I recently learned about a type of vase known as the tulip vase. Originating in - where else - the Netherlands, it's defined by some number of spouts, usually five. One spout, one flower.
Here are two of my favorite entries in this genre:
It's a handy sort of vase in an era where half-rotten bouquets cost $25. Unlike a standard vase that demands a full bouquet, a tulip vase will dignify even a single flower.
My process for this piece began with rough form finding, followed by the creation of a parametric program in Rhino Grasshopper that allowed me to experiment with the positioning and proportions of the elements.
The complete program. Each grey block describes either a quantity, a relation, or a mathematical function.
The vase attributes I can control (click to zoom)
After spending three days building this program, I thought my work was done. Wrong. It quickly became apparent that changing one parameter - say the amount of arc on the top face - changes the feel of everything else. For example, if I added a bit more bulge to the arc of the top, the overall composition would only look resolved if the spouts were more tightly packed and the outer walls less sloped.
Once satisfied with the form factor, I moved on to the ornament. In an ideal world, it would've been defined by a reaction diffusion pattern, which is nature's preferred decoration formula (e.g. the stripes of zebras and the wrinkles of coral). But initial attempts to plagiarize nature failed, so I resorted to an off-the-shelf algorithm.
A shortest walk algorithm yields a single branching line
This simpler approach brought with it a new set of challenges, most frustratingly with the density of the line network. While, mathematically speaking, the line density may have been consistent across all faces, to my eye (and two other observers) it looked hideously concentrated on the curved surfaces of the top.
Thus began a design hell where I defined different network densities for each section of the vase, then manually stitched them together at all section intersections.
This done, I expected smooth sailing - I'd just give the lines some thickness and walk away. Wrong. That was but the first circle of hell. Subsequent steps required more algorithmic refinement, more manual assembly, and - by now at about the fourth circle of hell - hours of compute time for a single change (none of which were preview-able in advance).
It then came time to wait two days for a test print to complete.
Print #1: Heartbreak in White
The edges on version 1 ended up looking like they'd been strafed by machine gun fire. Also, the proportions were off.
I overhauled the design and spent hours fine-tuning print settings for v2.
The second print looked acceptable. I forced myself to abuse it for your sake, dear reader, to ensure that it was watertight and durable.
Wanting to see the full effect of the network pattern, I rebuilt the vase again to make it printable in two colors.
A 4.5 day print job ensued. I spent the fifth day removing thousands of burrs by hand. The result, imperfect but beautiful, is seen in the following gallery.