XYU ring is not merely an ornament, but a proof of the infinite possibilities of computational design. This algorithm uses splines to generate these infinite possibilities. The starting point is set by the user, who specifies the number of splines and the length and thickness of the ring. The control points of the splines are selected randomly and adapted to make them continuous on the ring. If the user does not like the result, the algorithm can be run again until an aesthetic shape is achieved.
In the following table the normalized measures of the circumference of the ring can be seen.
Maximum height of the ring. It is the height of the rectangle where the spline curves are generated.
Each of the curves of the ring is generated extruding a circumference along a path, the spline. The size of this circunference will determine the thicknees of the curves of the ring. This parameters has some limitations. There is a minimum thickness so the ring doesn´t bend.
The number of splines is the number of curves that will compose the ring. In the following image there are examples until 5 splines, but bigger numbers are also possible.
It is the number of random points that will be used to create each of the splines. The lower the number, the more smooth curves we will get and the higher the number, the rougher the curve. In this image 5, 6, 7, 13 and 21 control points have been used to generate the examples.
The lower the degree is, the sharper the curves of the ring will be. In this image the influence of the degree of the curve on the shape of the ring can be seen.
Once the users find the ring that they like, it is automatically modeled on Maya and the 3D model is sent to the jeweler. Each of the model is 3D printed and cast, so each of the pieces are unique.
