21

我开发了一个简单的 3D 引擎（不使用任何 API），成功地将我的场景转换为世界和视图空间，但是使用透视投影矩阵（OpenGL 样式）投影我的场景（从视图空间）时遇到了麻烦。我不确定 fov、near 和 far 值，而且我得到的场景是扭曲的。我希望有人可以指导我如何通过示例代码正确构建和使用透视投影矩阵。提前感谢您的帮助。

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...
}
4

2 回答 2

31

以下是透视投影矩阵的典型实现。这里是一个很好的链接来解释一切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;
}
于 2013-08-23T15:33:23.770 回答
3

另一个可能有用的功能。

这个是基于left/right/top/bottom/near/far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;

}
于 2015-12-26T19:15:02.173 回答