11.4 外接體（Bounding Volumes）
有時我們需要計算mesh的外接體（邊界范圍），常用的有兩種類型：立方體和球。也有使用其它方法的，如圓柱體，橢球體，菱形體，膠囊形。圖11.4演示了對同一個mesh分別使用立方體和球體類型。
邊界盒/球常常被用來加速可見性測試，碰撞檢測等。假如一個mesh的邊界盒/球不可見，那么我們就說mesh不可見。一個盒/球可見性測試是比分別測試 mesh中的每個三角形要廉價的多。對于一個碰撞檢測例子，如果一枚導彈點火起飛，我們需要檢測它是否擊中了同一場景中的目標。由于這些物體都是由大量三角形構成，我們可以依次檢測每個對象的每個三角形，來測試導彈（可以用射線數學模型）是否碰撞到了這些三角形。這個方法需要進行多次的射線/三角形交點的運算。一個更好的方法是使用邊界盒或邊界球，計算射線與場景中的每個對象的邊界盒/邊界球的交點。如果射線與對象的邊界范圍相交，可以認為該對象被擊中了。這是一個公平的近似方法，如果需要更高的精度，可以用邊界范圍法先去除那些明顯不會相撞的對象，然后用更精確地方法檢測很可能相撞的對象。如果邊界范圍檢測發現相撞，則該對象就很有可能相撞。
D3DX庫提供了計算mesh的邊界盒和邊界球的函數。這些函數使用頂點數組作為輸入計算邊界盒/球。這些函數本來就是設計的很靈活的，它們可以使用各種頂點格式：
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HRESULT D3DXComputeBoundingSphere(
LPD3DXVECTOR3 pFirstPosition,
DWORD NumVertices,
DWORD dwStride,
D3DXVECTOR3* pCenter,
FLOAT* pRadius
);
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pFirstPosition——指向在頂點數組中第一個頂點的向量，描述頂點位置。
NumVertices——在頂點數組中的的頂點數。
dwStride——每個頂點的字節大小。這很重要，因為頂點結構可能有一些額外信息如法向量和紋理坐標，函數需要知道應該跳過多少字節來得到下一個頂點的位置。
pCenter——返回邊界球的中心。
pRadius——返回邊界球的半徑。
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HRESULT D3DXComputeBoundingBox(
LPD3DXVECTOR3 pFirstPosition,
DWORD NumVertices,
DWORD dwStride,
D3DXVECTOR3* pMin,
D3DXVECTOR3* pMax
);
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前三個參數和D3DXComputeBoundingSphere的前三個參數是完全一樣的。最后兩個參數分別用來返回邊界盒的最小和最大點。< /p>
11.4.1一些新的特殊常量
const float INFINITY = FLT_MAX;
const float EPSILON = 0.001f;
常量INFINITY是用來表示一個浮點數所能存儲的最大數。因為我們找不到一個比FLT_MAX還要大的浮點數，我們可以將它視為無窮大。常量 EPSILON是一個很小的值，我們這樣定義它，凡是比它小的數就視為0。這也是很有必要的，因為得到的浮點是不精確的。因此，讓它和0比較相等肯定會失敗。我們因此可以通過把該值與0的差值與EPSILON比較來確定是否相等：
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bool Equals(float lhs, float rhs)
{
// if lhs == rhs their difference should be zero
return fabs(lhs - rhs) < EPSILON ? true : false;
}
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11.4.2外接體類型
為了更容易的使用邊界盒和邊界球，我們將它們分別封裝到兩個類中。
class cBoundingBox
{
public:
D3DXVECTOR3 m_min, m_max;
cBoundingBox();
bool is_point_inside(D3DXVECTOR3& point);
};
class cBoundingSphere
{
public:
D3DXVECTOR3 m_center;
float m_radius;
cBoundingSphere();
};
cBoundingBox::cBoundingBox()
{
m_min.x = INFINITY;
m_min.y = INFINITY;
m_min.z = INFINITY;
m_max.x = -INFINITY;
m_max.y = -INFINITY;
m_max.z = -INFINITY;
}
bool cBoundingBox::is_point_inside(D3DXVECTOR3 &point)
{
return (point.x >= m_min.x && point.y >= m_min.y && point.z >= m_min.z &&
point.x <= m_max.x && point.y <= m_max.y && point.z <= m_max.z);
}
cBoundingSphere::cBoundingSphere()
{
m_radius = 0.0f;
}
11.4.3實例程序：外接體
該實例程序主要演示使用D3DXComputeBoundingSphere和 D3DXComputeBoundingBox。程序讀取一個X文件并且計算該mesh的邊界球，它創建兩個ID3DXMesh對象，一個用來作為邊界球模型一個用來作為邊界盒模型（如下圖所示）。你能夠通過敲空格鍵在邊界球和邊界盒之間切換。
主程序：
/**************************************************************************************
Demonstrates how to use D3DXComputeBoundingSphere and D3DXComputeBoundingBox.
The spacebar key switches between rendering the mesh's bounding sphere and box.
**************************************************************************************/
#include <vector>
#include "d3dUtility.h"
#pragma warning(disable : 4100)
using namespace std;
const int WIDTH = 640;
const int HEIGHT = 480;
IDirect3DDevice9* g_device;
ID3DXMesh* g_mesh;
ID3DXMesh* g_sphere_mesh;
ID3DXMesh* g_box_mesh;
vector<D3DMATERIAL9> g_materials;
vector<IDirect3DTexture9*> g_textures;
bool g_is_render_bounding_sphere = true;
bool compute_bounding_sphere(ID3DXMesh* mesh, cBoundingSphere* sphere);
bool compute_bounding_box(ID3DXMesh* mesh, cBoundingBox* box);
////////////////////////////////////////////////////////////////////////////////////////////////////
bool setup()
{
// load the XFile data
ID3DXBuffer* adjacency_buffer = NULL;
ID3DXBuffer* material_buffer = NULL;
DWORD num_material = 0;
HRESULT hr = D3DXLoadMeshFromX("bigship1.x", D3DXMESH_MANAGED, g_device, &adjacency_buffer, &material_buffer,
NULL, &num_material, &g_mesh);
if(FAILED(hr))
{
MessageBox(NULL, "D3DXLoadMeshFromX() - FAILED", "ERROR", MB_OK);
return false;
}
// extract the materials, and load textures.
if(material_buffer != NULL && num_material != 0)
{
D3DXMATERIAL* materials = (D3DXMATERIAL*) material_buffer->GetBufferPointer();
for(DWORD i = 0; i < num_material; i++)
{
// the MatD3D property doesn't have an ambient value set when it load, so set it now.
materials[i].MatD3D.Ambient = materials[i].MatD3D.Diffuse;
// save the ith material
g_materials.push_back(materials[i].MatD3D);
// check if the ith material has an associative texture
if(materials[i].pTextureFilename != NULL)
{
// yes, load the texture for the ith subset.
IDirect3DTexture9* texture;
D3DXCreateTextureFromFile(g_device, materials[i].pTextureFilename, &texture);
// save the loaded texture
g_textures.push_back(texture);
}
else
{
// no texture for the ith subset
g_textures.push_back(NULL);
}
}
}
safe_release<ID3DXBuffer*>(material_buffer);
// optimize the mesh
hr = g_mesh->OptimizeInplace(D3DXMESHOPT_ATTRSORT | D3DXMESHOPT_COMPACT | D3DXMESHOPT_VERTEXCACHE,
(DWORD*) adjacency_buffer->GetBufferPointer(), NULL, NULL, NULL);
safe_release<ID3DXBuffer*>(adjacency_buffer);
if(FAILED(hr))
{
MessageBox(NULL, "OptimizeInplace() - FAILED", "ERROR", MB_OK);
return false;
}
// compute bounding sphere and bounding box
cBoundingSphere bounding_sphere;
cBoundingBox bounding_box;
compute_bounding_sphere(g_mesh, &bounding_sphere);
compute_bounding_box(g_mesh, &bounding_box);
D3DXCreateSphere(g_device, bounding_sphere.m_radius, 20, 20, &g_sphere_mesh, NULL);
float width = bounding_box.m_max.x - bounding_box.m_min.x;
float height = bounding_box.m_max.y - bounding_box.m_min.y;
float depth = bounding_box.m_max.z - bounding_box.m_min.z;
D3DXCreateBox(g_device, width, height, depth, &g_box_mesh, NULL);
// set texture filters
g_device->SetSamplerState(0, D3DSAMP_MAGFILTER, D3DTEXF_LINEAR);
g_device->SetSamplerState(0, D3DSAMP_MINFILTER, D3DTEXF_LINEAR);
g_device->SetSamplerState(0, D3DSAMP_MIPFILTER, D3DTEXF_LINEAR);
// set lights
D3DXVECTOR3 dir(1.0f, -1.0f, 1.0f);
D3DXCOLOR color(1.0f, 1.0f, 1.0f, 1.0f);
D3DLIGHT9 light = init_directional_light(&dir, &color);
g_device->SetLight(0, &light);
g_device->LightEnable(0, TRUE);
g_device->SetRenderState(D3DRS_NORMALIZENORMALS, TRUE);
g_device->SetRenderState(D3DRS_SPECULARENABLE, TRUE);
// set camera
D3DXVECTOR3 pos(4.0f, 12.0f, -20.0f);
D3DXVECTOR3 target(0.0f, 0.0f, 0.0f);
D3DXVECTOR3 up(0.0f, 1.0f, 0.0f);
D3DXMATRIX view_matrix;
D3DXMatrixLookAtLH(&view_matrix, &pos, &target, &up);
g_device->SetTransform(D3DTS_VIEW, &view_matrix);
// set the projection matrix
D3DXMATRIX proj;
D3DXMatrixPerspectiveFovLH(&proj, D3DX_PI * 0.5f, (float)WIDTH/HEIGHT, 1.0f, 1000.0f);
g_device->SetTransform(D3DTS_PROJECTION, &proj);
return true;
}
///////////////////////////////////////////////////////////////////////////////////////////////////////
void cleanup()
{
safe_release<ID3DXMesh*>(g_mesh);
safe_release<ID3DXMesh*>(g_sphere_mesh);
safe_release<ID3DXMesh*>(g_box_mesh);
for(DWORD i = 0; i < g_textures.size(); i++)
safe_release<IDirect3DTexture9*>(g_textures[i]);
}
///////////////////////////////////////////////////////////////////////////////////////////////////////
bool display(float time_delta)
{
// update: rotate the mesh
static float y = 0.0f;
D3DXMATRIX y_rot_matrix;
D3DXMatrixRotationY(&y_rot_matrix, y);
g_device->SetTransform(D3DTS_WORLD, &y_rot_matrix);
y += time_delta;
if(y >= 6.28f)
y = 0.0f;
// render now
g_device->Clear(0, NULL, D3DCLEAR_TARGET | D3DCLEAR_ZBUFFER, 0x00000000, 1.0f, 0);
g_device->BeginScene();
for(DWORD i = 0; i < g_materials.size(); i++)
{
g_device->SetMaterial(&g_materials[i]);
g_device->SetTexture(0, g_textures[i]);
g_mesh->DrawSubset(i);
}
// draw bounding volume in yellow and at 30% opacity
D3DMATERIAL9 blue_material = YELLOW_MATERIAL;
blue_material.Diffuse.a = 0.30f; // 30% opacity
g_device->SetMaterial(&blue_material);
g_device->SetRenderState(D3DRS_ALPHABLENDENABLE, TRUE);
g_device->SetRenderState(D3DRS_SRCBLEND, D3DBLEND_SRCALPHA);
g_device->SetRenderState(D3DRS_DESTBLEND, D3DBLEND_INVSRCALPHA);
if(g_is_render_bounding_sphere)
g_sphere_mesh->DrawSubset(0);
else
g_box_mesh->DrawSubset(0);
g_device->SetRenderState(D3DRS_ALPHABLENDENABLE, FALSE);
g_device->EndScene();
g_device->Present(NULL, NULL, NULL, NULL);
return true;
}
///////////////////////////////////////////////////////////////////////////////////////////////////////
LRESULT CALLBACK wnd_proc(HWND hwnd, UINT msg, WPARAM word_param, LPARAM long_param)
{
switch(msg)
{
case WM_DESTROY:
PostQuitMessage(0);
break;
case WM_KEYDOWN:
if(word_param == VK_ESCAPE)
DestroyWindow(hwnd);
if(word_param == VK_SPACE)
g_is_render_bounding_sphere = !g_is_render_bounding_sphere;
break;
}
return DefWindowProc(hwnd, msg, word_param, long_param);
}
///////////////////////////////////////////////////////////////////////////////////////////////////////
int WINAPI WinMain(HINSTANCE inst, HINSTANCE, PSTR cmd_line, int cmd_show)
{
if(! init_d3d(inst, WIDTH, HEIGHT, true, D3DDEVTYPE_HAL, &g_device))
{
MessageBox(NULL, "init_d3d() - failed.", 0, MB_OK);
return 0;
}
if(! setup())
{
MessageBox(NULL, "Steup() - failed.", 0, MB_OK);
return 0;
}
enter_msg_loop(display);
cleanup();
g_device->Release();
return 0;
}
///////////////////////////////////////////////////////////////////////////////////////////////////////
bool compute_bounding_sphere(ID3DXMesh* mesh, cBoundingSphere* sphere)
{
BYTE* v;
mesh->LockVertexBuffer(0, (void**)&v);
HRESULT hr = D3DXComputeBoundingSphere((D3DXVECTOR3*)v, mesh->GetNumVertices(),
D3DXGetFVFVertexSize(mesh->GetFVF()), &sphere->m_center, &sphere->m_radius);
mesh->UnlockVertexBuffer();
if(FAILED(hr))
return false;
return true;
}
bool compute_bounding_box(ID3DXMesh* mesh, cBoundingBox* box)
{
BYTE* v;
mesh->LockVertexBuffer(0, (void**)&v);
HRESULT hr = D3DXComputeBoundingBox((D3DXVECTOR3*)v, mesh->GetNumVertices(),
D3DXGetFVFVertexSize(mesh->GetFVF()), &box->m_min, &box->m_max);
mesh->UnlockVertexBuffer();
if(FAILED(hr))
return false;
return true;
}
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