While principal curvature lines seem to be currently very popular, they’ve been around in architecture since 1796.
Gaspard Monge, a french geometer, proposed the above design for an ellipsoidal vault that could be constructed out of mortarless masonry units. Not only did he come up with a completely new way to build such vaults, he actually solved a much bigger problem: how to construct freeform surfaces out of discrete units (see , , and ).
One major characteristic of the patterns that the principal curvature lines of a surface create is that while they are stable for small disturbances of the surface, larger disturbances will cause the overall pattern to “jump” to a new one. This kind of behaviour is called a bifurcation. Now, designing something that wants to bifurcate every time it is modified is fairly difficult. Maybe an understanding of what kinds of surfaces have the same principal curvature line pattern would make this easier? Limiting the design to such surfaces would embed the rationality of the curvature line pattern directly into the design process.
Here’s a quick video of the component in action. There’s still a lot of work to be done.
The Studio for Progressive Modelling (SPM) has started development of a couple custom GH components:
This one produces a principal curvature line emanating from a point on a surface – lines that are useful for constructing panelizations of freeform surfaces consisting entirely of planar quadrilaterals and prismatic structural members. It has been proven that surfaces with these characteristics are significantly more cost effective. However, the aesthetics of these panelization schemes are often quite pronouced, and so this component is a light weight solution that allows designers to see what kind of principal curvature mesh a given surface might suggest.
See Evolute and Daniel Piker’s work in this area for other aspects of panelization with planar elements. I find the latter approach very interesting, as it does not depend on a setting out the curvature lines as an initial guess – even though these are fundamental to the construction. Or are they?
We’re also working on some Rhino to Revit/SAP links, and hope to post some information on those soon.