We present a Java implementation of Lang's Universal Molecule algorithm, alongside with a visualization of its interconnected structures: the input metric tree and compatible convex polygon, whose 2D crease pattern and 3D uniaxial base are computed by the algorithm. The Java applet, the video, as well as further references and accompanying materials are available on our web site http://linkage.cs.umass.edu/origamiLang. We also include a recent example, found with the help of this implementation, of a Universal Molecule crease pattern which, as a flat-faced origami, is completely rigid; in particular, its corresponding uniaxial base cannot be reached through continuous folding without bending of the paper.

We employ 3D arrangements of curves to represent and analyze biological shapes, in particular, the anatomy of the human brain. The arrangements of curves may vary from fairly sparse - such as a collection of sulcal lines that coarsely approximates the global shape of the brain - to very dense decompositions of the cortical surface into space curves. A space of shapes of such arrangements is constructed equipped with geodesic metrics that can be used in conjunction with curve registration techniques to quantify shape resemblance or dissimilarity, as well as to identify the regions where anatomical differences are most pronounced. The metric is applied to the panellation and labeling of configurations associated with the left and right hemispheres of the brain. Examples are also given of geodesic interpolations between decompositions into space curves of surfaces representing the entire left hemisphere of the brain.