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
The class of simple cube-curves whose MLPs cannot have vertices at grid points
DGCI'05 Proceedings of the 12th international conference on Discrete Geometry for Computer Imagery
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
Shortest paths in a cuboidal world
IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
Finding the shortest path between two points in a simple polygon by applying a rubberband algorithm
PSIVT'06 Proceedings of the First Pacific Rim conference on Advances in Image and Video Technology
| Hi-index | 0.01 |
We consider simple cube-curves in the orthogonal 3D grid. 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 an MLP. A proof that this algorithm always converges to the correct curve, is still an open problem. This paper proves that the rubber-band algorithm is correct for the family of first-class simple cube-curves.