On shortest paths in polyhedral spaces
SIAM Journal on Computing
Offsetting operations in solid modelling
Computer Aided Geometric Design
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
Approximate Euclidean shortest path in 3-space
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Shelling and offsetting bodies
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Approximating weighted shortest paths on polyhedral surfaces
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Approximating shortest paths on a convex polytope in three dimensions
Journal of the ACM (JACM)
A Note on the Complexity of Dijkstra's Algorithm for Graphs with Weighted Vertices
IEEE Transactions on Computers
Practical methods for approximating shortest paths on a convex polytope in R3
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Computing approximate shortest paths on convex polytopes
Proceedings of the sixteenth annual symposium on Computational geometry
An algorithm for planning collision-free paths among polyhedral obstacles
Communications of the ACM
Comparing Offset Curve Approximation Methods
IEEE Computer Graphics and Applications
Approximating Shortest Paths on a Nonconvex Polyhedron
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Fast exact and approximate geodesics on meshes
ACM SIGGRAPH 2005 Papers
Efficiently determining a locally exact shortest path on polyhedral surfaces
Computer-Aided Design
Improving Chen and Han's algorithm on the discrete geodesic problem
ACM Transactions on Graphics (TOG)
Efficiently Computing Exact Geodesic Loops within Finite Steps
IEEE Transactions on Visualization and Computer Graphics
Constant-time all-pairs geodesic distance query on triangle meshes
I3D '12 Proceedings of the ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games
Texture brush: an interactive surface texturing interface
Proceedings of the ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games
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Geodesic offset curves are important for many industrial applications, such as solid modeling, robot-path planning, the generation of tool paths for NC machining, etc. Although the offset problem is well studied in classical differential geometry and computer-aided design, where the underlying surface is sufficiently smooth, very few algorithms are available for computing geodesic offsets on discrete representation, in which the input is typically a polyline curve restricted on a piecewise linear mesh. In this paper, we propose an efficient and exact algorithm to compute the geodesic offsets on triangle meshes by extending the Xin-Wang algorithm of discrete geodesics. We define a new data structure called parallel-source windows, and extend both the ''one angle one split'' and the filtering theorem to maintain the window tree. Similar to the original Xin-Wang algorithm, our extended algorithm has an O(n) space complexity and an O(n^2logn) asymptotic time complexity, where n is the number of vertices on the input mesh. We tested our algorithm on numerous real-world models and showed that our algorithm is exact, efficient and robust, and can be applied to large scale models with complicated geometry and topology.