Hands: a pattern theoretic study of biological shapes
Hands: a pattern theoretic study of biological shapes
On compatible triangulations of simple polygons
Computational Geometry: Theory and Applications
Warping and morphing of graphical objects
Warping and morphing of graphical objects
The computational complexity of knot and link problems
Journal of the ACM (JACM)
Constraining Plane Configurations in Computer-Aided Design: Combinatorics of Directions and Lengths
SIAM Journal on Discrete Mathematics
How to morph tilings injectively
Journal of Computational and Applied Mathematics
Controllable morphing of compatible planar triangulations
ACM Transactions on Graphics (TOG)
Computational Geometry in C
Morphing orthogonal planar graph drawings
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Acute Triangulations of Polygons
Discrete & Computational Geometry
Morphing planar graphs while preserving edge directions
GD'05 Proceedings of the 13th international conference on Graph Drawing
Parallel-redrawing mechanisms, pseudo-triangulations and kinetic planar graphs
GD'05 Proceedings of the 13th international conference on Graph Drawing
Morphing orthogonal planar graph drawings
ACM Transactions on Algorithms (TALG)
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Two simple polyhedra P and Q (not necessarily convex) are parallel if they share the same edge graph G and each face of P has the same outward-facing unit normal as the corresponding face in Q. Parallel polyhedra P and Q admit a parallel morph if the vertices can be moved in a continuous manner taking us from P to Q such that at all times the intermediate polyhedron determined by the vertex configuration and graph G is both simple and parallel with P (and Q). In this note, we show that even for very restrictive classes of orthogonal polyhedra, there exist parallel polyhedra that do not admit a parallel morph.