As cosmic_quanta mentioned it's called the terminator, and it's generally the dividing line between the 'illuminated' and 'unilluminated' part of a celestial bo

As cosmic_quanta mentioned it's called the terminator, and it's generally the dividing line between the 'illuminated' and 'unilluminated' part of a celestial body. You're right, the weird shape is due to the projection of "earth" in the X-Y plane, if you chose a different projection it would appear differently. The calculations make sure that the result is ±1 accurate all year long. The truth is that even the definition of 'daylight' and 'night-time' is not straightforward. The most common definitions include the Civil, Nautical and Astronomical Twilights [1], depending on the sun's position, so it should actually be a gradient. [1] https://en.wikipedia.org/wiki/Twilight https://en.wikipedia.org/wiki/Twilight