2 research outputs found
Shape Representation by Zippable Ribbons
Shape fabrication from developable parts is the basis for arts such as
papercraft and needlework, as well as modern architecture and CAD in general,
and it has inspired much research. We observe that the assembly of complex 3D
shapes created by existing methods often requires first fabricating many small
flat parts and then carefully following instructions to assemble them together.
Despite its significance, this error prone and tedious process is generally
neglected in the discussion. We propose an approach for shape representation
through a single developable part that attaches to itself and requires no
assembly instructions. Our inspiration comes from the so-called zipit bags,
which are made of a single, long ribbon with a zipper around its boundary. In
order to "assemble" the bag, one simply needs to zip up the ribbon. Our method
operates in the same fashion, but it can be used to approximate any shape.
Given a 3D model, our algorithm produces plans for a single 2D shape that can
be laser cut in few parts from flat fabric or paper. We can then attach a
zipper along the boundary for quick assembly and disassembly, or apply more
traditional approaches, such as gluing and stitching. We show physical and
virtual results that demonstrate the capabilities of our method and the ease
with which shapes can be assembled
Interpolation of a spline developable surface between a curve and two rulings
In this paper we address the problem of interpolating a spline developable
patch bounded by a given spline curve and the first and the last rulings of the
developable surface. In order to complete the boundary of the patch a second
spline curve is to be given. Up to now this interpolation problem could be
solved, but without the possibility of choosing both endpoints for the rulings.
We circumvent such difficulty here by resorting to degree elevation of the
developable surface. This is useful not only to solve this problem, but also
other problems dealing with triangular developable patches