Sorry, it’s my mistake the way I wrote things.
First, my sincerest apologies, good sir, I didn't realise that English was not your native tongue. Absolutely not your mistake but, rather, mine.
What is a curved departure? First time I see that.
Normally, we takeoff and maintain runway track to a suitable elevation and then turn to pick up the outbound course. If, however, a straight flight path departure is too restrictive for TOW, often we can find a curved, or turning takeoff departure, which gives a better RTOW and payload. Such turns can commence from very early in the departure, often at runway head, or at some specific position or altitude. There are various things which we take into account when designing such departures but, for the crew, the departure will be defined in the ops manual and the crew just follow what the book says for the runway. Flying a curved departure, though, is quite demanding as location and tracking is critical. As a consequence, speed and bank angle control is critical to keep the aircraft fairly close to the presumed tracking plan so that we don't get closer than intended to the obstacles of concern. At a suitable position or altitude, and once the critical obstacles have been passed, the procedure will direct the crew to turn to the departure track.