Matched $G^k$-constructions yield $C^k$-continuous iso-geometric elements

J\"org Peters

RECORD

Matched $G^k$-constructions yield $C^k$-continuous iso-geometric elements

Jörg Peters

Numerical Analysis · Submitted 17 Jun 2014

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

The authors' main claim The note shows how $G^k$ (geometrically continuous surface) constructions yield $C^k$ iso-geometric elements also at irregular quad mesh points where three or more than four elements come together.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗

Cite ▾

Claim paper

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.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 1,657 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.12 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.09 · compares with prior results 0.13 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

The note shows how $G^k$ (geometrically continuous surface) constructions yield $C^k$ iso-geometric elements also at irregular quad mesh points where three or more than four elements come together.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The note shows how $G^k$ (geometrically continuous surface) constructions yield $C^k$ iso-geometric elements also at irregular quad mesh points where three or more than four elements come together.	contribution 0.73	0.89	0.91	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.71 · evidence from proof or derivation 0.96.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

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

The note shows how $G^k$ (geometrically continuous surface) constructions yield $C^k$ iso-geometric elements also at irregular quad mesh points where three or more than four elements come together.

Human review

How Pith checks papers → · Full audit of this paper →

How the literature uses it

2 arXiv papers cite this in 4 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 3 sentences without a confident label

Cites it as background 1 paper

There is growing interest in geometric continuity, especially in Computer Aided Geometric Design [ref] , [ref] , [ref] and isogeometric analysis [ref] , [ref] .

Building geometrically continuous splines · Introduction · 0.95

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.