The pointed arch on this chair is struck from two centres, not one, and that is what makes it look like architecture rather than like a curve that happens to meet at the top.
A single-centre arch is a segment of a circle: it rises and meets in a soft, rounded apex. A pointed arch is drawn from two centres set apart on the springing line, so each side is a segment of a different circle, and where the two meet they arrive at an angle rather than a curve. That meeting point is the whole character of the form.
How far apart those two centres sit decides how sharp the point is. Set them close and the arch is gentle; set them wide and it becomes tall and emphatic. Our artisans strike the outline full size on a board and try several spacings before committing, because a pointed arch that is only slightly wrong looks like a mistake rather than a choice.
The pierced foliage inside is then set out to fill the arch it produces - drawn after the outline, never before, so the ornament serves the geometry.