Mapping Geometry Onto A Curved Plane

SUMMARY: We are attempting to map a geometry (think perhaps of a hexagon...) onto a curved plane (think of a cycloidal vault...whose normal changes constantly as one progresses up the curve from the bottom edge to the apex) and the problem we are encountering is that the geometry (hexagon) is NOT CURVED....it is STILL constructed of STRAIGHT LINES. We clearly want the geometry to curve in concert with whatever surface it is applied to. No exceptions.

With the referenced geometry conforming to the surface to which it is applied, now imagine the geometry has a thickness instead of just being flat. Imagine we now have hex tiles. The edge conditions must conform to the localized normals of the curved surface. On a sphere, tiles would all have the same edge conditions. In other words, they would not change in order to accommodate the macro geometry of the surface. But when you are working from anything BUT a perfect circle, the normals change.

THE QUESTION: How do we populate a curved surface with a referenced "tiled" geometry and maintain said curve within the "tiling."

Replies to This Discussion

Permalink Reply by taz on October 1, 2015 at 3:17pm

See this Kangaroo2 example:

http://www.grasshopper3d.com/photo/planar-hex?

From here:

http://www.grasshopper3d.com/group/kangaroo/page/kangaroo2-addition...

Permalink Reply by Lelouch on October 1, 2015 at 3:35pm

Taz,

Thank you very much for your response. Very grateful.

The problem is that the example you present here utilizes flat planar geometries, whose own surfaces (interior and exterior) are not curved along the initial reference surface. We have been successful with performing what is in your example without any problems. It is getting the pieces to curve that is our problem. We want curved, but separate, pieces and then to not have to draw that again and again and again in Rhino every time we change the design.

Permalink Reply by Hyungsoo Kim on October 2, 2015 at 12:14am