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Constructing Explicit B-Spline

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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R.O. Linger, H.R.N. van Erp, P.H.A.J.M. van Gelder

Numerical Analysis · Submitted 12 Sep 2014

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We introduce here a direct method to construct multivariate explicit B-spline bases.

how it is stated · asserted 1.00 read the record →

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arXiv ID1409.3824 (version 1)
Pith ID557CVIYD, Pith's permanent record of this paper and its review
CitationH.R.N. van Erp, P.H.A.J.M. van Gelder, R.O. Linger. "Constructing Explicit B-Spline." arXiv:1409.3824 (2014). https://pith.science/paper/557CVIYD
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,632 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.07 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.07 · mentions code or data availability 0.03.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We introduce here a direct method to construct multivariate explicit B-spline bases. B-splines are piecewise polynomials, which are defined on adjacent tetrahedra and which are $C^{r}$ continuous throughout. The $C^{r}$ continuity is enforced by making sure that all directional derivatives of order $r$, and lower, on the boundaries of adjacent tetrahedra give the same values for both tetrahedra. The method presented here is explicit, in that we will provide an algorithm with which one can analytically construct the B-spline base that enforces $C^{r}$ continuity for a given geometry.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We introduce here a direct method to construct multivariate explicit B-spline bases. contribution 1.00 0.93 0.51 asserted 1.00
s1 B-splines are piecewise polynomials, which are defined on adjacent tetrahedra and which are $C^{r}$ continuous throughout. background 1.00 0.09 0.07 asserted 1.00
s2 The $C^{r}$ continuity is enforced by making sure that all directional derivatives of order $r$, and lower, on the boundaries of adjacent tetrahedra give the same values for both tetrahedra. method 0.96 0.43 0.08 asserted 1.00
s3 The method presented here is explicit, in that we will provide an algorithm with which one can analytically construct the B-spline base that enforces $C^{r}$ continuity for a given geometry. contribution 0.53 0.91 0.34 asserted 1.00

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from proof or derivation 0.98.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We introduce here a direct method to construct multivariate explicit B-spline bases. B-splines are piecewise polynomials, which are defined on adjacent tetrahedra and which are $C^{r}$ continuous throughout. The $C^{r}$ continuity is enforced by making sure that all directional derivatives of order $r$, and lower, on the boundaries of adjacent tetrahedra give the same values for both tetrahedra. The method presented here is explicit, in that we will provide an algorithm with which one can analytically construct the B-spline base that enforces $C^{r}$ continuity for a given geometry.

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