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Tetrisation of triangular meshes and its application in shape blending

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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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Shizuo Kaji

Graphics · Submitted 19 Jan 2016

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

The authors' main claim We implemented a shape blender based on our algorithm and its MIT licensed source code is available online.

how it is stated · asserted 1.00 read the record →

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arXiv ID1601.04816 (version 1)
Pith IDERUAOTRT, Pith's permanent record of this paper and its review
CitationShizuo Kaji. "Tetrisation of triangular meshes and its application in shape blending." arXiv:1601.04816 (2016). https://pith.science/paper/ERUAOTRT
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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.

Open the compiled record

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,842 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.07 · human participants 0.02 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.14 · mentions code or data availability 0.98.

The abstract, sentence by sentence

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

The As-Rigid-As-Possible (ARAP) shape deformation framework is a versatile technique for morphing, surface modelling, and mesh editing. We discuss an improvement of the ARAP framework in a few aspects: 1. Given a triangular mesh in 3D space, we introduce a method to associate a tetrahedral structure, which encodes the geometry of the original mesh. 2. We use a Lie algebra based method to interpolate local transformation, which provides better handling of rotation with large angle. 3. We propose a new error function to compile local transformations into a global piecewise linear map, which is rotation invariant and easy to minimise. We implemented a shape blender based on our algorithm and its MIT licensed source code is available online.

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 The As-Rigid-As-Possible (ARAP) shape deformation framework is a versatile technique for morphing, surface modelling, and mesh editing. background 1.00 0.05 0.04 asserted 1.00
s1 We discuss an improvement of the ARAP framework in a few aspects: 1. contribution 0.98 0.50 0.04 asserted 0.58
s2 Given a triangular mesh in 3D space, we introduce a method to associate a tetrahedral structure, which encodes the geometry of the original mesh. 2. contribution 0.64 0.92 0.07 asserted 1.00
s3 We use a Lie algebra based method to interpolate local transformation, which provides better handling of rotation with large angle. 3. method 0.61 0.90 0.07 asserted 1.00
s4 We propose a new error function to compile local transformations into a global piecewise linear map, which is rotation invariant and easy to minimise. contribution 0.56 0.94 0.17 asserted 1.00
s5 We implemented a shape blender based on our algorithm and its MIT licensed source code is available online. contribution 0.91 0.91 0.08 asserted 1.00

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 0.79.

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
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 As-Rigid-As-Possible (ARAP) shape deformation framework is a versatile technique for morphing, surface modelling, and mesh editing. We discuss an improvement of the ARAP framework in a few aspects: 1. Given a triangular mesh in 3D space, we introduce a method to associate a tetrahedral structure, which encodes the geometry of the original mesh. 2. We use a Lie algebra based method to interpolate local transformation, which provides better handling of rotation with large angle. 3. We propose a new error function to compile local transformations into a global piecewise linear map, which is rotation invariant and easy to minimise. We implemented a shape blender based on our algorithm and its MIT licensed source code is available online.

Human review

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How the literature uses it

What this paper does with the arXiv papers it cites

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

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