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

....in the plane the neighboring surfaces around the modified contacts. The method, tested in the context of an interactive graphical manipulator, is very efficient and independent from the deformation mechanism. 1 Introduction For about three decades, boundary representations (b reps) [24, 18, 9] have been primarily used in the design of mechanical parts. In these applications, the models are usually not built once and for all, but undergo many modifications to account for new design constraints [29] Therefore, two complementary approaches to b rep modification using model parameters ....

C. M. Hoffmann. Geometric and Solid Modeling: An Introduction. Morgan Kaufmann, 1989. 338 pp.

....that was A(Open Set) ming in Figure 6. A includes the line segment. a) b) c) and thus B = T. B=T D 6o 7. Return A = the area of B Except for Step 1, all of the above steps are standard geometric operations, and descriptions of them can be found in geometric modeling books such as [4]. However, Step 1 is more problematic. It involves computing A(O,C) whose definition is similar to the offset operation found in popular geometric kernels, but with an important difference. A(O,C) is set of points Figure 7: A correct way to compute B for part shown in Figure 6 that are less ....

C. M. Hoffmann. Geometric and Solid Modeling: An Introduction, Morgan Kaufman Publishers, 1989.

....with Q. Algorithms based on arbitrary decisions on approximate data may produce invalid solid representations like in figure 1(b) where a dangling edge is created. Related Work A number of publications have addressed the geometric robustness problem. An overview can be found, for instance, in [12][13] In [9] 23] 32] and [33] precise computation is applied. Exact numbers (e.g. bounded or unbounded rational numbers, exact algebraic numbers or space grids) are used. Because no numerical error is introduced, the robustness of the algorithm is guaranteed. The approach is based on the ....

Hoffmann, C. M. Geometric and Solid Modeling: An Introduction. Morgan Kaufmann Publishers, 1989, ch. 4. 20

....base points, the implicit equation does not belong to the ideal I but to the saturated ideal of I by the ideal dening the base points. So, in this case, we need to compute this saturated ideal and a Gr#bner base of it to obtain the implicit equation. This method can be very slow in practice (see [21], 7] The second method for computing the implicit equation consists in computing a classical projective resultant of the polynomials p0 Gamma xp3 ; p1 Gamma yp3 ; p2 Gamma zp3 (see [10] 11] but this method failed in the presence of base points. In [8] and [5] perturbation techniques are ....

Hoffmann, C. M. Geometric and solid modeling : an introduction. Morgan Kaufmann publishers, Inc., 1989.

....over the alternative formats is the increased expressiveness of the vertex and edge labels available in the graphs. We believe that these labels will allow graph based model comparisons to be more semantically relevant than those using other types of graphs. The boundary representation (BRep) [23] essentially consists of a set of edges and a set of faces used by the solid modeler to describe the shape of the model in 3 dimensional space. An MSG for a solid model is defined as a labeled graph, # , where each face . is represented as a vertex D 2 , with attributes that ....

Christopher M. Hoffmann. Geometric and Solid Modeling: An Introduction. Morgan Kaufmann Publishers, Inc., California, USA, 1989.

....a Model Signature Graph (MSG) an example of which is shown in Figure 4. The MSG is constructed from the BRep of a solid model in a manner similar to that by Wysk et al. 20] and the Attributed Adjacency Graph (AAG) structures used to perform Feature Recognition from solid models [12] The BRep [10] essentially consists of a set of edges and a set of faces used by the solid modeler to describe the shape of the model in 3 dimensional space. A MSG for a solid model b is defined as a labeled graph, c edgf7 ihkj , where each face lnm b is represented as a vertex opmnf , with attributes ....

Christopher M. Hoffmann. Geometric and Solid Modeling: An Introduction. Morgan Kaufmann Publishers, Inc., California, USA, 1989.

....in the sense that the mathematical foundations and data structures used to define the object should leave nothing open for interpretation by users. A rendering of the representation should make it easy and straightforward to understand the geometric and topological structure. Solid modeling [Hof89, Man88] has found applications in engineering design, scientific visualization, animation, computer vision, and CAD CAM [RR92] Since its inception over 30 years ago, many different approaches to solid modeling have been developed. In this section we shall first give a short history of the field ....

C. M. Hoffmann. Geometric and Solid Modeling: An Introduction. Morgan Kaufmann, 1989.

....this problem can sometimes be circumvented by introducing some auxiliary polynomials into the Grobner system [12, 10] Nonetheless, Grobner bases are known to be very slow in implicitizing bicubic patches. Several other procedures have been devised to implicitize surfaces with base points [2, 9, 15, 16]. We don t review those methods here, but observe that those methods are generally more complicated than Dixon s method. Furthermore, base points are not arare occurrence; most of the teapot patches have numerous base points. This paper presents a fundamentally new procedure for implicitizing ....

....relationship between base points and degree becomes more complicated when considering base points with higher multiplicity [3, 13] Second, if base points exist, Dixon s resultant vanishes identically. To implicitize surfaces which contain base points, more complicated methods have been devised [2, 9, 15, 16] such as the method of undetermined coefficients, successive elimination, perturbations, and customized resultants. In general, these methods are much more complicated in the presence of base points. By contrast, the implicitization approach in this paper simplifies in the case of basepoints. In ....

Hoffmann, Christoph. Geometric and Solid Modeling: An Introduction. Morgan Kaufmann, 1989.

....open or closed halfspaces by a finite number of unions and intersections. This includes sets with dangling edges or faces, open or closed boundaries, etc. Other work. Considerable research effort has been directed at improving the numerical reliability of geometric algorithms; for surveys see [5,13,14,20]. One approach is to analyze the effect of rounding errors that result from floating point arithmetic [6,26,28] A second approach is to use software exact arithmetic for the evaluation of geometric predicates; to reduce performance cost, various researchers have suggested adaptive precision ....

....on polyhedral solids, as well as affine transformations such as rotation and translation. The design described here uses many ideas from Sugihara and Iri [27] though the rounding algorithm is different. The discussion in this section assumes general familiarity with polyhedral modelers [13,19]; only differences resulting from the use of integer arithmetic are highlighted. The discussion is relatively informal; the appendix contains technical details. 2.1 Coordinate data Face plane coordinates are the primary geometric representation of a polyhedral solid. A boolean operation on ....

[Article contains additional citation context not shown here]

C. Hoffmann, Geometric and Solid Modeling: an Introduction, Morgan Kauffmann, 1989.

....engineers are used to the limitations of physical devices, and then they considered that, anyhow, it was impossible to do otherwise. However, today, CADCAM engineers are more and more exasperated by this robustness lack, and robustness has become a key issue in CADCAM. From 1989 on, C. Hoffmann [Hof89] devoted in his book a comprehensive chapter to the robustness issue, studying examples of inaccuracy, pointing out the causes ( The difficulty seems to be rooted in the interaction of approximate numerical and exact symbolic data ) and proposing approaches like the quest for consistency or the ....

....c L d and so on, thus by exchanging vertices in order to obtain: ab cd = ab dc = ba cd = ba dc. ffl Use numerical input data rather than derived (thus corrupted) numerical data. ffl Prefer non redundant data structures, to limit the probability of contradictions. Quoting C. Hoffmann [Hof89] Conceptually we view these heuristics as attempts to reduce the logical interdependence of decisions that are based on numerical computations. M. Iri and K. Sugihara [IS89] have used this kind of approach for computing Voronoi s diagrams. They ensure that their program will never crash ....

[Article contains additional citation context not shown here]

C. M. Hoffmann. Geometric and Solid Modeling: An Introduction. Morgan Kaufmann, 1989.

....Note however, that it only has to be understood by the developer and not by the user. 2 Polyhedral Surfaces A boundary representation of a polyhedral surface consists of a set of vertices V , a set of edges E, a set of facets F , and an incidence relation on them. Introductions can be found in [14,20]. For a living example see Figure 1. 2 Fig. 1. Hammerhead, an orientable 2 manifold of 2560 vertices. This one is homeomorphic to a sphere. split facet(h,g) join facet(h) h g h join vertex(h) split vertex(h,g) h h g Fig. 2. Euler operator examples for polyhedral surfaces. The two ....

C. M. Hoffmann. Geometric and Solid Modeling -- An Introduction. Morgan Kaufmann, 1989. 31

....has a corresponding implicit representation and it is desirable to compute it. This process of converting from parametric to implicit is known 1 as implicitization. The implicit representation is useful for representing the object as a semi algebraic set and for surface intersections as shown in Hoffmann (1989) and Prakash Patriakalakis (1988) There are two known techniques for implicitization. Both these techniques reduce the problem of implicitizing rational surfaces to eliminating two variables from three parametric equations. The first technique involves the use of Elimination theory. In ....

....(1989) and Prakash Patriakalakis (1988) There are two known techniques for implicitization. Both these techniques reduce the problem of implicitizing rational surfaces to eliminating two variables from three parametric equations. The first technique involves the use of Elimination theory. In Hoffmann (1989) the two variables are eliminated in succession by using the Sylvester resultant for two equations. The resulting expression does not correspond to the resultant of three parametric equations and contains an extraneous factor, whose separation can be a time consuming task involving multivariate ....

[Article contains additional citation context not shown here]

Hoffmann, C. (1989). Geometric and Solid Modeling: An Introduction. Morgan Kaufmann Publishers Inc.

....lex 71.4 s 912.8 s s6 tot lex 5.7 s 55.0 s s7 tot lex 64.1 s 769.1 s Table 2 Timings of Walk vs. FGLM 7 Applications 7. 1 Implicitization in Computer Graphics In geometric modeling, the problem of converting parametrically defined varieties into their implicit form is of great importance [15]. The parametric representation of a surface is most suitable for rendering it on an output device. It is however ill suited for the computation of intersections, for which the implicit representation is more amenable. As mentioned in [9] the Grobner Walk should be an attractive tool for the ....

C. Hoffmann. Geometric and Solid Modeling: An Introduction. Morgan Kaufmann Publishers Inc., 1989.

....Background and Related Work 2.1 Constructive Solid Geometry (CSG) Constructive Solid Geometry (CSG) is a volumetric representation scheme for three dimensional solid geometric models. Solids are represented as a set theoretic boolean expression of primitive solid objects, of a simpler structure [8]. Regularized set boolean operations and motion operations are used to represent a composition of primitive geometric shapes. The standard primitives that are used in the CSG representation scheme are the parallelepiped or block, the triangular prism, the sphere, the cone, the cylinder, and the ....

....set boolean operations and motion operations are used to represent a composition of primitive geometric shapes. The standard primitives that are used in the CSG representation scheme are the parallelepiped or block, the triangular prism, the sphere, the cone, the cylinder, and the torus [8]. The set boolean operations that may be used are regularized union, regularized difference, and regularized intersection. The regularized boolean set operations are extensions of the typical boolean operations that prevent dangling edges and faces from resulting. A CSG representation of a solid ....

[Article contains additional citation context not shown here]

Christopher M. Hoffmann. Geometric and Solid Modeling: An Introduction. Morgan Kaufmann Publishers, Inc., California, USA, 1989.

....designing 3 D models, the great potential advantage of computer graphics is obvious, letting designers inspect their models from different viewpoints and at different scales and make fast modifications. We are interested in direct conceptual design of 3 D models. Constructive Solid Geometry (CSG) [Requicha80, Hoffmann89] is a well known representation scheme that represents 3 D solids by a graph whose leaves contain geometric primitives and whose nodes contain Boolean and affine operations. The arcs of the graph denote the fact that an operation uses an object as an argument. The native CSG modeling operations ....

Hoffmann, C., Geometric and Solid Modeling: an Introduction. Morgan Kaufmann, 1989.

.... se[17] 99999998430674944.000000 se[18] 999999984306749440.000000 se[19] 9999999980506447872.000000 se[20] 100000002004087734272.000000 se[21] 1000000020040877342720.000000 se[22] 9999999778196308361216.000000 se[23] 99999997781963083612160.000000 se[24] 1000000013848427855085568.000000 se[25]=10000000714945030854279168.000000 se[26] 100000002537764290115403776.000000 se[27] 1000000062271131048573140992.000000 se[28] 10000000622711310485731409920.000000 se[29] 100000001504746621987668885504.000000 se[30] 1000000015047466219876688855040.000000 ....

....se[16] 0.0000000000002328306276 se[17] 0.0000000000005820765961 se[18] 0.0000000000014551914361 se[19] 0.0000000000036379785903 se[20] 0.0000000000090949461504 se[21] 0.0000000000227373658096 se[22] 0.0000000000568434153914 se[23] 0.0000000001421085332742 se[24] 0. 0000000003552713401245 se[25]= 0.0000000008881783641890 se[26] 0.0000000022204458272057 se[27] 0.0000000055511146790366 se[28] 0.0000000138777869196360 se[29] 0.0000000346944659668225 se[30] 0.0000000867361649170562 se[31] 0.0000002168404193980678 se[32] 0.0000005421010200734599 se[33] 0.0000013552526070270687 se[34] ....

[Article contains additional citation context not shown here]

C. M. Hoffmann. Geometric and Solid Modeling: An Introduction. Morgan Kaufmann, San Mateo CA, 1989; 335 pages; ISBN 1-55860067 -1, 1989.

....subdivide X into cells of uniform classification against primitives and (2) combine the binary results of classifying these cells against the primitives according to the corresponding Boolean expression. CSG to boundary conversion algorithms are often based on such set membership classifications [Requicha85, Mantyla86, Hoffmann89, Rossignac86]. Subdivision typically involves computing intersections between the carrier of X (i.e. its supporting manifold [Rossignac98b] and the surfaces that bound the primitives. Classification may in general be expressed as a combination of binary values [Rossignac86, Rossignac89, Banerjee96] which ....

C. Hoffmann, Geometric and Solid Modeling: An introduction, Morgan Kaufmann, San Mateo, CA, 1989.

No context found.

C. M. Hoffmann. Geometric and Solid Modeling: An Introduction. Morgan Kaufmann, 1989.

No context found.

HOFFMANN, C. 1989. Geometric and Solid Modeling: An Introduction, Morgan Kaufmann.

No context found.

Hoffmann, C. M. Geometric and solid modeling : an introduction. Morgan Kaufmann publishers, Inc., 1989.

No context found.

Hoffmann, C. (1989), Geometric and Solid Modeling: An Introduction, Morgan Kaufmann, San Mateo, California.

No context found.

Christopher M. Hoffmann. Geometric and Solid Modeling: An Introduction. Morgan Kaufmann Publishers, Inc., California, USA, 1989.

No context found.

Hoffmann, C. (1989) Geometric and Solid Modeling: An Introduction, Morgan Kaufmann Publishers Inc..

No context found.

C. Hoffmann, Geometric and Solid Modeling: An introduction, Morgan Kaufmann, San Mateo, CA, 1989.

First 50 documents

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC