glDepthRange, glEnable, glPolygonOffset
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glDepthFunc: man4/glDepthFunc.xml
glDepthFunc specifies the function used to compare each incoming pixel depth value with the depth value present in the depth buffer. The comparison is performed only if depth testing is enabled. (See glEnable and glDisable of GL_DEPTH_TEST.) func specifies the conditions under which the pixel will be drawn. The comparison functions are as follows: The initial value of func is GL_LESS. Initially, depth testing is disabled. If depth testing is disabled or if no depth buffer exists, it is as if the depth test always passes.
Even if the depth buffer exists and the depth mask is non-zero, the depth buffer is not updated if the depth test is disabled. In order to unconditionally write to the depth buffer, the depth test should be enabled and set to GL_ALWAYS.