The DOI matches its Crossref record.
The Numerical Evaluation of B-Splines
Abstract
The conventional method of evaluating B-splines by means of divided differences is numerically unstable. A relation between B-splines of consecutive degrees is derived which enables B-splines to be evaluated in a stable and efficient fashion. Analyses of error growth in the conventional and the stable methods are carried out. For the stable method an a priori relative error bound is obtained.
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
Cited by
A Spline-Based Trajectory Representation for Sensor Fusion and Rolling Shutter Cameras
Patron-Perez, A., Lovegrove, S., & Sibley, G. (2015) · International Journal of Computer Vision · doi:10.1007/s11263-015-0811-3 · Cited by 104
Tkalčić, H. (2024) · Geophysical Research Letters · doi:10.1029/2023gl107043 · Cited by 4
“…for the continuous temporal ddt changes with clamped B ‐spline fitting: where B i ,3 ( t ; u 1 , u 2 , u 3 , … , u N ) are basis functions depending on the knots ( u 0 , u 1 , u 2 , u 3 , … , u N , u N + 1 ), and can be derived employing the Cox‐de Boor recursion formula (Cox, 1972; de Boor, 1972).”
Method
Metadata
- Authors
- COX, M. G.
- Venue
- IMA Journal of Applied Mathematics
- Publisher
- Oxford University Press (OUP)
- Published
- 1972
- Volume
- 10
- Issue
- 2
- Pages
- 134-149
- ISSN
- 0272-4960 (ISSN-L)
- 1464-3634
- OpenAlex
- W2116334708
- Cited by
- 874
- References
- 0
- FWCI
- 1.93
- Type
- journal article
- Language
- en
- Open access
- closed
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
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.
