H. Lamure and D. Michelucci. Solving geometric constraints by homotopy. IEEE Trans. Vis. Comp. Graph., 2:28--34, 1996. Home/Search Document Details and Download
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Automatic Reasoning for Design Under Geometric Constraints - Shpitalni, Lipson (Correct)
....that reveals the topological relationships among the geometrical entities. Constraint problems are traditionally solved using a numeric approach, whereby geometrical constraints are translated into general algebraic expressions solved using iterative methods, such as Newton Raphson or homotopy [7]. However, despite their generality, numerical solvers often prove to be inadequate for large sets of non linear equations and rely to a great extent on the quality of the initial sketch. Numeric solvers are also unable to explore the solution space and provide almost no information upon failure. ....
Lamure H., Michelucci D., 1996, Solving geometric constraints by homotopy, IEEE Transactions on Visualization and Computer Graphics, 2(1): 28-34.
Boundary Representation Deformation in Parametric Solid.. - Raghothama, Shapiro (1998) (2 citations) (Correct)
....including shape optimization, tolerancing, and constraint solving. For example, some heuristic methods proposed in [6] for identifying the correct solutions in constraint solving resemble the necessary conditions implied by our definitions, and the use of homotopy was also proposed in [19]. The principle of continuity is stated in terms of a particular representation scheme for solids. The same principle of continuity could be used to develop notions of parametric families with respect to other representation schemes. For example, it may be feasible to define a parametric family ....
H. Lamure and D. Michelucci. Solving geometric constraints by homotopy. In 3rd ACM Symposium on Solid Modeling and Applications, Salt Lake City, Utah, May, 1995.
Applying Homotopy to Surface-Surface Intersections - Thompson (1997) (Correct)
....the roots of some H(x, #) #f(x) 1 #)g(x) as we changed our artificial parameter # from 0 to 1. This is shown in Figure 2. The top view provides a clear picture of the paths that the roots follow as the equation is changed. This technique has been shown to be more stable than Newton s method [LM95]. It tracks all of the roots of a function, not just one, like Newton s method. This can be a problem, however, since the roots to be tracked can be complex numbers and have paths that diverge, bifurcate, or lead to undesired solutions (such as complex values for variables that must be real valued ....
Herve Lamure and Dominique Michelucci. Solving geometric constraints by homotopy. In Proceedings of ACM Solid Modeling Symposium. ACM, 1995.
Qualitative Study of Geometric Constraints - Lamure, Michelucc (1997) (3 citations) Self-citation (Lamure) (Correct)
....or Grobner Bases [AM95] Due to their exponential running time, they can be used only for small systems. Numerical methods typically improve the initial and rough guess interactively provided by the user during the sketching stage, by using some Newton iterations [AM95] or the homotopy method [LM96] which has a more intuitive convergence. Decomposition methods reduce constraint systems into basic problems, the solutions of which are then stuck back together (to quote a few: Owe91, VSR92, BFH 95, But79] In 2D basic problems are triangles: the relative location of their 3 vertices are ....
H. Lamure and D. Michelucci. Solving geometric constraints by homotopy. IEEE Trans. Visualization and Comp. Graphics, 2(1):28--34, 1996.
Tolerances in Geometric Constraint Problems - Wallner, Schröcker, Hu (Correct)
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H. Lamure and D. Michelucci. Solving geometric constraints by homotopy. IEEE Trans. Vis. Comp. Graph., 2:28--34, 1996.
Constraint Solver - Jianjun Oung Of (Correct)
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Lamure H. and Michelucci D. Solving geometric constraints by homotopy. IEEE Transaction on Visualization and Computer Graphics, 2:22--34, 1996.
Geometric Constraint Satisfaction by Generalized Degrees of Freedom .. - Pae (1997) (Correct)
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Lamure, H., Michelucci, D. `Solving geometric constraints by homotopy' IEEE Transaction on Visualization and Computer Graphics' Vol 2(1996) pp 22-34
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