The curves bordering your blue region look like (cubic) Bézier curves. Each Bézier curve is defined by four points. Two of these points are its end-points, which are shown as black squares in your picture. The other two points are interior "control points", which are shown as white squares in your picture.
Where two Bézier curves meet, you get a black point (which is the common end-point of the two Bézier curves), and two white points, one from each curve. These three points are often collinear, which causes the two curves to meet smoothly.
Just look up "editing of Bézier curves".