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RESEARCH PAPERS

Priority-Based Geometric Constraint Satisfaction

[+] Author and Article Information
Jiantao Pu

Imaging Research Laboratory, The University of Pittsburgh, Pittsburgh, PA 15213jip13@pitt.eduPurdue Research and Education Center for Information System in Engineering, Purdue University, West Lafayette, IN 47907jip13@pitt.edu

Karthik Ramani

Imaging Research Laboratory, The University of Pittsburgh, Pittsburgh, PA 15213ramani@purdue.eduPurdue Research and Education Center for Information System in Engineering, Purdue University, West Lafayette, IN 47907ramani@purdue.edu

J. Comput. Inf. Sci. Eng 7(4), 322-329 (Jun 14, 2007) (8 pages) doi:10.1115/1.2795301 History: Received June 13, 2006; Revised June 14, 2007

Abstract

A well-constrained geometric system seldom occurs in practice, especially at the sketch-based initial conceptual design stage. Usually, it is either under- or overconstrained because design is a progressive process and it is difficult for a designer to specify all involved constraints in a consistent way. This paper presents a priority-based graph-reduction solution, in which each constraint is assigned with a priority to guide the reduction of a geometric constraint graph. The advantage of this method lies in its ability to find the optimal solutions to a geometric constraint system automatically, without requiring interactive intervention from users.

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Figures

Figure 1

An arc (a) can be equally represented by two line segments and an angle constraint (b)

Figure 2

GCG representation: (b) is the GCG of (a)

Figure 3

Four types of CPs between geometric primitives: the node represents a geometric entity and its value is the DOF of the entity; the edge represents the constraint between two entities and its value is the DOF of the constraint

Figure 4

A geometric constraint system whose DC is 3: The relative position of the triangle S1S2S3 with respect to triangle P1P2P3 is determined by the positions of three primitives, i.e., points P1, P2, and P3

Figure 5

A graph-reduction process [(a)–(q)] using the interface-open and reconstruction strategy. The detailed explanation is presented in Sec. 3.

Figure 6

The reduction trees of the example in Fig. 5: (a) is the reduction tree comprised of primitives p1, l6, p6, l5, and p5, (b) is the reduction tree comprised of primitives p4, l4, p5, l3, and p3, and (c) is the reduction tree comprised of primitives p2, l2, p3, l1, p1, and p5

Figure 7

Example of ill-constrained systems: (a) This triangle is underconstrained because there are not enough constraints for a unique solution. (b) Here, it is overconstrained because there are too many constraints for a unique triangle.

Figure 8

(a) is the PGCG of the example in Fig.  77, is the PGCG of the example in Fig. 7

Figure 9

Geometric entity reconstruction process [(a)–(h)]. Detailed explanation is presented in Sec. 5.

Figure 10

An example using our geometric constraint solver. Changing the parameters will automatically lead to the results that satisfy the specified constraints and the implied constraints.

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