Difference between conical meshes and circular meshes

[eghbalpourf]

hello friends

Recently, I’m studying Pottmann’s Architectural Geometry. Actually, although I’m very interested in this topic, it is difficult for me.
What is the difference between conical meshes and circular meshes and how are they drawn?

[DanielPiker]

A conical mesh has faces around each vertex tangent to a common cone.
These are nice because they can be offset with a constant distance between parallel faces and no torsion in the beams. Here’s an example:

About PQ Mesh, conjugate curvature network

…and here’s an example definition showing a way to generate such a conical planar quad mesh, its constant distance face-face offset, and the corresponding torsion free beam layout, on a given target surface: conical_demo.gh (52.0 KB) [image] In this example I’ve started with a simple regular flat square grid, and pulled it onto the surface. As you slowly slide up the strength of the planarization/conicalization constraints, it will naturally slide and rotate on the surface to find an orienta…

Circular meshes have the vertices of each face sharing a common circle. These also have an offset with torsion free beams, but at a constant distance between corresponding vertices.

I wrote some explanation of torsion free beam layouts here:

About PQ Mesh, conjugate curvature network

First to try and summarise the main advantages of torsion-free nodes/beam layouts- Say we have some curved surface which we want to build as a structure of steel beams. One geometrically easy way to do this is to simply extrude the grid lines all in a vertical direction: [image] This keeps the beams planar, and they intersect in a single line at each node, which can be simple to fabricate. However, we might need the beams to be oriented more perpendicular to the surface, especially if we h…