## Dynamic approximation of complex graphical constraints by linear constraints (2002)

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Venue: | In Proceedings of the Fifteenth ACM Symposium on User Interface Software and Technology |

Citations: | 8 - 4 self |

### BibTeX

@INPROCEEDINGS{Hurst02dynamicapproximation,

author = {Nathan Hurst and Kim Marriott and Peter Moulder},

title = {Dynamic approximation of complex graphical constraints by linear constraints},

booktitle = {In Proceedings of the Fifteenth ACM Symposium on User Interface Software and Technology},

year = {2002},

pages = {191--200},

publisher = {ACM Press}

}

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### Abstract

Current constraint solving techniques for interactive graphical applications cannot satisfactorily handle constraints such as non-overlap, or containment within non-convex shapes or shapes with smooth edges. We present a generic new technique for efficiently handling such kinds of constraints based on trust regions and linear arithmetic constraint solving. Our approach is to model these more complex constraints by a dynamically changing conjunction of linear constraints. At each stage, these give a local approximation to the complex constraints. During direct manipulation, linear constraints in the current local approximation can become active indicating that the current solution is on the boundary of the trust region for the approximation. The associated complex constraint is notified and it may choose to modify the current linear approximation. Empirical evaluation demonstrates that it is possible to (re-)solve systems of linear constraints that are dynamically approximating complex constraints such as non-overlap sufficiently quickly to support direct manipulation in interactive graphical applications. KEYWORDS: Constraint-solving, direct manipulation, trust regions, linearization of constraints, non-overlap, containment.

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27 |
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Citation Context ...on linear arithmetic constraint solving. Simplex-based algorithms for incremental solving of conjunctions of linear arithmetic inequality constraints are very efficient and reasonably well understood =-=[3, 11]-=-. However, such solvers cannot directly handle the above sort of constraints because when couched in terms of linear constraints they are inherently disjunctive in nature. Our key idea is very simple:... |

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Citation Context ... of these techniques support the kind of complex multi-way constraints, such as non-overlap, considered here. Non-overlap constraints have been considered by Baraff [1] and Harada, Witkin, and Baraff =-=[6]-=-, who use a specialised force based approach, modelling the non-overlap constraint between objects by a repulsion between them if they touch. Our approach is technically quite different because it rel... |

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(Show Context)
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(Show Context)
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