The DOI matches its Crossref record; 21 of the 21 references it cites were found in a registry or an index.
Fast exact and approximate geodesics on meshes
Open accessAbstract
The computation of geodesic paths and distances on triangle meshes is a common operation in many computer graphics applications. We present several practical algorithms for computing such geodesics from a source point to one or all other points efficiently. First, we describe an implementation of the exact "single source, all destination" algorithm presented by Mitchell, Mount, and Papadimitriou (MMP). We show that the algorithm runs much faster in practice than suggested by worst case analysis. Next, we extend the algorithm with a merging operation to obtain computationally efficient and accurate approximations with bounded error. Finally, to compute the shortest path between two given points, we use a lower-bound property of our approximate geodesic algorithm to efficiently prune the frontier of the MMP algorithm. thereby obtaining an exact solution even more quickly.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
A Global Geometric Framework for Nonlinear Dimensionality Reduction
Tenenbaum, J. B., Silva, V. D., & Langford, J. C. (2000) · Science · doi:10.1126/science.290.5500.2319 · Cited by 13,585
Topology matching for fully automatic similarity estimation of 3D shapes
Hilaga, M., Shinagawa, Y., Kohmura, T., & Kunii, T. L. (2001) · Proceedings of the 28th annual conference on Computer graphics and interactive techniques · doi:10.1145/383259.383282 · Cited by 2,187
Smooth Subdivision Surfaces Based on Triangles
Loop, C. (1987) · Cited by 1,319
Progress in Nonlinear Differential Equations and their Applications
Aftalion, A. (2006) · HAL (Le Centre pour la Communication Scientifique Directe) · Cited by 1,256
Computing geodesic paths on manifolds
Kimmel, R., & Sethian, J. A. (1998) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.95.15.8431 · Cited by 1,049
Mitchell, J. S. B., Mount, D. M., & Papadimitriou, C. H. (1987) · SIAM Journal on Computing · doi:10.1137/0216045 · Cited by 720
Computing the shortest path: A search meets graph theory
Goldberg, A. V., & Harrelson, C. (2005) · doi:10.5555/1070432.1070455 · Cited by 719
Interactive multi-resolution modeling on arbitrary meshes
Kobbelt, L., Campagna, S., Vorsatz, J., & Seidel, H.-P. (1998) · Proceedings of the 25th annual conference on Computer graphics and interactive techniques - SIGGRAPH '98 · doi:10.1145/280814.280831 · Cited by 655
Hierarchical mesh decomposition using fuzzy clustering and cuts
Katz, S., & Tal, A. (2003) · ACM SIGGRAPH 2003 Papers · doi:10.1145/1201775.882369 · Cited by 577
Funkhouser, T., Kazhdan, M., Shilane, P., Min, P., Kiefer, W., Tal, A., Rusinkiewicz, S., & Dobkin, D. (2004) · ACM Transactions on Graphics · doi:10.1145/1015706.1015775 · Cited by 506
Cited by
Registration of 3D Point Clouds and Meshes: A Survey from Rigid to Nonrigid
Tam, G. K. L., Cheng, Z.-Q., Lai, Y.-K., Langbein, F. C., Liu, Y., Marshall, D., Martin, R. R., Sun, X.-F., & Rosin, P. L. (2013) · IEEE Transactions on Visualization and Computer Graphics · doi:10.1109/tvcg.2012.310 · Cited by 679
Geodesics in heat: A new approach to computing distance based on heat flow
Crane, K., Weischedel, C., & Wardetzky, M. (2013) · ACM Transactions on Graphics · doi:10.1145/2516971.2516977 · Cited by 297
Metadata
- Authors
- Surazhsky, V., Surazhsky, T., Kirsanov, D., Gortler, S. J., & Hoppe, H.
- Venue
- ACM Transactions on Graphics
- Published
- 2005-07
- Volume
- 24
- Issue
- 3
- Pages
- 553-560
- ISSN
- 0730-0301 (ISSN-L)
- 1557-7368
- OpenAlex
- W2161253909
- Cited by
- 502
- References
- 21
- FWCI
- 36.37
- Type
- journal article
- Language
- en
- Open access
- green
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Fast exact and approximate geodesics on meshes. https://app.cochat.ai/papers/10.1145/1073204.1073228
- The paper
- Surazhsky, V., Surazhsky, T., Kirsanov, D., Gortler, S. J., & Hoppe, H. (2005). Fast exact and approximate geodesics on meshes. ACM Transactions on Graphics. https://doi.org/10.1145/1073204.1073228
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
