Linear time algorithms for visibility and shortest path problems inside simple polygons
SCG '86 Proceedings of the second annual symposium on Computational geometry
On shortest paths in polyhedral spaces
SIAM Journal on Computing
Approximation algorithms for shortest path motion planning
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
SIAM Journal on Computing
Shortest paths on a polyhedron
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Approximating shortest paths on a convex polytope in three dimensions
Journal of the ACM (JACM)
Efficient computation of geodesic shortest paths
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Constructing Approximate Shortest Path Maps in Three Dimensions
SIAM Journal on Computing
Practical methods for approximating shortest paths on a convex polytope in R3
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
SIAM Review
Computing approximate shortest paths on convex polytopes
Proceedings of the sixteenth annual symposium on Computational geometry
Fast computation of shortest watchman routes in simple polygons
Information Processing Letters
An augmented Fast Marching Method for computing skeletons and centerlines
VISSYM '02 Proceedings of the symposium on Data Visualisation 2002
Some Improvements of the Fast Marching Method
SIAM Journal on Scientific Computing
Texture Mapping Using Surface Flattening via Multidimensional Scaling
IEEE Transactions on Visualization and Computer Graphics
Touring a sequence of polygons
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Approximating Shortest Paths on a Nonconvex Polyhedron
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
GMP '00 Proceedings of the Geometric Modeling and Processing 2000
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Applying improved fast marching method to endocardial boundary detection in echocardiographic images
Pattern Recognition Letters
New results on shortest paths in three dimensions
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Geodesic Paths on Triangular Meshes
SIBGRAPI '04 Proceedings of the Computer Graphics and Image Processing, XVII Brazilian Symposium
Iso-charts: stretch-driven mesh parameterization using spectral analysis
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Fast exact and approximate geodesics on meshes
ACM SIGGRAPH 2005 Papers
Short note: O(N) implementation of the fast marching algorithm
Journal of Computational Physics
A modified fast marching method
SCIA'03 Proceedings of the 13th Scandinavian conference on Image analysis
Improving Chen and Han's algorithm on the discrete geodesic problem
ACM Transactions on Graphics (TOG)
A survey of geodesic paths on 3D surfaces
Computational Geometry: Theory and Applications
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In this paper, we present an efficient visibility-based algorithm for determining a locally exact shortest path (LESP) from a source point to a destination point on a (triangulated) polyhedral surface. Our algorithm, of a finitely-iterative scheme, evolves an initial approximately shortest path into a LESP. During each iteration, we first compute the exact shortest path restricted on the current face sequence according to Fermat's principle which affirms that light always follows the shortest optical path, and then optimize the face sequence where the path is not locally shortest on the polyhedral surface. Since the series of paths we obtained are monotonic decreasing in length, the algorithm gives a LESP which is shorter than the initial path, at conclusion. For comparison, we use various methods to provide an initial path. One of the methods is Dijkstra's algorithm, and the others are the Fast Marching Method (FMM) and its improved version. Our intention for improvement is to overcome the limitation of acute triangulations in the original version. To achieve this goal, we classify all the edges into seven types according to different wavefront propagation manners, and dynamically determine the type of each edge for controlling the subsequent wavefront expansion. Furthermore, we give two approaches for backtracing the approximately shortest paths directed at the improved FMM. One exploits the known propagation manners of the edges as well as the Euler's method. This is another contribution in this paper.