from a circular to a pointed arc

from a circular to a pointe arc

The pointed arc isn't an invention of the gotic style. It was used in romanesque style to. In next applet you can see houw the pointed arc is derived from the circular arc. Drag the green poit to the left.
A pointed arc is formed by two intersecting circular arcs with midpoints that no loger coincide with the center of the vault. With an increasing distance the arc becomes more pointed. By experience one learned that the horizontal forces diminished by making the arcs pointed instead of circular. Drag the green point to the right to increase the span. Drag the purple point to the left to make the arc pointed instead of circular.