齐次坐标下的MVP变换

Question

我正在尝试使用python和numpy计算MVP转换，我的代码可能有问题，因为我最终得到了w=0。我改变了操作顺序，因为numpy数组的C顺序，我按照这个顺序应用模型、视图和投影。在这个例子中，变换原点会产生一个w=0的同质坐标，这当然会阻止我将结果除以w

import numpy as np

def frustum(left, right, bottom, top, znear, zfar):
    M = np.zeros((4, 4), dtype=np.float32)
    M[0, 0] = +2.0 * znear / (right - left)
    M[2, 0] = (right + left) / (right - left)
    M[1, 1] = +2.0 * znear / (top - bottom)
    M[2, 1] = (top + bottom) / (top - bottom)
    M[2, 2] = -(zfar + znear) / (zfar - znear)
    M[3, 2] = -2.0 * znear * zfar / (zfar - znear)
    M[2, 3] = -1.0
    return M

def perspective(fovy, aspect, znear, zfar):
    h = np.tan(fovy / 360.0 * np.pi) * znear
    w = h * aspect
    return frustum(-w, w, -h, h, znear, zfar)

def lookat(eye, center, up):
    normalize = lambda x: x/np.linalg.norm(x)
    M = np.eye(4)
    eye = np.asarray(eye)
    center = np.asarray(center)
    z = normalize(eye-center)
    x = normalize(np.cross(up,z))
    y = normalize(np.cross(z,x))
    M[:3,0], M[:3,1], M[:3,2], M[3,:3] = x, y, z, -eye
    return M

proj  = perspective(45.0, 1.0, 2.0, 100.0)
model = np.eye(4)
view  = lookat([0,0,5], [0,0,0], [0,1,0])

P = [0,0,0,1]
P = proj @ view @ model @ P
print(P) # Probably wrong because P[3] = 0