C.M. Hooemann. Geometric and Solid Modeling. Morgan Kaufmann, 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....now become one of the major issue in the eld of computational geometry [4, chap. 10] Some attempts have been made to design geometric algorithms such that robust implementations can be obtained using only the inaccurate but fast arithmetic provided by AEoating point processors (see for examples [17, 18, 15, 13, 10, 11, 8]) Such solutions, although very useful in some domains like solid modeling and CSG applications, are still painful to design and known only for a few geometric problems. Another approach is to turn to exact arithmetic which makes robustness a non issue. The use of exact arithmetic has been ....

C. Hooemann. Geometric and Solid Modeling. Morgan Kaufmann, San Mateo, California, 1989.

.... through a number of concrete applications in the forward and inverse kinematics of robots and mechanisms as well as the computation of their motion plans [Can88, RR95] the geometric structure of molecules [BMB94, EM96b] geometric and solid modeling, graphics, and computer aided design [BGW88, Hof89, MD95], as well as quantier elimination [CG84, Ren92, Can93, BPR94] and the solution of systems of inequalities [GV87] This survey is organized as follows. The next section sketches the basic notions of elimination theory, starting with notation, then the classical theory and, nally, discusses sparse ....

C.M. Hooemann. Geometric and Solid Modeling. Morgan Kaufmann, 1989.

....geometry (for a discussion, see [C 96, chap. 10] Some attempts have been made to design geometric algorithms such that robust implementations can be obtained using only the inaccurate but fast arithmetic provided by AEoating point processors (see for examples [SI89, SI94, Mil89, LM90, Hof89, HHK88, For92] Such solutions, although very useful in some domains like solid modeling and CSG applications, are diOEcult to design and known only for a few geometric problems. Another approach is to turn to exact arithmetic which makes robustness a non issue. The use of exact arithmetic has ....

C. Hooemann. Geometric and Solid Modeling. Morgan Kaufmann, San Mateo, California, 1989.

.... through a number of concrete applications in the forward and inverse kinematics of robots and mechanisms as well as the computation of their motion plans [Can88, RR95] the geometric structure of molecules [BMB94, EM96b] geometric and solid modeling, graphics, and computer aided design [BGW88, Hof89, MD95], as well as quantier elimination [Ren92, Can93, BPR97] and the solution of systems of inequalities [GV88] A linear algebra approach using resultant matrices is also present in a series of articles exploiting a dioeerent model of sparseness, namely Straight Line Programs; see, e.g. GHMP95, ....

C.M. Hooemann. Geometric and Solid Modeling. Morgan Kaufmann, 1989.

.... through a number of concrete applications in the forward and inverse kinematics of robots and mechanisms as well as the computation of their motion plans [Can88, RR95] the geometric structure of molecules [BMB94, EM96b] geometric and solid modeling, graphics, and computer aided design [BGW88, Hof89, MD95] as well as quantier elimination [CG84, Ren92, Can93, BPR94] and the solution of systems of inequalities [GV87] This survey is organized as follows. The next section sketches the basic notions of elimination theory, starting with notation, then the classical theory and, nally, discusses ....

C.M. Hooemann. Geometric and Solid Modeling. Morgan Kaufmann, 1989.

....an approximate GCD is the exact GCD of the perturbations of the input polynomials, within some prescribed tolerance. The question becomes relevant whenever laboratory measurements are involved, as in graphics, modeling, robotics, and control theory, where noise corrupts the input [SS87, Hof89, Mer90, Man94, CGTW95] It can also be seen as a stepping stone towards problems on polynomial systems, where the given data is characterized by limited accuracy. Consider the following pair of polynomials from [CGTW95] Their exact GCD is 1 but, under some tolerance ffl 0, there is a quadratic ....

.... and surfaces, of distances between points and surfaces, of birational maps, spline and nite element approximations of real surfaces, mesh generation, constraint based sketching, and data tting have all bene ted from this cross fertilization [SS87, Man94, Far88, BE97, Far97] The monograph [Hof89] provides a very appropriate introduction. Representation. For dioeerent problems, dioeerent representations of curves and surfaces may be suitable. The need arises to be able to convert between rational parametric and implicit representations. The former gives every point coordinate as a ....

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C.M. Hooemann. Geometric and Solid Modeling. Morgan Kaufmann, 1989.

....our solid based approach is eoeective even when the input polygons intersect, overlap, are wrongly oriented, have T junctions, or are unconnected. 1 Introduction We de ne a set of polygons in R 3 to be consistent if the union of the polygons is a closed 2 manifold (see Hooemann s book [12] for a de nition) in which each polygon is oriented with its normal pointing away from the interior of the volume enclosed by the manifold. We say that a consistent set of polygons is a correct representation of a polyhedral solid object in R 3 if the manifold formed by the polygons is ....

....In Section 6, we discuss techniques that we plan to implement to overcome these limitations. The nal section is a brief conclusion. 2 Previous Work In the computational geometry and solid modeling communities, there has been a lot of work on the related problem of robust geometric computing [7, 12, 13, 23, 25, 26, 29, 31]. These techniques are not applicable to our problem since they attempt to avoid errors caused by numerical imprecision and cannot clean up already incorrect data. It has been noted in the literature that there are currently no robust techniques to solve the solid reconstruction problem [10, 17] ....

C. Hooemann. Geometric and Solid Modeling. Morgan Kaufmann, San Mateo, California, 1989.

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C.M. Hooemann. Geometric and Solid Modeling. Morgan Kaufmann, 1989.

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C.M. Hooemann. Geometric and Solid Modeling. Morgan Kaufmann, 1989.

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