As-Rigid-As-Possible Surface Modeling
2007 · paper · Computer science
Proposes surface deformation and editing driven by keeping local transformations as rigid as possible, expressed as a non-linear energy minimized under modeling constraints. An iterative mesh-editing scheme based on it preserves detail and is easy to implement.
Checked: PDF from igl.ethz.ch, fetched 4 Oct 2026. Page numbers are those of that PDF.
1 finding
Wording Eq. (10) reads "p′_j = c_k, k ∈ F": the constrained-position index j does not match the quantified index k. p′_k = c_k is presumably meant.
- p. 5 Eq. (10)
p′j = ck , k ∈ F
- p. 5 Equation (10)
p′ j = ck , k ∈F,
Judge's note: Crop C009-b shows the subscript j on p′ and k on c and in the quantifier. The text defines F as 'the set of indices of the constrained vertices' and says the right-hand side is updated 'with the values c_k', so the vertex index should be k. j is otherwise used as the neighbour index.
Second check: another model agreed
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9 minor (typos and the like; most checked by the judge only)
Reference or label Figure 7 caption: "(d) and (e) show side and front views of forward bending, respectively". (d) appears to be the front view and (e) the side view.
- p. 7 Figure 7 caption
(d) and (e) show side and front views of forward bending, respectively
Only the authors can say what is right here.
Judge's note: I checked crop C013-a and page 7. In (d) the arms lie left–right in the image plane, as in the original (a), and the top is foreshortened as it bends toward the viewer. In (e) the bend appears as an arc in profile, with the arms foreshortened. On the natural reading, (d) is the front view and (e) the side view, the reverse of the caption. The authors may have defined 'front' differently, so this is a query for them.
Second check: another model agreed
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Wording "where b is an n-vector whose ith row contains the right-hand side expression from (8)". Each row of (8) is a 3-vector, and p′ is later said to consist of three columns, so b is n×3.
- p. 5 Text after Eq. (9)
where b is an n-vector whose ith row contains the right-hand side expression from (8)
- p. 5 Section 3, right column
since p′ consists of three columns (for the three coordinate functions)
Judge's note: Crop C011-a shows the definition of b. Crop C011-b (p. 5, right column) shows 'since p′ consists of three columns (for the three coordinate functions)'. Read one coordinate at a time, the wording is loose rather than wrong, so this is a minor notational ambiguity.
Second check: another model agreed
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Typo Introduction, para 1: "a shape has to to be stretched or sheared" has the word 'to' twice.
- p. 1 Introduction, para 1
a shape has to to be stretched or sheared
Judge's note: In crop C001-a, 'has to to be' sits on one line of the Introduction on page 1, so this is not a line-break artefact.
Second check: none (judge only)
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Typo Page 2, left column: "properly weighted in the objective funtion" should read 'function'.
- p. 2 Page 2, first paragraph
properly weighted in the objective funtion
- p. 2 Introduction, top of left column
weighted in the objective funtion
- p. 2 top of left column
objective funtion
- p. 2
cells needs to be properly weighted in the objective funtion.
Judge's note: Crop C003-a shows 'funtion' at the top of the left column on page 2.
Second check: none (judge only)
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Typo Section 2.1: "If the deformation C → C′ is rigid" drops the subscript i, although the sentence before introduces C_i and C′_i.
- p. 3 Section 2.1, before Eq. (2)
If the deformation C → C′
Judge's note: Crop C005-a shows C → C′ with no subscript, right after the definition of C_i and C′_i and before R_i in Eq. (2). The meaning is clear from context, so this is a cosmetic notation slip.
Second check: none (judge only)
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Typo "if more complex modeling constrains are admitted" (p. 3) and "positional modeling constrains (10)" (p. 6) should both read 'constraints'.
- p. 3 Section 1.1, first paragraph on page 3
modeling constrains are admitted
- p. 3 Section 1.1, top of left column
if more complex modeling constrains are admitted
- p. 3 top of page, first paragraph
more complex modeling constrains are admitted
- p. 6 Naive Laplacian editing
positional modeling constrains (10)
Judge's note: Crop C006-a (p. 3, top of left column) and crop C012-a (p. 6, Naive Laplacian editing) both show 'constrains' used as a noun.
Second check: none (judge only)
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Typo After Eq. (4): "We are thus remained with" is not idiomatic; 'We are thus left with' is meant.
- p. 3 Section 2.1 after Eq. 4
We are thus re- mained with
Judge's note: Crop C007-a shows 're-mained with' hyphenated across a line break. This is a minor wording issue.
Second check: none (judge only)
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Typo After Eq. (5): "P_i is the 3 × |N(v_i)| containing e_ij's as its columns" lacks the noun 'matrix' and writes N(v_i), where the paper elsewhere writes N(i).
- p. 4 Text after Eq. (5)
is the 3 × |N (vi)| containing eij’s as its columns
- p. 4 Text after Eq. (5)
Pi is the 3 × |N (vi)| containing eij’s as its columns
- p. 4 after Eq. 5
Pi is the 3 × |N (vi)| containing
Judge's note: Crop C008-a shows '3 × |N(v_i)| containing'. Eq. (5) just above and Section 2 use N(i), and v_i is not defined.
Second check: none (judge only)
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Typo "is non-other than the discrete Laplace-Beltrami operator" (p. 5) should read 'none other than'. Also "The user experience reminds a lot of" (p. 6) is not idiomatic.
- p. 5 Text after Eq. (8)
is non-other
- p. 5 Text after Eq. (8)
is non-other than the discrete Laplace-Beltrami operator
- p. 5 after Eq. 8
is non-other than the discrete Laplace-Beltrami
- p. 6 Previous frame
The user experience reminds a lot of
Judge's note: Crop C010-a (p. 5, after Eq. 8) and crop C012-a (p. 6, right column) show the wording as quoted.
Second check: none (judge only)