# Why we calculate z buffer value from plane equation $AX+BY+CZ+D=0$?

Suppose in perspective projection $$(x, y, z)$$ coordinate projects to point $$(x_p, y_p, z_{vp})$$ in projection plane $$AX+BY+CZ+D=0$$ where projection plane kept at $$z_{vp}$$ position. And the plane $$AX+BY+CZ+D=0$$ is satisfied by every point $$(x_p, y_p, z_{vp})$$ and in whole projection plane $$z_{vp}$$ is constant.

Also we know that Z value(Z buffer value) for an object doesn't come from the z-value $$z_{vp}$$ of the projection plane.

But in many websites I seen Z value(Z buffer value) is calculating by the plane equation $$AX+BY+CZ+D=0$$ of the point (x, y, z) which is the point of space point not the projection plane point. My question is why can we calculate Z value(Z buffer value) from the plane equation $$AX+BY+CZ+D=0$$ of the space point $$(x, y, z)$$ because $$AX+BY+CZ+D=0$$ is only satisfied by the point $$(x_p, y_p, z_{vp})?$$

• Your use of the plane equation with respect to projection sounds... familar. Jan 26, 2022 at 18:34
• ... So you're admitting that this was you. You deleted your account and created a new one so you could keep posting questions. Jan 26, 2022 at 18:42