Approximate Euclidean shortest path in 3-space
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Length Estimation in 3-D Using Cube Quantization
Journal of Mathematical Imaging and Vision
Digital Curves in 3D Space and a Linear-Time Length Estimation Algorithm
IEEE Transactions on Pattern Analysis and Machine Intelligence
Digital Geometry: Geometric Methods for Digital Picture Analysis
Digital Geometry: Geometric Methods for Digital Picture Analysis
New lower bound techniques for robot motion planning problems
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
Minimum-Length polygon of a simple cube-curve in 3d space
IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis
An approximation algorithm for computing minimum-length polygons in 3D images
ACCV'10 Proceedings of the 10th Asian conference on Computer vision - Volume Part IV
Approximate shortest paths in simple polyhedra
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
Minimum-length polygons of first-class simple cube-curves
CAIP'05 Proceedings of the 11th international conference on Computer Analysis of Images and Patterns
Shortest paths in a cuboidal world
IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
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We consider simple cube-curves in the orthogonal 3D grid of cells. The union of all cells contained in such a curve (also called the tube of this curve) is a polyhedrally bounded set. The curve's length is defined to be that of the minimum-length polygonal curve (MLP) fully contained and complete in the tube of the curve. So far only one general algorithm called rubber-band algorithm was known for the approximative calculation of such a MLP. There is an open problem which is related to the design of algorithms for calculation a 3D MLP of a cube-curve: Is there a simple cube-curve such that none of the vertices of its 3D MLP is a grid vertex? This paper constructs an example of such a simple cube-curve. We also characterize this class of cube-curves.