Point Set Surfaces
2001 · paper · Computer science
Advocates representing shapes as point sets and defines a smooth manifold surface from them using moving least squares. It gives tools to raise or lower point density and a point-rendering technique producing smooth shading and silhouettes at interactive frame rates.
Checked: PDF from sci.utah.edu, fetched 4 Oct 2026. Page numbers are those of that PDF.
3 findings
Reference or label Text: "applied on the set of red points depicted in (a). First, the red points are projected on the MLS surface to yield the blue points"; Figure 6 caption and panel (a) show green input points and orange projected points.
- p. 5 Figure 6 caption
Noisy input points (green points) are projected onto their smooth MLS curve (orange points).
- p. 5 Down-sampling, paragraph on Figure 6
First, the red points are projected on the MLS surface to yield the blue points.
- p. 5 Decimation text
First, the red points are projected on the
- p. 5 Figure 6 caption
Noisy input points (green points) are projected onto their
Judge's note: Looked at the full p.5 image. Panel (a) of Figure 6 shows green/yellow and orange points, with no red or blue. Red and blue appear only in panel (b), where they code error value. The colour names in the text do not match the figure or the caption.
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Wording Introduction states the surface is "guaranteed to be a 2-manifold and C∞ smooth", but Section 3.1 says Levin proves only the 2-manifold property and that infinite smoothness is a "conjecture".
- p. 2 Section 1, 'Smooth manifold surface' property
guaranteed to be a 2-manifold and C∞ smooth
- p. 3 Section 3.1, end
leads to the conjecture that the resulting surface is infinitely smooth
- p. 3 Section 3.1
leads to the conjecture that the
Only the authors can say what is right here.
Judge's note: Checked p.2 (Smooth manifold surface bullet) and p.3 Section 3.1 end: "Levin proves ... two-dimensional manifold [27]. Further, a general analysis of moving least squares [26] leads to the conjecture that the resulting surface is infinitely smooth as long as θ ∈ C∞". The introduction calls C∞ smoothness guaranteed, which is more than the body supports.
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Wording Conclusion: "We showed that the error of these approximations is bounded and dependent on the spacing among points", but no such bound is derived, stated or measured in the paper.
- p. 7 Section 6 Conclusion, second paragraph
We showed that the error of these approximations is bounded and dependent on the spacing among points.
Only the authors can say what is right here.
Judge's note: Searched the text for bound, error, tolerance, spacing and approximation order. Section 3 gives only qualitative remarks about h reflecting point spacing, and Section 5 says patches are "a good approximation". No error bound for the polynomial patches appears, and none is cited at that point. The authors may have meant Levin [26,27].
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13 minor (typos and the like; most checked by the judge only)
Reference or label Reference [30] (Lloyd, "Least squares quantization in PCM") gives the pages as "28:128–137, 1982"; the published first page is 129.
- p. 8
S. P. Lloyd. Least squares quantization in PCM. IEEE Transactions on Information Theory, 2
Only the authors can say what is right here.
Judge's note: Rests on outside knowledge: that Crossref (doi:10.1109/tit.1982.1056489) records pages 129–137 for this article. The page image confirms that ref [30] prints "28:128–137, 1982".
Second check: another model agreed, code check
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Wording Results: "The number of representation points ranges from 1000 (for the torus)", but the wavy torus depicted in Figure 7 originally has "800 points"; it is not stated which torus is meant.
- p. 5 Figure 7 caption
originally consisting of 800 points has been up-sampled to 20K points
- p. 6 Up-sampling, last sentence
the same object after adding 20K points over its MLS surface
- p. 7 Results, last paragraph
ranges from 1000 (for the torus)
- p. 5 Figure 7 caption
torus originally consisting of 800 points has been up-sampled to 20K points
Judge's note: Figure 10 caption (p.8) gives a torus mesh of "1000 vertices", which fits the Results value. The wavy torus in Figure 7 (p.5) and the p.6 text has 800 points, which is below the stated minimum for "all models depicted". The likely reading is that the 1000 refers to the Figure 10 torus, so this is an ambiguity, not an error. The 20K total-versus-added point is handled under C013.
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Wording Figure 7 caption: torus of 800 points "has been up-sampled to 20K points" (a total), while the p.6 text says "after adding 20K points over its MLS surface" (an increment).
- p. 6 Up-sampling text
after adding 20K points over its MLS surface
- p. 5 Figure 7 caption
has been up-sampled to 20K points
- p. 5 Figure 7 caption
up-sampled to 20K points
Judge's note: Both seen in the page images (p.5 caption, p.6 text). Adding 20K points gives about 20.8K, so the two phrasings describe different quantities. The difference is small and could be rounding or loose wording.
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Wording Section 5 says polynomials "are a good approximation to the surface inside a patch [−h, h]2 around a point", while the Figure 8 caption says "a square patch of [−h, h]2 would lead to unpleasant effects in some cases, as the polynomial might leave the ball of radius h".
- p. 6 Sampling additional points, first paragraph
are a good approximation to the surface inside a patch [−h, h]2 around a point
- p. 6 Figure 8 caption
a square patch of [−h, h]2 would lead to unpleasant effects in some cases
Judge's note: Both seen on the p.6 image. The two statements are in tension: the square's corners lie outside the radius-h ball. The text then defines the patch extent as the bounding box of the projected neighbours. Could be loose wording, but it is unresolved as printed.
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Typo Misspellings: "distance to a locally defined tangent plan" (plane) on p.2; in the references, "IEEE Transaltions on Pattern Analysis" [5] and "Geometric structues" [6].
- p. 2 Section 2 Consolidation
distance to a locally defined tangent plan
- p. 4 Section 3.2
main memroy of 512MB
- p. 2 Related work
locally defined tangent plan
- p. 6 Sampling additional points
displayed with the approach. pre-
Judge's note: Each was seen in the page images (p.2 right column; p.8 refs [5], [6]). The other items reviewers grouped here ('memroy', 'then', the stray full stop) are judged separately under C006, C009 and C012.
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Typo "The volumetric sign-distance techniques described above" should read "signed-distance", the term used in the preceding paragraph.
- p. 2 Section 2 Consolidation
The volumetric sign-distance techniques
Judge's note: Seen in the p.2 image. The previous paragraph says "signed distance" twice.
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Typo "the available main memroy of 512MB" should read "memory".
- p. 4 Section 3.2, last paragraph
main memroy of 512MB
- p. 4
available main memroy of 512MB
Judge's note: Seen in the p.4 image, end of Section 3.2.
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Typo "where the spacing among points is larger then a specified bound" should read "than".
- p. 5 Up-sampling, first paragraph
larger then a specified bound
- p. 5 Up-sampling
is larger then a specified bound
Judge's note: Seen in the p.5 image, Up-sampling paragraph.
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Typo Stray full stop: "can be readily displayed with the approach. presented here."
- p. 6 Sampling additional points
with the approach. pre-
- p. 6 Sampling additional points
displayed with the approach. pre-
- p. 6
displayed with the approach. pre-sented here
Judge's note: Seen in the p.6 image, Sampling additional points paragraph.
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Typo "An example of a environment mapping" should read "an environment mapping".
- p. 7 Results paragraph
An example of a environment mapping
Judge's note: Seen in the p.7 image, Results paragraph.
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Typo Reference [5] misspells the journal name: "IEEE Transaltions on Pattern Analysis and Machine Intelligence" should read "Transactions".
- p. 8 Reference [5]
Transaltions on Pattern Analysis and Machine Intelligence
- p. 8 Ref [5]
Transaltions on Pattern Analysis
- p. 8 Ref [6]
Geometric structues for
- p. 8 Ref [32]
Spatial Tesselations
Judge's note: The page image shows "Transaltions" in ref [5] on p. 8. The cluster also lists the [6] 'structues' and [32] 'Tesselations' quotes, but those are judged separately under C017 and C018. This verdict covers only the [5] misspelling.
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Typo Reference [6] misspells a word in the title: "Geometric structues for three-dimensional shape representation" should read "structures".
- p. 8 Reference [6]
Geometric structues for three-dimensional shape representa-
Judge's note: The page image shows "structues" in the title of ref [6] (Boissonnat) on p. 8.
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Typo Reference [32] gives the book title as "Spatial Tesselations — Concepts and Applications of Voronoi Diagrams"; the book's published title spells it "Tessellations".
- p. 8 Reference [32]
Spatial Tesselations
Only the authors can say what is right here.
Judge's note: Rests on outside knowledge: that the Okabe/Boots/Sugihara book (Wiley 1992) is titled 'Spatial Tessellations'. The page image confirms the printed text reads "Tesselations". 'Tesselation' is a variant spelling, so this is minor.
Second check: none (judge only)