understanding glm::perspective matrix

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I'm trying to implement a simple 3d render. I have implemented a perspective projection matrix similar to glm::perspective. I have read that a perspective projection matrix transforms vertices such that after the perspective division, visible region, i.e., objects that lie inside the specified frustum fall in the range [-1,1], but when I tested some values with a matrix returned by glm::perspective results are not similar to my understanding.

float nearPlane = 0.1f;
float farPlane = 100.0f;

auto per =
    glm::perspective(45.0f, (float)(window_width * 1.0 / window_height),
                        nearPlane, farPlane);
// z=nearplane
print(per * glm::vec4(1, -1, -0.1, 1));
// z=farplane
print(per * glm::vec4(1, -1, -100, 1));
// z between nearplane and farplane
print(per * glm::vec4(1, -1, -5, 1));
// z beyond far plane
print(per * glm::vec4(1, -1, -200, 1));
// z behind the camera
print(per * glm::vec4(1, -1, 0.1, 1));
// z between camera and near plane
print(per * glm::vec4(1, -1, -0.09, 1));

As per my understanding, if vertices have a z coordinate which lies towards positive z-direction from nearPlane then after perspective divide z/w value should be <-1 but as shown in the picture below it is not the case. what am I missing?

output of above print statements

glm-math 3d graphics
1 Answers

as per my understanding if vertices has z coordinate which is lies towards positive z direction from nearPlane then after perspective divide z/w value should be <-1 but as shown in picture below it is not the case. what am i missing?

That's simply not the case. There is a singularity at z=0 (camera plane), and the sign of the function flips (camera is looking to the left; blue vertical line is the near clipping plane):

graph

Those values are still outside the [-1,1] range, telling us that they are outside the camera frustum and should be clipped accordingly.

You might be confused because you're thinking that "smaller z/w values mean that the point is closer to the camera". But that's true only in-front of the camera. In fact the depth buffer values matter only if the fragment isn't clipped -- i.e. in the [-1,1] range, where that relation happens to be correct.

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