Do you mean such that the new map appears on top of the old one, first showing a little sliver between "12 o'clock" and a bit clockwise, and then gradually expanding the wedge all the way around?

Imagine a single 'hand' which extends from the centre of the screen straight up, and travels clockwise one full rotation over the duration of the visual effect. In each delta-time, you need to advance the hand angle by a few degrees, then draw the portion of the new map that lies between old and new hand positions. That "portion" will be a triangle between:

- the centre of the map
- the intersection of the old hand with the edge of the map
- the intersection of the new hand with the edge of the map.

You can get the slope of the line via atan2() in <cmath> (<math.h> in plain C), and thus find the equation for the current 'hand line' in y=mx+b form (although you will have to handle vertical lines separately I suppose). Then intersect the line with the edges of the map (standard line/line intersection; since the map edges will be vertical or horizontal, you can just plug in an x or y value into the line equation) to find those vertices. One problem will be when you pass by the corners of the map, which you will probably want to handle as a special case (or just make sure that for some valid delta-time value, the hand points exactly at the corner).