On embedding a graph in the grid with the minimum number of bends
SIAM Journal on Computing
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
Piecewise-linear interpolation between polygonal slices
Computer Vision and Image Understanding
A linear algorithm for 2-bend embeddings of planar graphs in the two-dimensional grid
Discrete Applied Mathematics
Warping and morphing of graphical objects
Warping and morphing of graphical objects
Spirality and Optimal Orthogonal Drawings
SIAM Journal on Computing
How to morph tilings injectively
Journal of Computational and Applied Mathematics
Embedding planar graphs on the grid
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Drawing graphs
Drawing graphs
Controllable morphing of compatible planar triangulations
ACM Transactions on Graphics (TOG)
Graph Drawing: Algorithms for the Visualization of Graphs
Graph Drawing: Algorithms for the Visualization of Graphs
GD '01 Revised Papers from the 9th International Symposium on Graph Drawing
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Morphing orthogonal planar graph drawings
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Geometric Folding Algorithms: Linkages, Origami, Polyhedra
Geometric Folding Algorithms: Linkages, Origami, Polyhedra
Morphing polyhedra with parallel faces: Counterexamples
Computational Geometry: Theory and Applications
Discrete & Computational Geometry
Morphing planar graphs while preserving edge directions
GD'05 Proceedings of the 13th international conference on Graph Drawing
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We give an algorithm to morph between two planar orthogonal drawings of a graph, preserving planarity and orthogonality. The morph uses a quadratic number of steps, where each step is a linear morph (a linear interpolation between two drawings). This is the first algorithm to provide planarity-preserving morphs with well-behaved complexity for a significant class of graph drawings. Our method is to morph until each edge is represented by a sequence of segments, with corresponding segments parallel in the two drawings. Then, in a result of independent interest, we morph such parallel planar orthogonal drawings, preserving edge directions and planarity.