how to create an outlined polygon with vector3 coordinates?

how to create an outlined polygon with vector3 coordinates?

I have a set of vector3 coordinates and I use them to draw a polygon in another app, my question is: how can I calculate a second set of coordinates to make it look like the line is outlined.  

in the above picture, the blue dots are the vector3s I have and the red dots are the one I need, can anyone help me with an algorithm or formula to calculate them?
thanks

Solutions/Answers:

Answer 1:

1)Find barycentric coordinates

for(int i = 0; i < verticesInPolygon; i++)
{
    bary.xyz += vertices[i].xyz;
}
bary.xyz /= verticesInPolygon;

2)Create new vertices using this formula

newVertex.coord = (vertices[desiredVertexInPolygon].coord - bary.coord)*offset+bary.coord;

Where coord is a desired coordinate(x, y or z) and offset is a scalar determining how far from the barycenter and how close to the original vertex a new vertex will be, i. e. 0.5 would make it appear right between, making new polygon being a half size of the original.

illustration

UPDATE:
So, you need a constant offset to make outline, right?
Here is a way to do it.

1)Find barycentric coordinates

We already know how to do this.

2)Find a unit direction vector from barycenter to the original vertex

dir.xyz = normalize(vertices[desiredVertexInPolygon].xyz - bary.xyz);

3)Create new vertices with a following formula

newVertex.xyz = vertices[desiredVertexInPolygon].xyz + dir.xyz * offset;

Where offset is now a real distance rather than scalar.

enter image description here

Note that in your case you should use a negative offset value, because you want outline to be inside the polygon.

References