Tag Archives: principal curvature

Principal Curvature Orbits

Here’s a quick preview of the May 20th release of the SPM Vector Components Grasshopper plug-in. These screenshots show the Orbit Detection parameters working with the new Line Continuity and Constrain to Surface modes. These new modes let the integrator pass over singular points and avoid awkward stops and kinks at the expense of directionality. Therefore it works very well with principal curvature fields, but maybe not so much with principal stress fields (where it would interchange the pure compression direction with pure tension….structurally not always a good idea).


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Filed under Architecture, Geometry, SPM Vector Components

Gaspard Monge Curvature Line Vault

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 [1], [2], and [3]).

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.

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Filed under Architecture, Geometry, Tilings

Principal Curvature Lines

Here’s a quick video of the component in action. There’s still a lot of work to be done.

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Filed under Architecture, Geometry, Grasshopper, Tilings