F, Schmitt, B. Barsky, and W, Du, An adaptive subdivision method for surface-fitting from sampled data, Computer Graphics, 20(4):179-188, 1986.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....least squares approximation and related methods have to deal with the problem of rank deficiency of the observation matrix. Alternatively, lower dimensional spaces and or adaptive refinement combined with precomputation in those areas where the approximation error is too high can be employed [39, 28, 45]. In [39] parametric bicubic splines possessing = geometric continuity are adaptively subdivided to approximate 3D points with a regular quadmesh structure. Multilevel B splines are used in [28] to approximate functional scattered data. Other spline methods are based on box splines [9, 24] ....

....approximation and related methods have to deal with the problem of rank deficiency of the observation matrix. Alternatively, lower dimensional spaces and or adaptive refinement combined with precomputation in those areas where the approximation error is too high can be employed [39, 28, 45] In [39], parametric bicubic splines possessing = geometric continuity are adaptively subdivided to approximate 3D points with a regular quadmesh structure. Multilevel B splines are used in [28] to approximate functional scattered data. Other spline methods are based on box splines [9, 24] simplex ....

F. J. M. Schmitt, B. B. Barsky, and W. Du. An Adaptive Subdivision Method for Surface-Fitting from Sampled Data. In Computer Graphics (SIGGRAPH '86 Conf. Proc.), pp. 179--188, 1986.

....triangles such that each blue point is covered by some triangle and no red point lies in any of the triangles. 1 Introduction In scientific computation, visualization, and computer graphics, the modeling and construction of surfaces is an important area. A small sample of some recent papers [2, 3, 5, 7, 10, 13, 20, 21] on this topic gives an indication of the scope and importance of this problem. The first author has been supported by National Science Foundation Grant CCR 93 01259 and an NYI award. Rather than delve into any specific problem studied in these papers, we focus on a general, abstract problem ....

F. Schmitt, B. Barsky, and W. Hui Du, An adaptive subdivision method for surface fitting from sampled data, Computer Graphics 20 (1986), 179--188.

....mesh simplification and reconstruction use the topology of the original mesh to produce a simplified mesh. For example, Turk [16] proposes a method in which polygonal surfaces are re tiled by triangulating a new set of vertices that replaces the original one using mutual tessellation. Schmitt [13] uses a top down approach to simplify a regular rectangular mesh by refining an approximation mesh of piecewise patches until it is within a given error bound of the original mesh. Kalvin and Taylor [8] present a domain independent method for simplifying polygonal meshes based on a bounded ....

F-J. M. Schmitt, B. A. Barsky and W-H. Du, An Adaptive Subdivision Method for Surface-Fitting from Sampled Data, Computer Graphics 20,4, 1986, pp. 179-188.

....sampled. Interpolating or approximating spline functions are then fit to the samples. Most work in this area has focused on representing the reconstructed surface as an embedding of a 2D parameter domain. Typically the parameter domains are topologically simple, such as a plane [9, 1] cylinder [19, 20, 8], or sphere [2] The method of surface fitting used in this thesis uses a parametric domain of a rectangular mesh of data points. D. Surface Fitting to a Rectangular Mesh An efficient method of finding a smooth spline approximation s to a function R, where the sample data points R q;r are given ....

F. Schmitt, B.A. Barsky, and W. Du, "An adaptive subdivision method for surface fitting from sampled data," Computer Graphics (ACM SIGGRAPH '86 Proceedings), New York, 1986, pp. 179-188.

....farther than ffl distance away from the input model I. ffl Min ffl Approximations: Here we are given the number of vertices of the approximation A and the objective is to minimize the error, or the difference, between A and I. Previous work in the area of min # approximations has been done by [SBD86, DZ91] where they adaptively subdivide a series of bicubic patches and polygons over a surface until they fit the data within the tolerance levels. In the second category, work has been done by several groups. Turk [Tur92] first distributes a given number of vertices over the surface depending on ....

F. J. Schmitt, B. A. Barsky, and W. Du. An adaptive subdivision method for surface-fitting from sampled data. Computer Graphics (SIGGRAPH '86 Proceedings), 20(4):179--188, 1986.

....in the topological type of the surface they can fit. There is a large body of literature on fitting embeddings of a rectangular domain; see Bolle and Vemuri [1] for a review. Schudy and Ballard [15, 16] Brinkley [2] and Sclaroff and Pentland [18] fit embeddings of a sphere. Schmitt et al. [13, 14] fit embeddings of a cylinder to data from cylindrical range scans. Goshtasby [8] works with embeddings of cylinders and tori. There is extensive literature on the smooth interpolation of triangulated data using parametric surfaces. However, these schemes cannot be used directly in the fitting of ....

F. Schmitt, B.A. Barsky, and W. Du. An adaptive subdivision method for surface fitting from sampled data. Computer Graphics, 20(4):179--188, 1986.

....fine geometric detail from coarse geometry. Particularly for very dense meshes, we find this separation both useful and preferable, as already explained. We compare some other aspects of the parameterization scheme of Eck et al. [11] with ours in section 4.10. We briefly mention some techniques [29, 31] that use hierarchical algorithms to fit parametric surfaces to scanned data sets. While these approaches work well for regular data, they do not address the problem of unparameterized, irregular polygon meshes. Finally, Sclaroff et al. [32] demonstrate the use of displacement maps in the context ....

Francis J. M. Schmitt, Brian A. Barsky, and Wen hui Du. An adaptive subdivision method for surface-fitting from sampled data. In Computer Graphics (SIGGRAPH '86 Proceedings), volume 20, pages 179--188, August 1986.

....Since the cross sections usually consist of a large number of data points, it may be required to filter out small local variations in the given data and thus to approximate the data in order to obtain a more compact representation of the resulting surface. Although several efficient methods [18 24] B Spline Surface Approximation to Cross Sections 877 have been proposed for surface approximation, most of them have been focused on approximating an array of points by piecewise rectangular surfaces. Only a few have dealt with approximating a set of 2D contours with branching problems, where the ....

F. Schmitt and B. Barsky, "An adaptive subdivision method for surface-fitting from sampled data", Computer Graphics, 20(4), pp. 179--188, 1986.

.... the approximationS to the unknown manifold M has attracted the interest of many authors (for a review, see [11] Several papers focus on building a piecewise linear surface [12, 13, 18, 25, 36] Other methods use parametric or functional surface patches for either local or global interpolation [9, 22, 24, 27, 32, 34]. A few papers (see [3, 14, 15, 23, 28, 35] use implicit surface patches. In this paper, we use an implicitly defined tensor product polynomial spline surface to approximate the unknown surface M. The problem of interpolating or approximating data defined over a given manifold in R 3 is ....

Schmitt, F., Barsky, B. A., and Du, W. An adaptive subdivision method for surface fitting from sampled data. Computer Graphics 20, 4 (1986), 179--188. Proceedings of SIGGRAPH 86.

....surfaces are often possible using curved surface primitives such as piecewise polynomial surfaces. The next class of models beyond piecewise linear surfaces are surfaces with tangent continuity. Schmitt and others have developed adaptive refinement methods for fitting rectangular Bezier patches [113] and triangular Gregory patches [111] to a grid of points in 3 D. The latter method is superior to the former because it is better able to adapt to features at an angle to the grid. Another curved surface primitive, the subdivision surface, has been fit to points in 3D by Hoppe et al. with very ....

Francis J. M. Schmitt, Brian A. Barsky, and Wen-Hui Du. An adaptive subdivision method for surface-fitting from sampled data. Computer Graphics (SIGGRAPH '86 Proc.), 20(4):179--188, Aug. 1986.

....a superface algorithm by merging faces. It guarantees a bounded approximation and can be applied on any polyhedral mesh that is a valid manifold. On the other hand, adaptive techniques produce more primitives in selected areas, such as an area with highly detailed features. For example, Schmitt [34] starts with a rough bi cubic patch approximation to sample data, and then subdivides those patches that are not sufficiently close to the underlying samples. Adaptive techniques have been used for terrains [13] implicit modeling [2] and general polygon meshes [10] As mentioned in the ....

Schmitt, F. J., Barsky, B. A. and Du, W., "An Adaptive Subdivision Method for Surface-fitting from Sample Data", Computer Graphics (SIGGRAPH '86 Proceedings), 20, 4 (1986), 179-188.

....Adaptive techniques generate more primitives in feature area of the object. Multiple models have been designed in different fields, e.g. triangulated irregular network (TIN) 9] in Geoscience, Geometrically Deformed Models (GDM s) 10] unstructured grid generation [11] Surface fitting [12], implicit defined surface modelling [13] and finite element mesh generation. This paper describes an application independent algorithm which integrates several adaptive and filterbased techniques under a resource allocation methodology known as Constraint Resource Planning (CRP) 14] By ....

F. J. M. Schmitt, B. A. Barsky, W. H. Du, " An Adaptive Subdivision Method for Surface-Fitting from Sampled Data", SIGGRAPH `86, Dallas, August 18-22, Vol. 20, No. 4, 1986, pp. 179-188.

....A is farther than # distance away from the input model I. # Min # Approximations: Here we are given the number of vertices of the approximation A and the objective is to minimize the error, or the difference, between A and I . Previous work in the area of min # approximations has been done by [6, 20] where they adaptively subdivide a series of bicubic patches and polygons over a surface until they fit the data within the tolerance levels. In the second category, work has been done by several groups. Turk [23] first distributes a given number of vertices over the surface depending on the ....

F. J. Schmitt, B. A. Barsky, and W. Du. An adaptive subdivision method for surface-fitting from sampled data. Computer Graphics (SIGGRAPH '86 Proceedings), 20(4):179--188, 1986.

....to achieve an interactive performance for motion editing. He also applied this technique for motion retargetting [13] 2.2 Hierarchical Curve Surface Manipulation There is a vast amount of literature devoted to investigating hierarchical representations of curves and surfaces. Schmitt et al. [29] presented an adaptive subdivision method to produce a smooth surface from sampled data. Forsey and Bartels [9] introduced a hierarchical B spline representation to enhance surface modeling capability. This representation allows details to be adaptively added to the surface through local ....

F. J. M. Schmitt, B. A. Barsky, and W. Du. An adaptive subdivision method for surface-fitting from sampled data. Computer Graphics (Proceedings of SIGGRAPH 86), 20(4):179-- 188, August 1986.

....ffl distance away from the input model I. ffl Min ffl Approximations: Here we are given the number of vertices of the approximation A and the objective is to minimize the error, or the difference, between A and I. In computer graphics, work in the area of min # approximations has been done by [Schmitt et al. 86] and [DeHaemer, Jr. Zyda 91] where they adaptively subdivide a series of bicubic patches and polygons over a surface until they fit the data within the tolerance levels. Turk 92, Schroeder et al. 92, Hinker Hansen 93] are a good representative collection in the second category. Turk first ....

F. J. Schmitt, B. A. Barsky, and W. Du. An adaptive subdivision method for surface-fitting from sampled data. Computer Graphics (SIGGRAPH '86 Proceedings), 20(4):179--188, 1986.

....simplification, visualization AMS subject classifications. 65Y25, 68Q20, 68Q25, 68U05. PII. S0097539794269801 1. Introduction. In scientific computation, visualization, and computer graphics, the modeling and construction of surfaces is an important area. A small sample of some recent papers [1, 2, 4, 8, 11, 14, 22, 23] on this topic gives an indication of the scope and importance of this problem. Rather than delve into any specific problem studied in these papers, we focus on a general, abstract problem that seems to underlie them all. In many scientific and computer graphics applications, computation takes ....

<F3.728e+05> F. Schmitt, B. Barsky, and W. H. Du,<F3.501e+05> An adaptive subdivision method for surface fitting from sampled data,<F3.842e+05> Computer Graphics, 20 (1986), pp. 179--188.

....of a chair at different LODs and suggested to automate the simplification process [Cro82] In fact, some papers proposed various elision strategies to simplify the representation of objects. Level of detail representations can be produced by surface fitting techniques from sampled data points [SBD86] Some of these scanned points are eliminated [JZ91] or automatically redistibuted [Tur92] to generate accurate polygonal representations. The simplification methods for an existing set of polygons are often more adapted to regular meshes [SZL92] HDD 94] while certain others run relatively ....

F. J. M. Schmitt, B. A. Barsky, and W. H. Du. An adaptive subdivision method for surface-fitting from sampled data. In D. C. Evans and R. J. Athay, editors, Computer Graphics (Siggraph'86 proc.), volume 20, pages 179--188, August 1986.

....surface fitting, is described in [3] see also Section 3.2, page 7) 3.2 Surface Fitting We have grouped in this Section methods based on approximating the set of points with a piecewise polynomial, parametric or implicit surface. An application of this method is described by Shmitt et al. [45]. The input points are assumed organized in a rectangular grid, and are adaptively fitted using Bernstein B ezier parametric bi cubic patches, joined to form a G 1 continuous surface. The approximation process begins with a rough approximating surface and uses subdivision to achieve the needed ....

F. Schmitt, B. A. Barsky, and W. Du. An adaptive subdivision method for surface fitting from sampled data. Computer Graphics, 20(4):179--188, 1986. Proceedings of SIGGRAPH 86.

....ONR grant N00014 941 0370 and NASA grant NAG 93 1 1473. y Additional partial support from CNR, Italy. The problem of reconstructing the approximation S to the unknown manifold M has attracted the interest of many authors. A number of methods have been developed for its solution [14, 5, 28, 9, 26, 7, 23, 20, 30, 17, 27, 8, 22, 2] Most of the known methods use parametric or functional surface patches in either local interpolation or global interpolation. A few papers (see [29, 10, 18, 4, 11, 3, 2] use implicit surface patches. In this paper, we use a piecewise implicitly defined tensor product algebraic surface to ....

SCHMITT, F., BARSKY, B. A., AND DU, W. An adaptive subdivision method for surface fitting from sampled data. Computer Graphics (Proc. of the SIGGRAPH Conf.) 20, 4 (1986), 179--188.

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F, Schmitt, B. Barsky, and W, Du, An adaptive subdivision method for surface-fitting from sampled data, Computer Graphics, 20(4):179-188, 1986.

No context found.

F. Schmitt, B.A. Barsky, and W. Du. An adaptive subdivision method for surface fitting from sampled data. Computer Graphics (SIGGRAPH '86 Proceedings), 20(4):179-- 188, 1986.

No context found.

F. Schmitt, B.A. Barsky, and W. Du. An adaptive subdivision method for surface fitting from sampled data. Computer Graphics (SIGGRAPH '86 Proceedings), 20(4):179--188, 1986.

No context found.

Schmitt, Francis J. M., Brian A. Barsky and WenHui Du, "An Adaptive Subdivision Method for Surface-Fitting from Sampled Data," Computer Graphics, Vol. 20, No. 4 (SIGGRAPH 86), pp. 179-188.

No context found.

Francis J. M. Schmitt, Brian A. Barsky, and Wen-Hui Du. An adaptive subdivision method for surface-fitting from sampled data. Computer Graphics (SIGGRAPH '86 Proc.), 20(4):179--188, August 1986.

No context found.

Schmitt, F. J., Barsky, B. A., and Du, W., "An Adaptive Subdivision Method for Surface-Fitting from Sampled Data," Computer Graphics, Vol. 20, No. 4, pp. 179-188, August 1986.

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