The computer graphics field has become more physical in recent years. While images are still considered the end goal by many, there is growing interest in the graphics community to create physical objects that can be touched and held. Cignoni and his co-authors developed a technique that allows a digitally stored 3D model to be physicalized. This technique is termed mesh joinery, as the end product is an interlocking structure of planar pieces that approximate a 3D model such as a human or animal. The goal for the physical model is physical stability: it should actually be able to stand on its own without falling or collapsing.

The trick is to make use of cross fields, mathematical objects that have found much use in geometric modeling in recent years. A cross is a collection of four vectors of the same length, with 90 degrees between neighboring vectors. To make a cross field on a surface means to assign a cross to each point on the surface or each face of the mesh representing the surface. The beauty of cross fields is that they can model structures such as the corners of a room. Curves on the surface following the cross fields give rise to a curve network, where two curves can intersect at approximately the right angle. By turning each curve into a flat piece, intersecting curves naturally lead to flat structures that not only approximate the 3D model, but can also be interlocked. This leads to mechanical stability.

This research should be interesting not only to artists and toy makers, but also to educators. Cross fields, topology, and geometry are difficult mathematical concepts. With mesh joinery, you can not only see the geometry, but directly interact with it. Who wouldn’t love that?