frustum plane extraction

// i extract planes from projection matrix using this class:
// mat is column major, mat[i] is ith column of matrix

class Frustum
{
    public:
        Frustum(const glm::mat4& mat, bool normalize_planes = true)
        // create frustum from  matrix
        // if extracted from projection matrix only, planes will be in eye-space
        // if extracted from view*projection, planes will be in world space
        // if extracted from model*view*projection planes will be in model space
        {
            // create non-normalized clipping planes
            planes[0] = Plane(mat[3]+mat[0]);       // left
            planes[1] = Plane(mat[3]-mat[0]);       // right
            planes[2] = Plane(mat[3]-mat[1]);       // top
            planes[3] = Plane(mat[3]+mat[1]);       // bottom
            planes[4] = Plane(mat[3]+mat[2]);       // near
            planes[5] = Plane(mat[3]-mat[2]);       // far
            // normalize the plane equations, if requested
            if (normalize_planes)
            {
                planes[0].normalize();
                planes[1].normalize();
                planes[2].normalize();
                planes[3].normalize();
                planes[4].normalize();
                planes[5].normalize();
            }
        }

    Plane planes[6];        // plane normals point into frustum
};

class Plane
{

    public:
        Plane(const glm::vec4& abcd)
         : normal(abcd.x, abcd.y, abcd.z), d(abcd.w) {}

        void normalize()
        {
            float mag = glm::length(normal);
            normal /= mag;
            d /= mag;
        }

        glm::vec3 normal;
        float d;        // distance from origin
};


// this is proj. matrix i use
glm::perspective(60.0f /*fovy*/, 800.0f/600 /*aspect*/, 0.01f /*near_dist*/, 100.0f/*far_dist*/);

// this is how this matrix looks when printed out
1.2990 0.0000 0.0000 0.0000
0.0000 1.7321 0.0000 0.0000
0.0000 0.0000 -1.0002 0.0200
0.0000 0.0000 -1.0000 0.0000

// and these are the planes constructed from this matrix when printed out
left = normal[0.999881 0.000000 -0.015396], d=-0.015396
right = normal[-0.999881 0.000000 -0.015396], d=-0.015396
top = normal[0.000000 -0.999933 -0.011547], d=-0.011547
bottom = normal[0.000000 0.999933 -0.011547], d=-0.011547
near = normal[0.000000 0.000000 -1.000000], d=-0.980198
far = normal[0.000000 0.000000 1.000000], d=1.020202

// i expect "d" to be distance from origin, which is camera space,
// so it should be 100 for far plane, and 0.01 for near plane, right ?