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創(chuàng)建3D圖形引擎（2）

本篇是創(chuàng)建3D圖形引擎（1）的續(xù)篇，3D圖形引擎的代碼以創(chuàng)建游戲內(nèi)核中編寫(xiě)的代碼為基礎(chǔ)進(jìn)行開(kāi)發(fā)。

視錐的介紹

視錐（viewing frustum）是6個(gè)平面的集合，它從觀察點(diǎn)向外擴(kuò)展，以確定某個(gè)多邊形是否能夠被觀察到。

首先，可以將視錐看作是一個(gè)以觀察者開(kāi)始擴(kuò)展的金字塔，如下圖所示：

這個(gè)金字塔代表了觀察范圍（field of view，FOV），位于觀察范圍內(nèi)的物體是可見(jiàn)的，而位于觀察范圍外的物體則是不可見(jiàn)的。

三維圖形引擎的每個(gè)物體都是由3D點(diǎn)（稱為頂點(diǎn)）構(gòu)成的，每個(gè)視錐包含6個(gè)面（前、后、左、右、上、下）。通過(guò)一些數(shù)學(xué)計(jì)算，可以確定哪些頂點(diǎn)位于視錐內(nèi)，哪些頂點(diǎn)位于視錐外。位于視錐內(nèi)的頂點(diǎn)被渲染，而位于視錐外的頂點(diǎn)則不被渲染。同樣，當(dāng)渲染多邊形時(shí)，只有那些在視錐內(nèi)的頂點(diǎn)才被渲染。

平面與裁剪

視錐的6個(gè)側(cè)面被稱為剪切平面（clipping plane），Direct3D使用了一個(gè)名為D3DXPLANE的特定對(duì)象去包含平面數(shù)據(jù)，D3DXPLANE包含了4個(gè)變量：a、b、c、d，它們都是浮點(diǎn)型數(shù)據(jù)。

定義好一個(gè)平面后，為它指定一個(gè)特定的方向，并將它從原點(diǎn)移到相應(yīng)的位置。事實(shí)上，一個(gè)平面就是由一條法線以及它與原點(diǎn)的距離進(jìn)行定義的，如下圖所示，它演示了一個(gè)平面在三維空間中的方位。

不需要指定X、Y、Z的具體數(shù)值，你只要使用變量A、B、C，同時(shí)還有一個(gè)數(shù)值D來(lái)確定平面離原點(diǎn)的距離。為了定義一個(gè)平面，將A、B、C設(shè)置為法向量的值，這樣就可以使用一個(gè)平面去檢測(cè)指定的點(diǎn)位于平面的前面或者后面。

為了計(jì)算視錐的6個(gè)平面，可以將當(dāng)前的觀察變換矩陣和投影矩陣組合起來(lái)，然后使用組合矩陣直接計(jì)算每個(gè)平面的A、B、C、D。

平面可見(jiàn)性檢測(cè)

為了檢測(cè)一個(gè)頂點(diǎn)位于平面的前方或后方，可以利用點(diǎn)積來(lái)計(jì)算，通過(guò)調(diào)用D3DXPlaneCoord函數(shù)來(lái)實(shí)現(xiàn)。

Computes the dot product of a plane and a 3D vector. The w parameter of the vector is assumed to be 1.

FLOAT D3DXPlaneDotCoord(
  CONST D3DXPLANE * pP,
  CONST D3DXVECTOR3 * pV
);

Parameters

pP: [in] Pointer to a source D3DXPLANE structure.
pV: [in] Pointer to a source D3DXVECTOR3 structure.

Return Values

The dot product of the plane and 3D vector.

Remarks

Given a plane (a, b, c, d) and a 3D vector (x, y, z) the return value of this function is a*x + b*y + c*z + d*1. The D3DXPlaneDotCoord function is useful for determining the plane's relationship with a coordinate in 3D space.

完整視錐的檢測(cè)

對(duì)于立方體和長(zhǎng)方體，需檢測(cè)所有的拐角頂點(diǎn)。如果所有的頂點(diǎn)都位于任一平面之后，那么立方體或長(zhǎng)方體就位于視錐之外（因而也在視野之外）。如果有任一頂點(diǎn)位于視錐之內(nèi)，或者說(shuō)位于任一平面前（也就是說(shuō)不是所有的頂點(diǎn)都位于任一平面后），那就意味著立方體或者長(zhǎng)方體是可見(jiàn)的。至于球體，只要它與每個(gè)平面的距離等于或大于球形的平面，那么它就是可見(jiàn)的。

FRUSTUM類

因?yàn)槊看问褂靡曞F所涉及的數(shù)學(xué)運(yùn)算都是一樣的，所以完全可以創(chuàng)建一個(gè)類，讓它處理好數(shù)學(xué)方面的問(wèn)題，包括創(chuàng)建視錐以及使用視錐去檢測(cè)一個(gè)物體是否可見(jiàn)等。

//==============================================================================
// This class encapsulate for frustum, judge whether other object is in frustum.
//==============================================================================
typedef class FRUSTUM
{
public:
    // Construct the six planes from current view and projection.
    // Can override the default depth value.
    BOOL construct(GRAPHICS_PTR graphics, float z_distance = 0.0f);

    // The following functions check a single point, cube, rectangle, and sphere if
    // contained in the frustum. A return value of TRUE means visible, FALSE not visible.
    // When checking cubes or rectangles, you can supply a BOOL variable that determines
    // if all the points are in the frustum.

    BOOL check_point(float x_pos, float y_pos, float z_pos);

    BOOL check_cube(float x_center, float y_center, float z_center,
                    float radius,
                    BOOL* completely_contained = NULL);

    BOOL check_rectangle(float x_center, float y_center, float z_center,
                         float x_radius, float y_radius, float z_radius,
                         BOOL* completely_contained = NULL);

    BOOL check_sphere(float x_center, float y_center, float z_center,
                      float radius);

private:
    D3DXPLANE _planes[6];       // the frustum planes
} *FRUSTUM_PTR;

每當(dāng)觀察或投影矩陣發(fā)生變化時(shí)，請(qǐng)調(diào)用construct去構(gòu)造6個(gè)測(cè)試平面，如果僅希望最接近的物體能被看到，則可以為遠(yuǎn)端剪切平面指定一個(gè)新的距離值。

//----------------------------------------------------------------------------
// Construct frustum.
//----------------------------------------------------------------------------
BOOL FRUSTUM::construct(GRAPHICS_PTR graphics, float z_distance)
{
    D3DXMATRIX matrix, mat_view, mat_proj;

    // error checking
    if(graphics == NULL)
        return FALSE;

    // calculate FOV data
    graphics->get_device_com()->GetTransform(D3DTS_PROJECTION, &mat_proj);

    if(! float_equal(z_distance, 0.0f))
    {
        // Calculate new projection matrix based on distance provided.
        //
        // projection matrix is:
        //
        // | xScale     0          0               0 |
        // | 0        yScale       0               0 |
        // | 0          0       zf/(zf-zn)         1 |
        // | 0          0       -zn*zf/(zf-zn)     0 |
        //
        // where:
        //      yScale = cot(fovY/2)
        //      xScale = yScale / aspect ratio

        float z_min = -mat_proj._43 / mat_proj._33;
        float q = z_distance / (z_distance - z_min);

        mat_proj._33 = q;
        mat_proj._43 = -q * z_min;
    }

    graphics->get_device_com()->GetTransform(D3DTS_VIEW, &mat_view);
    D3DXMatrixMultiply(&matrix, &mat_view, &mat_proj);

    // calculate the planes
    _planes[0].a = matrix._14 + matrix._13; // Near
    _planes[0].b = matrix._24 + matrix._23;
    _planes[0].c = matrix._34 + matrix._33;
    _planes[0].d = matrix._44 + matrix._43;
    D3DXPlaneNormalize(&_planes[0], &_planes[0]);

    _planes[1].a = matrix._14 - matrix._13; // Far
    _planes[1].b = matrix._24 - matrix._23;
    _planes[1].c = matrix._34 - matrix._33;
    _planes[1].d = matrix._44 - matrix._43;
    D3DXPlaneNormalize(&_planes[1], &_planes[1]);

    _planes[2].a = matrix._14 + matrix._11; // Left
    _planes[2].b = matrix._24 + matrix._21;
    _planes[2].c = matrix._34 + matrix._31;
    _planes[2].d = matrix._44 + matrix._41;
    D3DXPlaneNormalize(&_planes[2], &_planes[2]);

    _planes[3].a = matrix._14 - matrix._11; // Right
    _planes[3].b = matrix._24 - matrix._21;
    _planes[3].c = matrix._34 - matrix._31;
    _planes[3].d = matrix._44 - matrix._41;
    D3DXPlaneNormalize(&_planes[3], &_planes[3]);

    _planes[4].a = matrix._14 - matrix._12; // Top
    _planes[4].b = matrix._24 - matrix._22;
    _planes[4].c = matrix._34 - matrix._32;
    _planes[4].d = matrix._44 - matrix._42;
    D3DXPlaneNormalize(&_planes[4], &_planes[4]);

    _planes[5].a = matrix._14 + matrix._12; // Bottom
    _planes[5].b = matrix._24 + matrix._22;
    _planes[5].c = matrix._34 + matrix._32;
    _planes[5].d = matrix._44 + matrix._42;
    D3DXPlaneNormalize(&_planes[5], &_planes[5]);

    return TRUE;
}

使用check系列函數(shù)判斷物體在視錐內(nèi)是否可見(jiàn)。

//----------------------------------------------------------------------------
// Check one point whether in frustum.
//----------------------------------------------------------------------------
BOOL FRUSTUM::check_point(float x_pos, float y_pos, float z_pos)
{
    // make sure point is in frustum
    for(short i = 0; i < 6; i++)
    {
        if(D3DXPlaneDotCoord(&_planes[i], &D3DXVECTOR3(x_pos, y_pos, z_pos)) < 0.0f)
            return FALSE;
    }

    return TRUE;
}

//----------------------------------------------------------------------------
// Check whether a cube in frustum, if total cube in frustum then
// completely_contained will be set TRUE.
//----------------------------------------------------------------------------
BOOL FRUSTUM::check_cube(float x_center, float y_center, float z_center,
                         float radius,
                         BOOL* completely_contained)
{
    DWORD num_points_in_frustum = 0;

    // count the number of points inside the frustum
    for(short i = 0; i < 6; i++)
    {
        DWORD count = 8;
        BOOL in_all_planes = TRUE;

        // test all eight points against plane

        if(D3DXPlaneDotCoord(&_planes[i], &D3DXVECTOR3(x_center - radius, y_center - radius, z_center - radius)) < 0.0f)
        {
            in_all_planes = FALSE;
            count--;
        }

        if(D3DXPlaneDotCoord(&_planes[i], &D3DXVECTOR3(x_center + radius, y_center - radius, z_center - radius)) < 0.0f)
        {
          in_all_planes = FALSE;
          count--;
        }

        if(D3DXPlaneDotCoord(&_planes[i], &D3DXVECTOR3(x_center - radius, y_center + radius, z_center - radius)) < 0.0f)
        {
          in_all_planes = FALSE;
          count--;
        }

        if(D3DXPlaneDotCoord(&_planes[i], &D3DXVECTOR3(x_center + radius, y_center + radius, z_center - radius)) < 0.0f)
        {
          in_all_planes = FALSE;
          count--;
        }

        if(D3DXPlaneDotCoord(&_planes[i], &D3DXVECTOR3(x_center - radius, y_center - radius, z_center + radius)) < 0.0f)
        {
          in_all_planes = FALSE;
          count--;
        }

        if(D3DXPlaneDotCoord(&_planes[i], &D3DXVECTOR3(x_center + radius, y_center - radius, z_center + radius)) < 0.0f)
        {
          in_all_planes = FALSE;
          count--;
        }

        if(D3DXPlaneDotCoord(&_planes[i], &D3DXVECTOR3(x_center - radius, y_center + radius, z_center + radius)) < 0.0f)
        {
          in_all_planes = FALSE;
          count--;
        }

        if(D3DXPlaneDotCoord(&_planes[i], &D3DXVECTOR3(x_center + radius, y_center + radius, z_center + radius)) < 0.0f)
        {
          in_all_planes = FALSE;
          count--;
        }

        // if none contained, return FALSE.
        if(count == 0)
            return FALSE;

        // update counter if they were all in front of plane.
        if(in_all_planes)
            ++num_points_in_frustum;
    }

    // store BOOL flag if completely contained
    if(completely_contained)
        *completely_contained = (num_points_in_frustum == 6);

    return TRUE;
}

//----------------------------------------------------------------------------
// Check whether a rectangle is in frustum, if total in then completely_contained
// will be set TRUE.
//----------------------------------------------------------------------------
BOOL FRUSTUM::check_rectangle(float x_center, float y_center, float z_center,
                              float x_radius, float y_radius, float z_radius,
                              BOOL* completely_contained)
{
    DWORD num_points_in_frustum = 0;

    // count the number of points inside the frustum
    for(short i = 0; i < 6; i++)
    {
        DWORD count = 8;
        BOOL  in_all_planes = TRUE;

        // Test all eight points against plane

        if(D3DXPlaneDotCoord(&_planes[i],
            &D3DXVECTOR3(x_center - x_radius, y_center - y_radius, z_center - z_radius)) < 0.0f)
        {
          in_all_planes = FALSE;
          count--;
        }

        if(D3DXPlaneDotCoord(&_planes[i],
            &D3DXVECTOR3(x_center + x_radius, y_center - y_radius, z_center - z_radius)) < 0.0f)
        {
          in_all_planes = FALSE;
          count--;
        }

        if(D3DXPlaneDotCoord(&_planes[i],
            &D3DXVECTOR3(x_center - x_radius, y_center + y_radius, z_center - z_radius)) < 0.0f)
        {
          in_all_planes = FALSE;
          count--;
        }

        if(D3DXPlaneDotCoord(&_planes[i],
            &D3DXVECTOR3(x_center + x_radius, y_center + y_radius, z_center - z_radius)) < 0.0f)
        {
          in_all_planes = FALSE;
          count--;
        }

        if(D3DXPlaneDotCoord(&_planes[i],
            &D3DXVECTOR3(x_center - x_radius, y_center - y_radius, z_center + z_radius)) < 0.0f)
        {
          in_all_planes = FALSE;
          count--;
        }

        if(D3DXPlaneDotCoord(&_planes[i],
            &D3DXVECTOR3(x_center + x_radius, y_center - y_radius, z_center + z_radius)) < 0.0f)
        {
          in_all_planes = FALSE;
          count--;
        }

        if(D3DXPlaneDotCoord(&_planes[i],
            &D3DXVECTOR3(x_center - x_radius, y_center + y_radius, z_center + z_radius)) < 0.0f)
        {
          in_all_planes = FALSE;
          count--;
        }

        if(D3DXPlaneDotCoord(&_planes[i],
            &D3DXVECTOR3(x_center + x_radius, y_center + y_radius, z_center + z_radius)) < 0.0f)
        {
          in_all_planes = FALSE;
          count--;
        }

        // If none contained, return FALSE
        if(count == 0)
          return FALSE;

        // Update counter if they were all in front of plane
        if(in_all_planes)
            ++num_points_in_frustum;
    }

    // Store BOOL flag if completely contained
    if(completely_contained)
        *completely_contained = (num_points_in_frustum == 6);

    return TRUE;
}

//----------------------------------------------------------------------------
// Check whether a sphere is in frustum.
//----------------------------------------------------------------------------
BOOL FRUSTUM::check_sphere(float x_center, float y_center, float z_center,
                           float radius)
{
    // make sure radius is in frustum
    for(short i = 0; i < 6; i++)
    {
        if(D3DXPlaneDotCoord(&_planes[i], &D3DXVECTOR3(x_center, y_center, z_center)) < -radius)
            return FALSE;
    }

    return TRUE;
}

測(cè)試代碼：

/************************************************************************************
PURPOSE:
    frustum test.
************************************************************************************/

#include "core_global.h"
#include "frustum.h"

#define MAX_OBJECTS 256

class APP : public APPLICATION
{
public:
    APP()
    {
        _width  = 640;
        _height = 480;

        APPLICATION::_x_pos = (get_screen_width()  - _width) / 2;
        APPLICATION::_y_pos = (get_screen_height() - _height) / 4;

        _style = WS_BORDER | WS_CAPTION | WS_MINIMIZEBOX | WS_SYSMENU;

        strcpy(_class_name, "object clipping class");
        strcpy(_caption, "object clipping demo");
    }

    BOOL init()
    {
        // initialize graphics and set display mode
        _graphics.init();
        _graphics.set_mode(get_hwnd(), TRUE, TRUE);
        _graphics.set_perspective(D3DX_PI / 4, 1.3333f, 1.0f, 10000.0f);

        // create a font
        _font.create(&_graphics, "Arial", 16, TRUE, FALSE);

        // initialize input and input device
        _input.init(get_hwnd(), get_inst());
        _mouse.create(&_input, MOUSE, TRUE);

        // load mesh
        if(! _mesh.load(&_graphics, "..\\Data\\Yodan.x", "..\\Data\\"))
            return FALSE;

        for(short i = 0; i < MAX_OBJECTS; i++)
        {
            _objects[i].create(&_graphics, &_mesh);

            _objects[i].move((float) (rand() % 4000) - 2000.0f, 0.0f, (float) (rand() % 4000) - 2000.0f);
        }

        return TRUE;
    }

    BOOL frame()
    {
        // read mouse data
        _mouse.read();

        // position camera and rotate based on mouse position

        _camera.move(0.0f, 100.0f, 0.0f);

        // _mouse.get_y_delta():
        //      get mouse's relative x movement coordinate.
        //
        // _mouse.get_x_delta():
        //      get mouse's relative y movement coordinate.

        _camera.rotate_rel(_mouse.get_y_delta() / 200.0f, _mouse.get_x_delta() / 200.0f, 0.0f);

        // set camera
        _graphics.set_camera(&_camera);

        // render everything
        _graphics.clear(D3DCOLOR_RGBA(0, 64, 128, 255));

        // begin render now
        if(_graphics.begin_scene())
        {
            FRUSTUM frustum;
            frustum.construct(&_graphics);

            long num_drawn = 0;

            // render each object in frustums
            for(short i = 0; i < MAX_OBJECTS; i++)
            {
                float radius;

                _objects[i].get_bounds(NULL, NULL, NULL, NULL, NULL, NULL, &radius);

                if(frustum.check_sphere(_objects[i].get_x_pos(), _objects[i].get_y_pos(), _objects[i].get_z_pos(),
                                        radius))
                {
                    _objects[i].render();
                    num_drawn++;
                }
            }

            char stats[128];

            // display statistics
            sprintf(stats, "%lu of 256 objects drawn.", num_drawn);
            _font.print(stats, 0, 0, 400, 100);

            _graphics.end_scene();
        }

        _graphics.display();

        return TRUE;
    }

    BOOL shutdown()
    {
        return TRUE;
    }

private:
    GRAPHICS        _graphics;
    CAMERA          _camera;
    FONT            _font;

    INPUT           _input;
    INPUT_DEVICE    _mouse;

    MESH            _mesh;
    OBJECT          _objects[MAX_OBJECTS];
};

int WINAPI WinMain(HINSTANCE inst, HINSTANCE, LPSTR cmd_line, int cmd_show)
{
    APP app;

    return app.run();
}

截圖：

posted on 2007-10-19 19:59 lovedday 閱讀(1184) 評(píng)論(0) 編輯收藏引用

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創(chuàng)建3D圖形引擎（2）

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青青草原综合久久大伊人导航_色综合久久天天综合_日日噜噜夜夜狠狠久久丁香五月_热久久这里只有精品

天行健 君子當(dāng)自強(qiáng)而不息

創(chuàng)建3D圖形引擎（2）

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Return Values

Remarks

公告

導(dǎo)航

統(tǒng)計(jì)

常用鏈接

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