**Regular polygon disk**

Use n+1 vertices and n triangular faces.

Vertex n
is located at
(0,0,0).

Each vertex 0 <= i < n
is located at
(cos(θ),sin(θ),0), where: θ = 2 π i / n.

The normal for every vertex is (0,0,1).

Faces are the n triangles:
(0,1,n),(1,2,n) ... (n-2,n-1,n),(n-1,0,n).

Notice that all the faces contain the center vertex n.

**Cylindrical tube**

Use 2n vertices and n rectangular faces.

Each vertex 0 <= i < n
is located at
(cos(θ),sin(θ),1), and

each vertex n <= i < 2n
is located at
(cos(θ),sin(θ),-1), where: θ = 2 π i / n.

Surface normals are (cos(θ),sin(θ),0).

Faces are the n rectangles: (0,n,n+1,1) , (1,n+1,n+2,2) ... (n-1,2n-1,n,0).

**Cylinder**

Use two polygonal disks and one cylindrical tube.

Translate the first disk by (0,0,1).

Translate the other disk by (0,0,-1), and scale it by (1,-1,-1);

**Superquadric**

Start with a sphere mesh.

Choose some power p. p=4 gives nice looking shapes.

For every vertex:

- compute S = (|x|^{p}+|y|^{p}+|z|^{p})^{1/p}.

- divide the x,y and z coordinates of the vertex by S.

Regenerate the mesh normals.