TODO: Perform any application-level cleanup here

return DXUTGetExitCode();
}

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