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CAD and the Product Master Model
 In Computer Aided Design
, 1997
"... We develop an architecture for a product master model that federates CAD systems with downstream application processes for different feature views that are part of the design process. The architecture addresses especially the need to make persistent associations of design information with net shape ..."
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We develop an architecture for a product master model that federates CAD systems with downstream application processes for different feature views that are part of the design process. The architecture addresses especially the need to make persistent associations of design information with net shape elements. Moreover, the design respects the need of commercial CAD systems (and of downstream applications) to maintain proprietary information that must not be disclosed in the master model. Two case studies consider the requirements on the master model architecture, for geometric dimensioning and tolerancing, and for manufacturing process planning using NC machining. We discuss how to reconcile the associated feature views and how to update them under net shape redesign. The case studies indicate that many design changes that arise from these downstream views can be formalized by a welldefined problem on dimensional and geometric constraints. Supported in part by ONR Contract N0001496...
CONSTRAINTENABLED DESIGN INFORMATION REPRESENTATION FOR MECHANICAL PRODUCTS OVER THE INTERNET
, 2003
"... This dissertation was presented by ..."
Wellconstrained Completion and Decomposition for Underconstrained Geometric Constraint Problems
, 2005
"... Abstract. In this paper, we consider the optimal wellconstrained completion problem, that is, for an underconstrained geometric constraint problem, add automatically new constraints in such a way that the new geometric constraint problem G is wellconstrained and the set of equations need to be so ..."
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Abstract. In this paper, we consider the optimal wellconstrained completion problem, that is, for an underconstrained geometric constraint problem, add automatically new constraints in such a way that the new geometric constraint problem G is wellconstrained and the set of equations need to be solved simultaneously in order to solve G has the smallest size. We propose a polynomial time algorithm which gives a partial solution to the above problem.
On the Domain of Constructive Geometric Constraint Solving Techniques
 in SCCG ’01: Proceedings of the 17th Spring conference on Computer graphics
, 2001
"... We study the domain of two constructive geometric constraint solving techniques. Both deal with constraints represented by a geometric constraint graph. The rst technique analyses the graph bottomup, from the edges to the whole graph. The second technique analyses the graph topdown, from the whol ..."
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We study the domain of two constructive geometric constraint solving techniques. Both deal with constraints represented by a geometric constraint graph. The rst technique analyses the graph bottomup, from the edges to the whole graph. The second technique analyses the graph topdown, from the whole graph to the individual edges. We describe these techniques using abstract reduction systems which simpli es the study of their properties. We present an abstract description of the domain of each technique. Finally, we show that both techniques have the same domain, that is, they solve the same kind of problems de ned by geometric constraints.
Kinematic Chain Substitution for Geometric Constraint Solving
 In WSCG 98
, 1998
"... Assembly modelling is an important task within the design process for mechanical engineering. Constraintbased modelling is an adequate approach to this task. Kinematic mechanisms often have multiple interacting loops which are difficult to solve by a geometric constraint solver. In this paper, we i ..."
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Assembly modelling is an important task within the design process for mechanical engineering. Constraintbased modelling is an adequate approach to this task. Kinematic mechanisms often have multiple interacting loops which are difficult to solve by a geometric constraint solver. In this paper, we introduce kinematic chain substitution, which is an elegant method to solve loops. Kinematic chains are open paths of simply connected components in which  unlike rigid chains  relative mobility between their components is possible. For kinematic chain substitution, the chain between the first and last component is substituted temporarily with one arc, by eliminating the other components in between. Our algorithm, called Concatenate, calculates the relative mobility restriction between the first and last component of a kinematic chain with 3 components. By repeatedly applying Concatenate, a kinematic chain substitution for chains with any number of components is possible. The main appli...
Spatial Geometric Constraint Solving Based on kconnected Graph Decomposition
 Proc. of The 21st Annual ACM Symposium on Applied Computing
, 2006
"... We propose a geometric constraint solving method based on connectivity analysis in graph theory, which can be used to decompose a wellconstrained problem into some smaller ones if possible. We also show how to merge two rigid bodies if they share two or three geometric primitives in a biconnected o ..."
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We propose a geometric constraint solving method based on connectivity analysis in graph theory, which can be used to decompose a wellconstrained problem into some smaller ones if possible. We also show how to merge two rigid bodies if they share two or three geometric primitives in a biconnected or triconnected graph respectively. Based on this analysis, problems similar to the “double banana problem” could be easily detected.
Geometric constraint solving based on connectivity of graph
, 2003
"... We propose a geometric constraint solving method based on connectivity analysis in graph theory, which can be used to decompose a structurally wellconstrained problem in 2D into some smaller ones if possible. We also show how to merge two rigid bodies if they share two or three geometric primitives ..."
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We propose a geometric constraint solving method based on connectivity analysis in graph theory, which can be used to decompose a structurally wellconstrained problem in 2D into some smaller ones if possible. We also show how to merge two rigid bodies if they share two or three geometric primitives in a biconnected or triconnected graph respectively.
CONSTRAINTS FOR MODELLING COMPLEX OBJECTS
"... When complex scenes are modelled using measured data, such as mass data from laser scanners, the objects generated do not only have to fit the data, but also have to fulfill additional constraints, like incidence, distance, or angle relations. Weak primitives have been proposed as a means to automat ..."
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When complex scenes are modelled using measured data, such as mass data from laser scanners, the objects generated do not only have to fit the data, but also have to fulfill additional constraints, like incidence, distance, or angle relations. Weak primitives have been proposed as a means to automatically introduce larger numbers of constraints into the modelling process. In this article, several aspects of constraint modelling are discussed, in particular constraint graphs and maximum matchings, polynomial constraints and Gröbner bases, and linearization. The application to the problem of interactively modifying constrained geometries is shown. 1
Characterizing 1Dof HennebergI graphs with efficient configuration spaces
, 810
"... We define and study exact, efficient representations of realization spaces of a natural class of underconstrained 2D Euclidean Distance Constraint Systems(EDCS, Linkages, Frameworks) based on 1degreeoffreedom(dof) HennebergI graphs. Each representation corresponds to a choice of parameters and y ..."
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We define and study exact, efficient representations of realization spaces of a natural class of underconstrained 2D Euclidean Distance Constraint Systems(EDCS, Linkages, Frameworks) based on 1degreeoffreedom(dof) HennebergI graphs. Each representation corresponds to a choice of parameters and yields a different parametrized configuration space. Our notion of efficiency is based on the algebraic complexities of sampling the configuration space and of obtaining a realization from the sample (parametrized) configuration. Significantly, we give purely combinatorial characterizations that capture (i) the class of graphs that have efficient configuration spaces and (ii) the possible choices of representation parameters that yield efficient configuration spaces for a given graph. Our results automatically yield an efficient algorithm for sampling realizations, without missing extreme or boundary realizations. In addition, our results formally show that our definition of efficient configuration space is robust and that our characterizations are tight. We choose the class of 1dof HennebergI graphs in order to take the next step in a systematic and graded program of combinatorial characterizations of efficient configuration spaces. In particular, the results presented here are the first characterizations that go beyond graphs that have connected and convex configuration spaces.
NPHardness In Geometric Construction Problems With One Interval Parameter
"... this paper, we will show that even if we have only one interval parameter, the above problems are, in general, NPhard (i.e., crudely speaking, computationally infeasible), and unsolvable by rulerandcompass constructions. Before we proceed to exact formulations and proofs, we will briefly remind t ..."
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this paper, we will show that even if we have only one interval parameter, the above problems are, in general, NPhard (i.e., crudely speaking, computationally infeasible), and unsolvable by rulerandcompass constructions. Before we proceed to exact formulations and proofs, we will briefly remind the readers what NPhard means.