如何构建透视投影矩阵（无 API）

Question

如何构建透视投影矩阵（无 API）

21

我开发了一个简单的3D引擎（没有使用任何API），已经成功地将我的场景转换到世界和视图空间，但是在使用透视投影矩阵（类似于OpenGL）将场景（从视图空间）投影时遇到了问题。我不确定fov、near和far值，而且得到的场景有畸变。我希望有人可以指导我如何正确构建和使用透视投影矩阵，并提供一些代码示例。非常感谢您提供的任何帮助。

矩阵构建：

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 } 
};

矩阵的使用：

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...
}

- reznic

我也推荐之前的课程（投影点和3D视图）。http://www.scratchapixel.com/lessons/3d-basic-rendering/perspective-and-orthographic-projection-matrix - user18490

2个回答

3

另一个可能有用的功能。

这个功能基于左/右/上/下/近/远参数（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;

}

- vir us

网页内容由stack overflow 提供, 点击上面的

可以查看英文原文，
原文链接

- Wayne Wang · Accepted Answer

以下是一种典型的透视投影矩阵实现方法。这里有一个很好的链接，可以解释所有内容：OpenGL投影矩阵

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;
}