Twisted Cylinder (Hyperboloid of one sheet)

Question

I want to create a mesh like this:

with a vertex on every edge-crossing so that every face is kite (nearly rhombus) shaped.

The above image was created just by rotating the top of two cylinders in different directions and placing them on the same position.

But here I wouldn't have these many small faces and the result of the overlapping twisted cylinders looks like this in solid display:

Can you please tell me if there is a way the create these kite-faces. Is there a tool that automatically creates a new vertex and a face for every intersection of edges?

Answer 1

I think this solves the issue with moonbots answer. Use the TinyCAD addon to create vertices at the edge itersections

EDIT steps:

1. rotate top face 90 degrees (R, Z, 90)
2. duplicate (Shift-D) and mirror along any axis (e.g. Ctrl-M, X)
3. press W and select TinyCAD ⯈ XALL
4. press F to fill faces
5. press W and select Remove Doubles

Answer 2

Edit: Ok this is not what you need. What you need is to use the TinyCad addon as explained in another answer. Anyway I thought you wanted this:

• Create a cylinder and subdivide it horizontally
• Triangulate with alt P
• Delete vertical and horizontal edges: Select an edge and shift G > Select Similar > Direction, or if it's not enough select the Edge Loop with the B selector then shift G > Select Similar > Direction. Delete with X > Delete > Edge Loop. Now you only have triangles
• Select the middle of your shape, activate the Proportional Editing, and squeeze with shift Z so it constraints on X and Z axis
• If the shape is not symmetrical you can cut the top or the bottom half and copy bottom/top, rotate it 180° and merge with its opposite

Maybe there are cleaner solutions, I don't know ;)

Answer 3

Take those two cylinders you've got, and apply the script discussed in this other answer to create points where the edges intersect each other:

How can I add vertices to intersection of two edges?

The script provided by @Zeffi:

import bmesh import bpy from mathutils import geometry

def add_vertex_to_intersection():

    obj = bpy.context.object
    me = obj.data
    bm = bmesh.from_edit_mesh(me)

    edges = [e for e in bm.edges if e.select]

    if len(edges) == 2:
        [[v1, v2], [v3, v4]] = [[v.co for v in e.verts] for e in edges]

        iv = geometry.intersect_line_line(v1, v2, v3, v4)
        iv = (iv[0] + iv[1]) / 2
        bm.verts.new(iv)
        bmesh.update_edit_mesh(me)

add_vertex_to_intersection()

The answer also discusses a similar option available from mesh_tiny_cad. Specifically the X part of the VTX operations:

Or perhaps the XAll operation:

Once the add-on is enabled, you can access it from the context menu like this: