如何構建透視投影矩陣（無API）

我開發了一個簡單的3D引擎（不使用任何API），成功地將我的場景轉換爲世界和視圖空間，但無法使用視角投影我的場景（從視圖空間）投影矩陣（OpenGL樣式）。我不確定fov，near和far的值，我得到的場景被扭曲了。我希望如果有人能指導我如何用示例代碼適當地構建和使用透視投影矩陣。預先感謝您的幫助。如何構建透視投影矩陣（無API）

基質構建：

double f = 1/Math.Tan(fovy/2); 
return new double[,] { 

    { f/Aspect, 0, 0, 0 }, 
    { 0, f, 0, 0 }, 
    { 0, 0, (Far + Near)/(Near - Far), (2 * Far * Near)/(Near - Far) }, 
    { 0, 0, -1, 0 } 
};

該矩陣使用：

foreach (Point P in T.Points) 
{  
    . 
    .  // Transforming the point to homogen point matrix, to world space, and to view space (works fine) 
    .  

    // projecting the point with getProjectionMatrix() specified in the previous code :  

    double[,] matrix = MatrixMultiply(GetProjectionMatrix(Fovy, Width/Height, Near, Far) , viewSpacePointMatrix); 

    // translating to Cartesian coordinates (from homogen): 

    matrix [0, 0] /= matrix [3, 0]; 
    matrix [1, 0] /= matrix [3, 0]; 
    matrix [2, 0] /= matrix [3, 0]; 
    matrix [3, 0] = 1; 
    P = MatrixToPoint(matrix); 

    // adjusting to the screen Y axis: 

    P.y = this.Height - P.y; 

    // Printing... 
}

來源

2013-08-23 reznic

http://www.scratchapixel.com/lessons/3d-basic-rendering/perspective-and-orthographic-projection-matrix 我也推薦以前的課程（投影點和3D查看）。 – user18490

以下是透視投影矩陣的一個典型的實行。這裏是一個很好的鏈接來解釋一切OpenGL Projection Matrix

void ComputeFOVProjection(Matrix& result, float fov, float aspect, float nearDist, float farDist, bool leftHanded /* = true */) 
{ 
    // 
    // General form of the Projection Matrix 
    // 
    // uh = Cot(fov/2) == 1/Tan(fov/2) 
    // uw/uh = 1/aspect 
    // 
    // uw   0  0  0 
    // 0  uh  0  0 
    // 0   0  f/(f-n) 1 
    // 0   0 -fn/(f-n) 0 
    // 
    // Make result to be identity first 

    // check for bad parameters to avoid divide by zero: 
    // if found, assert and return an identity matrix. 
    if (fov <= 0 || aspect == 0) 
    { 
     Assert(fov > 0 && aspect != 0); 
     return; 
    } 

    float frustumDepth = farDist - nearDist; 
    float oneOverDepth = 1/frustumDepth; 

    result[1][1] = 1/tan(0.5f * fov); 
    result[0][0] = (leftHanded ? 1 : -1) * result[1][1]/aspect; 
    result[2][2] = farDist * oneOverDepth; 
    result[3][2] = (-farDist * nearDist) * oneOverDepth; 
    result[2][3] = 1; 
    result[3][3] = 0; 
}

來源

2013-08-23 15:33:23

非常有幫助，謝謝 –

抱歉，呃和uw在這裏是什麼？用戶寬度和用戶高度？ – ReX357

@ ReX357 uw = near/right，uh = near/top，其中right是右剪貼圖的座標，top是上剪貼平面的座標。由於上面的透視投影是對稱的，所以右=水平寬度的一半並且頂部=垂直高度的一半，那麼uw/uh = top/right = height/width = 1/aspect –

可能有用的其它功能。

這一種是基於左/右/頂/底/遠/近參數（在OpenGL中使用）：

static void test(){ 
    float projectionMatrix[16]; 

    // width and height of viewport to display on (screen dimensions in case of fullscreen rendering) 
    float ratio = (float)width/height; 
    float left = -ratio; 
    float right = ratio; 
    float bottom = -1.0f; 
    float top = 1.0f; 
    float near = -1.0f; 
    float far = 100.0f; 

    frustum(projectionMatrix, 0, left, right, bottom, top, near, far); 

} 

static void frustum(float *m, int offset, 
        float left, float right, float bottom, float top, 
        float near, float far) { 

    float r_width = 1.0f/(right - left); 
    float r_height = 1.0f/(top - bottom); 
    float r_depth = 1.0f/(far - near); 
    float x = 2.0f * (r_width); 
    float y = 2.0f * (r_height); 
    float z = 2.0f * (r_depth); 
    float A = (right + left) * r_width; 
    float B = (top + bottom) * r_height; 
    float C = (far + near) * r_depth; 
    m[offset + 0] = x; 
    m[offset + 3] = -A; 
    m[offset + 5] = y; 
    m[offset + 7] = -B; 
    m[offset + 10] = -z; 
    m[offset + 11] = -C; 
    m[offset + 1] = 0.0f; 
    m[offset + 2] = 0.0f; 
    m[offset + 4] = 0.0f; 
    m[offset + 6] = 0.0f; 
    m[offset + 8] = 0.0f; 
    m[offset + 9] = 0.0f; 
    m[offset + 12] = 0.0f; 
    m[offset + 13] = 0.0f; 
    m[offset + 14] = 0.0f; 
    m[offset + 15] = 1.0f; 

}

來源

2015-12-26 19:15:02

如何構建透視投影矩陣（無API）

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