The manufacturing industry constantly needs to verify machined objects against their original CAD models. Given a prototype design, an engineer should be able to determine whether the part was manufactured well; that is, whether it fits the CAD model exactly. However, derivative computations are unstable for real data, and the estimated curvature is thus very sensitive to noise. Moreover, in many cases, spatial fitting of corresponding points is not sufficient. The current work utilizes the curvature properties to inspect manufactured parts that have been reconstructed from noisy and densely sampled data.

1.
Karbacher
,
S.
,
Babst
,
J.
, and
Häusler
,
G.
, 1999, “
Visualization and Detection of Small Defects on Car-Bodies
,
Modeling and Visualization ’99
,
Sankt Augustin
, pp.
1
8
.
2.
Kase
,
K.
,
Makinouchi
,
A.
,
Nakagawa
,
T.
,
Suzuki
,
H.
, and
Kimura
,
F.
, 1999, “
Shape Error Evaluation Method of Free-Form Surfaces
,”
Comput.-Aided Des.
0010-4485,
31
(
8
), pp.
495
505
.
3.
Mortara
,
M.
,
Patanè
,
G.
,
Spagnuolo
,
M.
,
Falcidieno
,
B.
, and
Rossignac
,
J.
, 2003, “
Blowing Bubbles for Multi-scale Analysis and Decomposition of Triangle Meshes
,”
Algorithmica
0178-4617,
38
(
2
), pp.
227
248
.
4.
Taubin
,
G.
, 1995, “
Estimating the Tensor of Curvature of a Surface From Polyhedral Approximation
,”
Proc. 5th Intl. Conf. on Computer Vision (ICCV 95)
, Cambridge, MA, pp.
902
907
.
5.
Meyer
,
M.
,
Desbrun
,
M.
,
Schröder
,
P.
, and
Barr
,
A. H.
, 2003, “
Discrete Differential Geometry Operators for Triangulated 2-Manifolds
,” in
Visualization and Mathematics III
, edited by
H.-C.
Hege
and
K.
Polthier
,
Springer
, Heidelberg, pp.
35
57
.
6.
Cohen-Steiner
,
D.
, and
Morvan
,
J. M.
, 2003, “
Restricted Delaunay Triangulations and Normal Cycle
,”
Proc. of the 19th Conference on Computational Geometry
, San Diego, CA, pp.
312
321
.
7.
Page
,
D. L.
,
Koschan
,
A.
,
Sun
,
Y.
,
Paik
,
J.
, and
Abidi
,
M. A.
, 2001, “
Robust Crease Detection and Curvature Estimation of Piecewise Smooth Surfaces from Triangle Mesh Approximations Using Normal Voting
,”
Proc. Intl. Conf. on Computer Vision and Pattern Recognition
,
Kauai
, Hawaii, pp.
162
167
.
8.
Hameiri
,
Y.
, and
Shimshoni
,
I.
, 2002, “
Estimating the Principal Curvatures and the Darboux Frame from Real 3D Range Data
,”
1st Intl. Symposium on 3D Data Processing Visualization and Transmission (3DPVT2002)
, Padova, Italy, pp.
258
267
.
9.
Hamann
,
B.
, 1993, “
Curvature Approximation for Triangulated Surfaces
,”
Computing
0010-485X, (
8
), pp.
139
153
.
You do not currently have access to this content.