Optimal approximate conversion of spline surfaces

Hoschek, Josef; Schneider, Franz-Josef; Wassum, Peter

doi:10.1016/0167-8396(89)90030-7

Cited by 43 publications

(20 citation statements)

References 7 publications

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“…in which ti = (fi ui vi) is the parametrization of the projection of pi onto S. Iterative methods have been developed to solve this type of nested minimization problem in the context of B-spline surface fitting [15,30]. In these methods, each iteration consists of two steps: Usually the fit accuracy is improved considerably after only a few iterations (we typically use 4).…”

Section: B-spline Fittingmentioning

confidence: 99%

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Automatic reconstruction of B-spline surfaces of arbitrary topological type

Eck

Hoppe

1996

Proceedings of the 23rd Annual Conference on Computer Graphics and Interactive Techniques

301

182

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Creating freeform surfaces is a challenging task even with advanced geometric modeling systems. Laser range scanners offer a promising alternative for model acquisition-the 3D scanning of existing objects or clay maquettes. The problem of converting the dense point sets produced by laser scanners into useful geometric models is referred to as surface reconstruction.In this paper, we present a procedure for reconstructing a tensor product B-spline surface from a set of scanned 3D points. Unlike previous work which considers primarily the problem of fitting a single B-spline patch, our goal is to directly reconstruct a surface of arbitrary topological type. We must therefore define the surface as a network of B-spline patches. A key ingredient in our solution is a scheme for automatically constructing both a network of patches and a parametrization of the data points over these patches. In addition, we define the B-spline surface using a surface spline construction, and demonstrate that such an approach leads to an efficient procedure for fitting the surface while maintaining tangent plane continuity. We explore adaptive refinement of the patch network in order to satisfy user-specified error tolerances, and demonstrate our method on both synthetic and real data.

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Section: B-spline Fittingmentioning

confidence: 99%

“…For instance, Dietz [4], Hoschek and Schneider [15], Rogers and Fog [30], and Sarkar and Menq [31] assume that the surface is a single open B-spline patch (a deformed quadrilateral region), possibly with trimmed boundaries. Forsey and Bartels [9] consider fitting a single hierarchical B-spline patch to gridded data.…”

Section: Related Workmentioning

confidence: 99%

Automatic reconstruction of B-spline surfaces of arbitrary topological type

Eck

Hoppe

1996

Proceedings of the 23rd Annual Conference on Computer Graphics and Interactive Techniques

301

182

View full text Add to dashboard Cite

show abstract

“…Hence, after solving the system we apply a parameter correction t1-+ t; i.e. P1 -+Pi = F(ti), thus, D1 -+ Di, d-+ d*, as described in [Hos89] and then solve the new system, which results from :~: = 0 and :~: = O. This process is iterated in order to force nearly a.11 error vectors tobe perpendicular to X(t) in X(t 1 ).…”

Section: Free Form Deformationmentioning

confidence: 99%

Bézier Representation of Trim Curves

Lasser

Bonneau

1995

Geometric Modelling

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Abstract. The composition of Bezier curves and tensor product Bezier surfaces, polynomial as weil as rational, is applied to exactly and explicitely represent trim curves of tensor product Bezier surfaces. Trimming curves are assumed tobe defined as Bezier curves in surface parameter domain. A Bezier spline approximation of lower polynomial degree is built up as weil which is based on the ' exact trim curve representation in coordinate space.

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“…This is done by an algorithm developed by Hoschek [12], which créâtes the subdivision into generic curves according to the minimal absolute values of the spline curvature (vertices, inflection points). Séparation points are determined midway between these absolute values according to the degree of the generic curve.…”

Section: =0mentioning

confidence: 99%

“…Their method is based on a combination of Hermitian interpolation and least square approximation. Another approach to the approximation problem (as well as the construction of offset curves) using Bézier curves, was presented by Hoschek [8,9,10,11,12]. It is a discrete method in which transformations of parametrization and geometrie continuity conditions are considered.…”

Section: Introductionmentioning

confidence: 99%