GLSL Making LOD curves from lines

Question

Solution: Drawing tessallated LineLoops in OpenGL/GLSL

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I am using OpenGL and GLSL to draw LineLoops on a sphere (Borders on a Planet).

Since the points defining the lines are given by user input they do not have high enough precion to prevent clipping inside the sphere.

I want to use Tesselation and/or Geometry Shaders to create extra points in between existing points so the distance between points does not exceed a certain value (lines no longer clip inside the sphere).

Before:

After:

Sadly there is not much information about Tesselation Shaders, so I am not quite sure how they work, but I know that I can subdivide primitives with them.

Here is my current vertexShader:

#version 400

in layout(location = 0) vec3 position;

uniform float maxDist;
uniform float sphereRadius;
uniform mat4 view;
uniform mat4 projection;

void main()
{
    gl_Position = projection * view * vec4(position, 1.0);
}

How can I use Tessalation/Geometry Shaders to create more vertices in between points and offset the newly created vertices so they have the given length of the sphereRadius uniform.

I am not looking for a solution that does one subdivision for every line. I look for a solution that does as many subdivisions as needed to get a certain distance between points that does not exceed maxDist.

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I am currently drawing like this:

glBindVertexArray(_vao);
glDrawArrays(GL_LINE_LOOP, 0, _size);
glBindVertexArray(0);