Hugues Hoppe, Tony DeRose, Tom Duchamp, Mark Halstead, Huber Jin, John McDonald, Jean Schweitzer, and Werner Stuetzle. Piecewise smooth surface reconsruction. In Computer Graphics Proceedings, Annual Conference Series, pages 295--302. ACM Siggraph, 1994.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....Often, only an approximate definition is required for the interior of the surface, whereas the boundary conditions may be significantly more restrictive. For example, it is often necessary to join several surfaces along their boundaries. Boundary subdivision rules lead to rules for sharp creases [8] and soft creases [3] In addition to specifying the boundary or crease curves, it is often desirable to be able to specify tangent planes on the boundary; existing subdivision schemes do not allow to control tangent plane behavior. The goal of this paper is to present two complete sets of ....

....rotational symmetry of the subdivision rules and applies only to the interior rules. Subdivision rules for Doo Sabin dual surfaces for the boundary were discussed by Doo [4] and Nasri [12, 13, 11] but only partial theoretical analysis was performed. Our work builds on the work of Hoppe et al. [8] and partially on the ideas of Nasri [14] To the best of our knowledge, the boundary subdivision rules proposed in work [8] are the only ones that result in provably C continuous surfaces (the analysis can be found in Schweitzer [19] However, these rules suffer from two problems: The ....

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Hugues Hoppe, Tony DeRose, Tom Duchamp, Mark Halstead, Huber Jin, John McDonald, Jean Schweitzer, and Werner Stuetzle. Piecewise smooth surface reconsruction. In Computer Graphics Proceedings, Annual Conference Series, pages 295--302. ACM Siggraph, 1994.

....or animate a given high resolution mesh hierarchical representations are necessary: we want to a#ect large scale smooth changes to the surface shape as easily as minute edits at the individual vertex level. While it is possible to build smoother approximations to the original mesh using patches [12], high frequency detail will be lost. This could be partially recovered through the use of displacement maps [15] but the management of arbitrary topology settings is di#cult in this approach. # dzorin gg.caltech.edu holst ama.caltech.edu # ps cs.caltech.edu Figure 1: Before the Armadillo ....

Hoppe, H., DeRose, T., Duchamp, T., Halstead, M., Jin, H., McDonald, J., Schweitzer, J., and Stuetzle, W. Piecewise Smooth Surface Reconsruction. In Computer Graphics Proceedings, Annual Conference Series, 295--302, 1994.

....# . The requirement is a formal way of saying that if some complex K is locally isomorphic to a k regular complex, then no matter how we tag complex K, it is locally isomorphic to a tagged k regular complex. Tagged complexes can be used to define schemes with creases such as the one described in [32], and to reduce other types of refinement rules (Catmull Clark, Doo Sabin) to refinement of simplicial complexes (Appendix A) Subdivision schemes. The most general definition of subdivision simply states that a subdivision scheme computes values at finer subdivision levels from the values at the ....

....of maximal order must be unique. The second condition of the corollary directly follows from Theorem 3.4. There are some interesting cases for which the assumptions of Corollary 3.5 are not satisfied; most notable exception are piecewise smooth schemes of the type described by H. Hoppe and others [32]. The assumption is easy to verify for piecewise polynomial schemes, as for such schemes Jacobians also can be expressed in polynomial bases, and the nondegeneracy assumption is reduced to checking independence of vectors of control values for the Jacobians. The conditions on D # and #S T ....

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H. Hoppe, T. DeRose, T. Duchamp, M. Halstead, H. Jin, J. McDonald, J. Schweitzer, and W. Stuetzle. Piecewise smooth surface reconsruction. In Computer Graphics Proceedings, Annual Conference Series, pages 295--302. ACM Siggraph, 1994. 272

....Our rules allow modeling surfaces with piecewise smooth boundaries and different types of corner vertices and prescribed normals on on the boundary or the interior. At the same time, only minimal changes are introduced to the basic Catmull Clark and Loop algorithms (with crease modifications of [7] and [3] We use a uniform approach to derive the desired subdivision rules, which can be applied to any stationary subdivision scheme. In this paper, we focus on the Loop and Catmull Clark subdivision schemes as schemes having the greatest practical importance. 2 Previous Work A number of ....

....noteable exception is the work of Schweitzer [14] and the recent work of Levin. Subdivision rules for Doo Sabin dual subdivision surfaces for the boundary were discussed by Doo [4] and Nasri [9, 10] but only partial theoretical analysis was performed. Our work builds on the work of Hoppe et al. [7] and partially on the ideas of Nasri [11] To the best of our knowledge, the subdivision rules proposed in work [7] are the only ones that result in provably C 1 continuous surfaces (the analysis can be found in Schweitzer [14] However, these rules suffer from two problems: the shape of ....

[Article contains additional citation context not shown here]

Hugues Hoppe, Tony DeRose, Tom Duchamp, Mark Halstead, Huber Jin, John McDonald, Jean Schweitzer, and Werner Stuetzle. Piecewise smooth surface reconsruction. In Computer Graphics Proceedings, Annual Conference Series, pages 295--302. ACM Siggraph, 1994.

.... the characteristic map [18] In the case of Loop s scheme the surface is globally C 2 except at the extraordinary vertices where it is only C 1 [22] For completeness we mention that one can develop appropriately modified stencils for boundaries and surface features such as creases and corners [10, 20, 2]. The scheme of Catmull and Clark generalizes bi cubic splines to arbitrary topology control meshes. In this case the initial polyhedron consists entirely of quadrilaterals. Subdivision proceeds as before by quadrisection, i.e. every face is replaced by four faces (see Figure 4, left) This time ....

HOPPE, H., DEROSE,T.,DUCHAMP,T.,HALSTEAD, M., JIN, H., MCDONALD, J., SCHWEITZER, J., AND STUETZLE, W. Piecewise Smooth Surface Reconsruction. In Computer Graphics Proceedings, Annual Conference Series, 295--302, 1994.

....of the mesh needs to provide control at a large scale, so that one can change the mesh in a broad, smooth manner, for example. Additionally designers will typically also want control over the minute features of the model (cf. Fig. 1) Smoother approximations can be built through the use of patches [15], though at the cost of loosing the high frequency details. Such detail can be reintroduced by combining patches with displacement maps [18] However, this is difficult to manage in the arbitrary topology setting and across a continuous range of scales and hardware resources. ....

....structure of the basic algorithm greatly facilitates the design of adaptive and local versions. ffl Uniformity of Representation: subdivision provides a single representation of a surface at all resolution levels. Boundaries and features such as creases can be resolved through modified rules [15, 25], eliminating the need for trim curves, for example. 1.3 Our Contribution Aside from our perspective, which unifies the earlier approaches, our major contribution and the main challenge in this program is the design of highly adaptive and dynamic data structures and algorithms, which allow ....

[Article contains additional citation context not shown here]

Hoppe, H., DeRose, T., Duchamp, T., Halstead, M., Jin, H., McDonald, J., Schweitzer, J., and Stuetzle, W. Piecewise Smooth Surface Reconsruction. In Computer Graphics Proceedings, Annual Conference Series, 295--302, 1994.

....[22] The scheme is based on the three directional box spline, which produces C 2 continuous surfaces on the regular meshes. The Loop scheme produces surfaces that are C 2 continuous everywhere except at extraordinary vertices, where they are C 1 continuous. Hoppe, DeRose, Duchamp et al. [8] proposed a piecewise C 1 continuous extension of the Loop scheme, with special rules defined for edges. The scheme can be applied to arbitrary polygonal meshes, after the mesh is converted to a triangular mesh, for example, by triangulating each polygonal face. Subdivision rules The masks ....

....that are outside the boundary crease. Figure 3.14: The Loop subdivision. In the picture above, b can be chosen to be either 1 n (5 8 ( 3 8 1 4 cos 2p n ) 2 ) original choice of Loop [10] or, for n 3, b = 3 8n as proposed by Warren [21] For n = 3, b = 3 16 can be used. In [8], the rules for extraordinary crease vertices and their neighbors on the crease were modified to produce tangent plane continuous surfaces on either side of the crease (or on one side of the boundary) In practice, for reasons discussed in [25] this modification does not lead to a significant ....

[Article contains additional citation context not shown here]

HOPPE, H., DEROSE, T., DUCHAMP, T., HALSTEAD, M., JIN, H., MCDONALD, J., SCHWEITZER, J., AND STUETZLE, W. Piecewise Smooth Surface Reconsruction. In Computer Graphics Proceedings, Annual Conference Series, 295--302, 1994.

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Hugues Hoppe, Tony DeRose, Tom Duchamp, Mark Halstead, Huber Jin, John McDonald, Jean Schweitzer, and Werner Stuetzle. Piecewise smooth surface reconsruction. In Computer Graphics Proceedings, Annual Conference Series, pages 295--302. ACM Siggraph, 1994.

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