投影矩阵实现 [英] Projection matrix implementation

问题描述

我试图从头开始构建自己的Rasteriser / Graphics管线（模仿OpenGL），我在实现工作透视投影矩阵时遇到问题。这是我目前的尝试：

I'm trying to build my own Rasteriser/Graphics pipeline (mimicking OpenGL) from scratch and I'm having problems with implementing a working perspective projection matrix. This is my current attempt:

template<typename T>
Matrix<T,4,4> Perspective(T fov,T aspect, T near, T far)
{
    T mat00 = 1 / (aspect*tan(0.5f*fov));
    T mat11 = 1 / tan(0.5f*fov);
    T mat22 = (-near-far)/(near-far);
    T mat32 = (2*near*far)/(near-far);
    T data[] = 
    {
        mat00,     0,     0,    0,
        0    , mat11,     0,    0,
        0    ,     0, mat22,mat32,
        0    ,     0,     1,    0
    };
    return Matrix<T,4,4>(data);
}

然后将其传递给执行以下操作的顶点处理：

This is then passed to the vertex processing which performs the following:

    printf("Vertex inital:");vert.Print();
    vert = vert* m_ModelMatrix;

    printf("Vertex model:");vert.Print();
    vert = vert* m_ProjectionMatrix;

    printf("Vertex projection:");vert.Print();

其输出是（对于随机选择的顶点）：

The output of which is (for a randomly selected vertex):

Vertex inital:(1.000000,0.000000,-1.000000,1.000000)
Vertex model:(-1.900000,-2.300000,2.599999,1.000000)
Vertex projection:(-3.669604,-5.552692,2.405004,2.599999)

的顶点：$ b​​ $ b

The above vertex corresponds to one of the vertices in this triangle:

我的问题是投影矩阵看起来是完全错误的。当我增加Z平移时，三角形朝向右上角对角线移动，同时看起来较小，当我减小 Z值时，三角形移动对角线朝向左下角，同时显示为较大。有没有人遇到这个问题？

My problem is the projection matrix appears to be completely wrong. When I increase the Z translation the triangle moves diagonally towards the top-right corner while appearing smaller, when I decrease the Z value the triangle moves diagonally towards the bottom-left corner while appearing larger. Has anyone else encountered this issue?

作为参考，我的矢量*矩阵操作的实现：

For reference, my implementation of the vector*matrix operation:

template<typename T,unsigned int length>
Vector<T,length> Vector<T,length>::operator* (const Matrix<T,length,length> & matrix) const
{
    T temp[length];
    memset(temp,0,length*sizeof(T));
    const T * matrixData = matrix.GetData();
    //For each row in the matrix & in the returned vector...
    for(unsigned int iRow = 0; iRow < length; ++iRow)
    {
        //For each column in this vector & matrix...
        for(unsigned int iColumn = 0; iColumn < length; ++iColumn)
        {
            temp[iRow] += m_Data[iColumn]*matrixData[iRow*length + iColumn];
        }
    }
    return Vector<T,length>(temp);
}

推荐答案

项目后相当一些休息，我意识到，我的投影鸿沟（aka / w）只是划分xyz坐标。因此，当我应用屏幕空间矩阵时，translate列被乘以大于一个W值，导致三角形随着Z减小而移动到右上角。

So I came back to this project after quite some break and I realised that my projection divide (aka /w) was only dividing the xyz coords. So when I applied the screenspace matrix the translate column was being multiplied by the 'greater than one' W value causing the triangle to move to the upper right as Z decreases.

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