Steve Sistare. Interaction techniques in constraint-based geometric modeling. In Proceedings of Graphics Interface '91, pages 85--92, Calgary, Alberta, June 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....simulation continually updates the position of the nodes in the layout. Although they are not represented graphically, the forces on a node become apparent to users through observation and manipulation. CONCLUSIONS Constraint based techniques have been utilized in numerous drawing editors, e.g. [6, 8, 10, 13, 14], but they have so far enjoyed only limited success in this role. One reason for this apparent failure is the generality and complexity of most constraint based drawing editors: the constraint vocabularies have often been chosen for orthogonality, coverage, and tractability, but may not be ....

Steve Sistare. Interaction techniques in constraint-based geometric modeling. In Proceedings of Graphics Interface '91, pages 85--92, Calgary, Alberta, June 1991.

....and exploring toleranced behavior[24] Since the earliest interactive graphical systems[29] constraints have been used to aid in the manipulation of geometry. From the early systems, numerical techniques to solve these constraints have been employed. Modern constraint based systems, such as [4, 9, 19, 26], employ iterative numerical techniques. These non linear system solving techniques, like the techniques for physical simulation and constrained optimization, all rely on repeatedly setting up and solving systems of linear equations based on the derivatives of model functions. All of these ....

....For example, a system might only gather variables which are likely to change on the current iteration and only solve the subset of constraints which act on these variables. A related technique is to partition the constraint problem into several smaller problems, which is examined extensively by [26]. 5 IMPLEMENTATION Our efforts to build general purpose Snap Together Mathematics tools began with our original efforts to construct interactive systems[33] Our early implementations are discussed in [12] Experience using these tools has caused them to evolve into what has been described here. ....

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Steven Sistare. Interaction techniques in constraint-based geometric modeling. In Proceedings Graphics Interface '91, pages 85--92, June 1991.

....the ability to trade precision for performance by adjusting tolerance parameters. While there are techniques, such as singular value decomposition, which better handle singular and near singular matrices, these techniques do not exploit sparsity as easily nor permit the performance adjustments. In [22], the tradeoffs between SVD and conjugate gradient are explored more closely. 5 Scalability and Performance Performance is important to interactive graphical applications so they can achieve the appearance of continuous motion. In a conventional drawing program this can be achieved easily as ....

....However, because the matrices which arise in graphical constraint problems are typically sparse, the complexity can be lower. Because each constraint only affects at most a small constant number of objects, the matrices only have O(n) entries in them, and can therefore be solved in O(n 2 ) time[22]. For certain classes of constraint problems, the linear system can be solved in linear time[24] To maintain interactive performance, it is critical to reduce the complexity of solving algorithm by exploiting the sparsity of the systems which are solved. However, without severely restricting the ....

[Article contains additional citation context not shown here]

Steven Sistare. Interaction techniques in constraint-based geometric modeling. In Proceedings Graphics Interface '91, pages 85--92, June 1991.

....systems of non linear algebraic equations must be solved from arbitrary starting points. While this problem is intractable[11] systems can usually operate by limiting the class of constraints which can be handled (as done by [6, 14] or using temperamental numerical techniques (as done by [9, 12]) If no configuration is found that satisfies the constraints, it can be difficult to determine whether none exists or if the solver was just unable to find one. If no solution exists, the conflicts must be diagnosed and debugged. If the solver does find a new configuration, it must help the user ....

....must be able to edit this structural information as well as the geometry. Although textual languages for describing constraints, such as in [9, 14] are easy to edit, they are distinct from the drawing and can be difficult to connect to their corresponding places in the model. Visual representations[5, 12] superimpose symbols for constraints directly on the model. Unfortunately, devising clear visual representations is challenging and editing such representations is often difficult. When differential constraints are used, the continuousmotion and ability for users to experiment with models can ....

Steven Sistare. Interaction techniques in constraintbased geometric modeling. In Proceedings Graphics Interface '91, pages 85--92, June 1991.

....[24] these relaxation or penalty methods are described, including a discussion of why they are not good. such as singular value decomposition, which better handle singular and near singular matrices, these techniques do not exploit sparsity as easily nor permit the performance adjustments. In [26], the tradeoffs between SVD and conjugate gradient are explored more closely. 5 Scalability and Performance Performance is important to interactive graphical applications so they can achieve the appearance of continuous motion. In a conventional drawing program this can be achieved easily as ....

....number of objects, its function can only depend on a small constant number of variables so the corresponding row of the matrix can only have a similarly small number of entries. Therefore, the matrices only have O(n) entries in them, and can the linear systems can be solved in O(n 2 ) time[26]. For certain classes of constraint problems, the linear system can be solved in linear time[28] To maintain interactive performance, it is critical to reduce the complexity of solving algorithm by exploiting the sparsity of the systems which are solved. However, without severely restricting the ....

[Article contains additional citation context not shown here]

Steven Sistare. Interaction techniques in constraint-based geometric modeling. In Proceedings Graphics Interface '91, pages 85--92, June 1991.

....simulation continually updates the position of the nodes in the layout. Although they are not represented graphically, the forces on a node become apparent to users through observation and manipulation. CONCLUSIONS Constraint based techniques have been utilized in numerous drawing editors, e.g. [6, 8, 10, 13, 14], but they have so far enjoyed only limited success in this role. One reason for this apparent failure is the generality and complexity of most constraint based drawing editors: the constraint vocabularies have often been chosen for orthogonality, coverage, and tractability, but may not be ....

Steve Sistare. Interaction techniques in constraintbased geometric modeling. In Proceedings of Graphics Interface '91, pages 85--92, Calgary, Alberta, June 1991.

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