Automatic creation of B-rep models of engineering objects from freehand sketches would benefit designers. One step aims to take a line drawing (with hidden lines removed), and from it deduce an initial three-dimensional (3D) geometric realization of the visible part of the object, including junction and line labels, and depth coordinates. Most methods for producing this frontal geometry use line labeling, which takes little or no account of geometry. Thus, the line labels produced can be unreliable. Our alternative approach inflates a drawing to produce provisional depth coordinates, and from these makes deductions about line labels. Assuming many edges in the drawing are parallel to one of three main orthogonal directions, we first attempt to identify groups of parallel lines aligned with the three major axes of the object. From these, we create and solve a linear system of equations relating vertex coordinates, in the coordinate system of the major axes. We then inflate the drawing in a coordinate system based on the plane of the drawing and depth perpendicular to it. Finally, we use this geometry to identify which lines in the drawing correspond to convex, concave, or occluding edges. We discuss alternative realizations of some of the concepts, how to cope with nonisometric-projection drawings, and how to combine this approach with other labeling techniques to gain the benefits of each. We test our approach using sample drawings chosen to be representative of engineering objects. These highlight difficulties often overlooked in previous papers on line labeling. Our new approach has significant benefits.

1.
Jenkins
,
D. L.
, 1992, “
The Automatic Interpretation of Two-Dimensional Freehand Sketches
,” PhD Thesis, University of Wales College of Cardiff.
2.
Grimstead
,
I. J.
, 1997, “
Interactive Sketch Input of Boundary Representation Solid Models
,” PhD Thesis, Cardiff University.
3.
Company
,
P.
,
Contero
,
M.
,
Conesa
,
J.
, and
Piquer
,
A.
, 2004, “
An Optimisation-Based Reconstruction Engine for 3D Modelling by Sketching
,”
Comput. Graphics
0097-8493,
28
(
6
), pp.
955
979
.
4.
Parodi
,
P.
,
Lancewicki
,
R.
,
Vijh
,
A.
, and
Tsotsos
,
J. K.
, 1998, “
Empirically-Derived Estimates of the Complexity of Labeling Line Drawings of Polyhedral Scenes
,”
Artif. Intell.
0004-3702,
105
, pp.
47
75
.
5.
Sashikumar
,
V.
, and
Sohoni
,
M.
, 2002, “
Reconstruction of Feature Volumes and Feature Suppression
,” in
Proc. Seventh ACM Symposium on Solid Modelling and Applications SM’02
, edited by
Lee
,
K.
, and
Patrikalakis
,
N.
, pp.
60
71
,
ACM Press
.
6.
Sashikumar
,
V.
,
Sohoni
,
M.
, and
Rajadhyaksha
,
R.
, 2002, “
Removal of Blends from Boundary Representation Models
,” in
Proc. Seventh ACM Symposium on Solid Modelling and Applications SM’02
, edited by
Lee
,
K.
, and
Patrikalakis
,
N.
, pp.
83
94
,
ACM Press
.
7.
Palmer
,
S. E.
, 1999, “
Vision Science. Photons to Phenomenology
,”
MIT
, Cambridge, MA.
8.
Mills
,
B. I.
,
Langbein
,
F. C.
,
Marshall
,
A. D.
, and
Martin
,
R. R.
, 2001, “
Estimate of Frequencies of Geometric Regularities for use in Reverse Engineering of Simple Mechanical Components
,” Technical Report GVG 2001-1, Geometry and Vision Group, Department of Computer Science,
Cardiff University
.
9.
Samuel
,
M. M.
,
Requicha
,
A. A. G.
, and
Elkind
,
S. A.
, 1976, “
Methodology and Results of an Industrial Parts Survey
,” Technical Memorandum 21, Production Automation Project,
University of Rochester
.
10.
Varley
,
P. A. C.
,
Takahashi
,
Y.
,
Mitani
,
J.
, and
Suzuki
,
H.
, 2004, “
A Two-Stage Approach for Interpreting Line Drawings of Curved Objects
,” in
Proc. Sketch-Based Interfaces and Modeling 2004
, edited by
Hughes
,
J. F.
, and
Jorge
,
J. A.
, pp.
117
126
.
11.
Shesh
,
A.
, and
Chen
,
B.
, 2004, “
SMARTPAPER: An Interactive and User Friendly Sketching System
,”
Comput. Graph. Forum
1067-7055,
23
(
3
), pp.
301
310
.
12.
Farrugia
,
P. J.
,
Borg
,
J. C.
,
Camilleri
,
K. P.
,
Spiteri
,
C.
, and
Bartolo
,
A.
, 2004, “
A Cameraphone-Based Approach for the Generation of 3D Models from Paper Sketches
,” in
Proc. Sketch-Based Interfaces and Modeling 2004
, edited by
Hughes
,
J. F.
, and
Jorge
,
J. A.
, pp.
33
42
.
13.
Varley
,
P. A. C.
, 2003, “
Automatic Creation of Boundary-Representation Models from Single Line Drawings
,” PhD Thesis, Cardiff University.
14.
Varley
,
P. A. C.
,
Suzuki
,
H.
, and
Martin
,
R. R.
, 2004, “
Interpreting Line Drawings of Objects with K-Junctions
,” in
Proc. Geometric Modeling and Processing
, ed.
Hu
,
S.-M.
,
Pottmann
,
H.
,
IEEE
, Los Alamitos, CA, USA, pp.
249
358
.
15.
Clowes
,
M. B.
, 1970, “
On Seeing Things
,”
Artif. Intell.
0004-3702,
2
, pp.
79
116
.
16.
Huffman
,
D. A.
, 1971, “
Impossible Objects as Nonsense Sentences
,”
Machine Intelligence
,
6
,
B.
Meltzer
and
D.
Michie
, Eds.,
Edinburgh U. Press
, Edinburgh, UK, 1971.
17.
Guzman
,
A.
, 1968, “
Decomposition of a Visual Scene into Three-Dimensional Bodies
,”
Proc. AFIPS Fall Joint Computer Conference
,
33
, pp.
291
304
.
18.
Varley
,
P. A. C.
, and
Martin
,
R. R.
, 2001, “
The Junction Catalogue for Labelling Line Drawings of Polyhedra with Tetrahedral Vertices
,”
Int. J. Shape Model.
0218-6543,
7
(
1
), pp.
23
44
, World Scientific, Singapore.
19.
Varley
,
P. A. C.
,
Martin
,
R. R.
, and
Suzuki
,
H.
, “
Frontal Geometry of Engineering Objects: Is Line Labelling Necessary?
,”
Comput.-Aided Des.
0010-4485, (to be published).
20.
Malik
,
J.
, 1987, “
Interpreting Line Drawings of Curved Objects
,”
Int. J. Comput. Vis.
0920-5691,
1
, pp.
73
103
.
21.
Huffman
,
D. A.
, 1977, “
Realizable Configurations of Lines in Pictures of Polyhedra
,” in
Machine Intelligence 8
, edited by
Elcock
,
E. W.
, and
Michie
,
D.
, pp.
493
509
,
Ellis Horwood
, Chichester, UK.
22.
Kanatani
,
K.
, 1990, “
Group-Theoretical Methods in Image Understanding
,”
Number 20 in Springer Series in Information Sciences
,
Springer-Verlag
, Berlin.
23.
Varley
,
P. A. C.
, and
Martin
,
R. R.
, 2003, “
Deterministic and Probabilistic Approaches to Labelling Line Drawings of Engineering Objects
,”
Int. J. Shape Model.
0218-6543,
9
(
1
), pp.
79
99
, World Scientific, Singapore.
24.
Kittler
,
J.
, and
Hancock
,
E. R.
, 1989, “
Combining Evidence in Probabilistic Relaxation
,”
Int. J. Pattern Recognit. Artif. Intell.
0218-0014,
3
, pp.
29
52
.
25.
Lipson
,
H.
, and
Shpitalni
,
M.
, 1996, “
Optimization-based Reconstruction of a 3D Object from a Single Freehand Line Drawing
,”
Comput. Aided Geom. Des.
0167-8396,
28
(
8
), pp.
651
663
.
26.
Bauer
,
L.
, 1971, “
Elimination with Weighted Row Combinations for Solving Linear Equations and Least Squares Problems
,” in
Handbook for Automatic Computation II, Linear Algebra
, eds.
Wilkinson
,
J. H.
, and
Reinsch
,
C.
,
Springer-Verlag
.
27.
Lipson
,
H.
, 1998, “
Computer Aided 3D Sketching for Conceptual Design
,” PhD Thesis, Technion-Israel Institute for Technology, Haifa.
28.
Perkins
,
D. N.
, 1968, “
Cubic Corners
,” Quarterly Progress Report 89,
207
214
,
MIT Research Laboratory of Electronics
.
29.
Lamb
,
D.
, and
Bandopadhay
,
A.
, 1990, “
Interpreting a 3D Object From a Rough 2D Line Drawing
,” in
Proc. First IEEE Conference on Visualization
ed.
Kaufman
,
A. E.
,
59
66
, IEEE.
30.
Varley
,
P. A. C.
, 2003, “
Sketches of Polyhedral Solids
,” http://ralph.cs.cf.ac.uk/Data/Sketch.htmlhttp://ralph.cs.cf.ac.uk/Data/Sketch.html.
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