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- Michael D. Frachetti, Cameron Smith, Cynthia Traub, Tim Williams
- Nature
- 2017

There are many unanswered questions about the evolution of the ancient 'Silk Roads' across Asia. This is especially the case in their mountainous stretches, where harsh terrain is seen as an impediment to travel. Considering the ecology and mobility of inner Asian mountain pastoralists, we use 'flow accumulation' modelling to calculate the annual routes of… (More)

Consider all geodesics between two given points on a polyhedron. On the regular tetrahedron, we describe all the geodesics from a vertex to a point, which could be another vertex. Using the Stern– Brocot tree to explore the recursive structure of geodesics between vertices on a cube, we prove, in some precise sense, that there are twice as many geodesics… (More)

- Erin W. Chambers, Kyle Sykes, Cynthia Traub
- CCCG
- 2012

We prove that rectangle-faced orthostacks, a restricted class of orthostacks, can be grid-edge unfolded without additional refinement. We prove several lemmas applicable to larger classes of orthostacks, and construct an example to illustrate that our algorithm does not directly extend to more general classes of orthostacks.

We obtain a complete classification of all simple closed geodesics on the eight convex deltahedra. In particular, up to symmetry and parallel translation, there is exactly one simple closed geodesic on the triangular dipyramid, one on the pentagonal dipyramid, five on the snub disphenoid, two on the triaugmented triangular prism, and four on the… (More)

- Diana Davis, Victor Dods, Cynthia Traub, Jed Yang
- Discrete Mathematics
- 2017

- Cynthia Traub
- Comput. Geom.
- 2015

- Cynthia Traub
- 2005

Let mwt(X ) denote the sum of the Euclidean edge lengths of a minimum weight triangulation of a point set X ∈ R2. We investigate the conditions under which an n-point set X will allow an (n + 1)st point P (called a Steiner point) to give mwt(X ∪ {P}) < mwt(X ). We call the regions of the plane where such a P reduces the length of the minimum weight… (More)

- Cynthia Traub
- CCCG
- 2012

This paper develops techniques for computing the minimum weight Steiner triangulation of a planar point set. We call a Steiner point P a Steiner reducing point of a planar point set X if the weight (sum of edge lengths) of a minimum weight triangulation of X ∪{P} is less than that of X. We define the Steiner reducing set St(X) to be the collection of all… (More)

- Kyle A. Lawson, James L. Parish, Cynthia Traub, Adam G. Weyhaupt
- 2013

We obtain a complete classification of all simple closed geodesics on the eight convex deltahedra by solving a related graph coloring problem. Geodesic segments in the neighborhood of each deltahedron vertex produce a limited number of crossing angles with deltahedron edges. We define a coloring on the edge graph of a deltahedron based on these angles, and… (More)

- Erin W. Chambers, Di Fang, Kyle Sykes, Cynthia Traub, Philip Trettenero
- 2013

A zipper folding of a polygon P given a source point x ∈ ∂P is the polyhedron generated by identifying all points in ∂P equidistant from x, measured along the perimeter of P , in essence “zipping” the boundary of the polygon. A theorem of Alexandrov shows that as long as every glued point has nonnegative curvature, then any zipper folding of a convex… (More)

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