Developing a patterned surface can be fairly simple when the surface you are working with is flat, but if you were to develop the same pattern from scratch on a curved surface then things become a little more difficult. Luckily, there is a way to convert a flat pattern to a curve pattern through the use of each surface’s UV coordinates.
Here’s an example using the component in Grasshopper which generates a planar hexagon grid. Once the grid is created a bounding surface is found for all the grid cells. The closest point on the bounding surface for each vertices is then found which returns the surface UV coordinates. An important step there is to make sure that the surface is reparameterized so that the units are normalized, meaning that the U and V intervals range from 0 to 1. Now any surface that is also reparameterized can be evaluated according to these UV coordinates. Any prior path structure organizing the points will be retained, and the cell boundaries can be recreated.
This definition was created using GH version 0.0.6.0059: Download Hexagonal-grid.ghx, 17.21 kB
Obligatory disclaimer: the author does not guarantee that these parametric models are bug-free or that they will solve all of your problems. If you find bugs or have suggestions for improvements, please let us know.
