The DOI matches its Crossref record.
The Curve of Least Energy
Open accessAbstract
The curve which has the smallest integral of the square of curvature while passing through two given points with given orientation is searched for.This is the true shape of a spline used in lofting.In computer-aided design, curves have been sought which maximize "smoothness."The curve discussed is the one arising in this way from a commonly used measure of smoothness.The human visual system may use such a curve when it constructs a subjective contour.
Overview
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Citations
Cited by
Mumford, D. (1994) · Algebraic Geometry and its Applications · doi:10.1007/978-1-4612-2628-4_31 · Cited by 458
Stochastic completion fields: A neural model of illusory contour shape and salience.
Williams, L. R., & Jacobs, D. W. (1997) · Neural Computation · doi:10.1162/neco.1997.9.4.837 · Cited by 331
Metadata
- Authors
- Horn, B. K. P.
- Venue
- ACM Transactions on Mathematical Software
- Published
- 1983-12
- Volume
- 9
- Issue
- 4
- Pages
- 441-460
- ISSN
- 0098-3500 (ISSN-L)
- 1557-7295
- OpenAlex
- W2138722428
- Cited by
- 231
- References
- 0
- FWCI
- 2.16
- Type
- journal article
- Language
- en
- Open access
- bronze
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.
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How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
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- CoChat. (2026). Citation check: The Curve of Least Energy. https://app.cochat.ai/papers/10.1145/356056.356061
- The paper
- Horn, B. K. P. (1983). The Curve of Least Energy. ACM Transactions on Mathematical Software. https://doi.org/10.1145/356056.356061
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.
