1. Center the circle primitive to the 3d cursor or the initial mouse cursor location. You can for instance set the cursor before adding a primitive to the center of a face or to the mid-point of an edge and execute exact booelan operations then.

2. Define the number of segments of a circle primitive. This feature lets you create a variety of shapes with the circle like triangles or squares.

I also show the python code for the new features and explain the implementation.

Download Fast Carve addon for free from my github:
https://github.com/jayanam/fast-carve/tree/fast-carve-2-8

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