doi:10.1016/j.cag.2006.01.027
Copyright © 2006 Elsevier Ltd All rights reserved.
Reconstruction of 3D curvilinear wire-frame from three orthographic views
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Jie-Hui Gonga, b, 
, 
, Gui-Fang Zhangc, Hui Zhangb and Jia-Guang Suna, b
aDepartment of Computer Science and Technology, Tsinghua University, Beijing 100084, China
bSchool of Software, Tsinghua University, Beijing 100084, China
cSchool of Sciences, Beijing Forestry University, Beijing 100083, China
Available online 2 March 2006.
Abstract
The reconstruction of 3D objects from 2D orthographic views is very important for the maintenance and continued development of existing product designs. An efficient method for generating 3D curvilinear wire-frames from three orthographic views is presented, which is the pivotal stage of solid reconstruction by wire-frame-oriented approaches. By unifying the recovery of spatial conics without restrictions on their positions, our method can improve the efficiency and reliability of curvilinear wire-frame reconstruction. A projection matching algorithm is proposed to efficiently reveal all match projections according to the projective properties of spatial edges. Furthermore, a four-point method, which is based on the rational Bézier form of conics, is proposed to uniformly generate various types of conics in arbitrary positions. Several examples are provided.
Keywords: Reconstruction; Curvilinear wire-frame; Orthographic views
Fig. 1. e is a conic edge; Lf, Ls, and Lt are projected images of e in front view, side view, and top view; Bf, Bs, and Bt are match bounding boxes of the projections.
Fig. 2. Corresponding examples of different types of 3D linear edges in Table 1.
Fig. 3. Corresponding examples of different types of 3D conic edges in Table 2.
Fig. 4. Tag for projections in three views.
Fig. 5. Decision trees: (a) for front-view-entry processing; (b) for side-view-entry processing; and (c) for top-view-entry processing. (fl: front-view link set, sl: side-view link set, tl: top-view link set; fn: front-view node set, sn: side-view node set, tn: top-view node set; PX: linear link parallel to x-axis, PY: linear link parallel to y-axis, PZ: linear link parallel to z-axis, SL: slanting linear link, CO: conic link; MB: match bounding boxes.)
Fig. 6. Rational Bézier form of conics: (a) P0, P1, and P2 are control points of conic c; (b) S is the shoulder point of conic c.
Fig. 7. Splitting a rational Bézier conic arc at its shoulder point [19].
Fig. 8. Projection of a spatial conic: (a) under non-degenerate parallel projection; (b) under degenerate parallel projection.
Fig. 9. Match types of projected conics (lines): (a) three projected conics under non-degenerate parallel projections; (b) two projected conics with one projected line under degenerate parallel projection; and (c) one projected conic with two projected lines under degenerate parallel projections.
Fig. 10. An example is bounded by cylindric surfaces aligned with its natural axes: (a) the one-to-one correspondence between projected entities in the three views does not hold because of the self-alignment; (b) the reconstructed wire-frame model includes 54 vertices and 81 edges.
Fig. 11. An example is bounded by several incomplete cylinders: (a) the three-view drawing includes some circular arcs sweeping various angles; (b) the wire-frame model with 54 vertices and 77 edges is generated.
Fig. 12. The object is bounded by three types of quadric surfaces: the cylindrical, the conical, and the elliptical–cylindrical: (a) the input drawing is composed of straight lines, circles, circular arcs, and ellipses; (b) the wire-frame containing 46 vertices and 69 edges is constructed.
Fig. 13. The components of the object are coaxially nested cylinders, slanting cylinders, and an array of cylinders: (a) the input drawing is composed of straight lines, circles, circular arcs, and elliptic arcs; (b) the generated wire-frame model consists of 129 vertices and 200 edges.
Table 1.
Classification of 3D linear edges
Table 2.
Classification of 3D conic edges
Corresponding author. Tel.: +86 10 6279 5459; fax: +86 10 6279 5460.
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