I see. You want to create a circle of vertices in 3D modeling, and you have some specifications for the number of octants and vertices. Let me try to help you with that.
First, let me explain what an octant is. An octant is one-eighth of a circle, or a 45-degree arc. If you divide a circle into 8 equal parts, each part is an octant. Here is an example of a circle with 8 octants:
o
/ \
/ \
o o
| |
| |
o-----o
\ /
\ /
o
Each point where the circle intersects the horizontal or vertical line is called a boundary vertex. Each octant has two boundary vertices, one at each end of the arc. For example, the top-right octant has the boundary vertices at (0,1) and (1,0).
Now, you said you want to have at least three vertices within the boundary vertices of each octant. That means you want to have at least four vertices per octant, including the boundary vertices. For example, here is a possible way to have four vertices in the top-right octant:
o
/ \
/ \
o--o--o
| |
| |
o-----o
\ /
\ /
o
The vertex at (0.5,0.5) is within the boundary vertices of the top-right octant.
To find the total number of vertices you need for the whole circle, you can multiply the number of vertices per octant by the number of octants. In this case, you have 8 octants and 4 vertices per octant, so you need 8 x 4 = 32 vertices.
However, this is not the only way to create a circle of vertices with your specifications. You can also have more than three vertices within the boundary vertices of each octant, as long as they are evenly distributed along the arc. For example, here is another way to have six vertices in the top-right octant:
o
/ \
/ \
o-o-o-o
| |
| |
o-----o
\ /
\ /
o
The vertices at (0.25,0.75), (0.5,0.5), and (0.75,0.25) are within the boundary vertices of the top-right octant.
In this case, you have 8 octants and 6 vertices per octant, so you need 8 x 6 = 48 vertices.
The more vertices you have within the boundary vertices of each octant, the smoother your circle will look in 3D modeling. However, it will also increase the complexity and size of your model.
Therefore, the answer to your question depends on how smooth and detailed you want your circle to be. The minimum number of vertices you need is 32, but you can have more if you want.
If you want to learn more about how to create a circle of vertices in 3D modeling, you can check out these web pages [links]. They have some useful tips and examples for different software and methods.
I hope this helps!
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