Do you mean that you like to generate a shape like these?

You can do this with Geomerative's RPolygon class.

Code Example:

1. import geomerative.*;
2. RPolygon circle, polygon;
3. RPoint[] points = new RPoint[4];
4.  
5. void setup () {
6.   size(500, 500);
7.   RG.init(this);
8. }
9.  
10. void draw () {
11.   background(12, 200, 170);
12.   circle = RShape.createCircle(width/2, height/2, width/2).toPolygon();
13.   points[0] = new RPoint(mouseX, mouseY-width/3);
14.   points[1] = new RPoint(mouseX+width/3, mouseY);
15.   points[2] = new RPoint(mouseX, mouseY+width/3);
16.   points[3] = new RPoint(mouseX-width/3, mouseY);
17.   polygon = new RPolygon(points);
18.   circle = circle.intersection(polygon);
19.   fill(255);
20.   circle.draw();
21.   noFill();
22.   polygon.draw();
23. }

Thanks for the tip. I need to look look into Geomerative library. Looking at the code, it seems that the circle is converted into a polygon before clipping. I need to test if there is any visible difference compared with an actual circle.

The geomerative library is very useful. Thanks for pointing at it!