Generalized Hermitian Radial Basis Functions Implicits from polygonal mesh constraints

Góis, João Paulo; Trevisan, Diogo Fernando; Batagelo, Harlen Costa; Macêdo, Ives

doi:10.1007/s00371-013-0802-8

Cited by 12 publications

(4 citation statements)

References 35 publications

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“…It is worth noting that the RBF-based methods are the dual form of the kriging-based methods. For example, the generalized radial basis functions (GRBF) method [18][19][20] is the dual form of the universal co-kriging method. Therefore, the geological rules of the potential field method can be also applied to the RBF-based methods.…”

Section: Related Workmentioning

confidence: 99%

Combination Constraints of Multiple Fields for Implicit Modeling of Ore Bodies

Zhong

Wang

2021

Applied Sciences

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In this paper, we introduce combination constraints for modeling ore bodies based on multiple implicit fields interpolation. The basic idea of the method is to define a multi-labeled implicit function that combines different sub-implicit fields by the combination operations, including intersection, union and difference operators. The contribution of this paper resides in the application of combination of more general implicit fields with combination rules for the implicit modeling of ore bodies, such that the geologist can construct constraints honoring geological relationships more flexibly. To improve the efficiency of implicit surface reconstruction, a pruning strategy is used to avoid unnecessary calculations based on the hierarchical bounding box of the operation tree. Different RBF-based methods are utilized to study the implicit modeling cases of ore bodies. The experimental results of several datasets show that the combination constraints are useful to reconstruct implicit surfaces for ore bodies with mineralization rules involving multiple fields.

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Section: Related Workmentioning

confidence: 99%

Combination Constraints of Multiple Fields for Implicit Modeling of Ore Bodies

Zhong

Wang

2021

Applied Sciences

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“…Based on the theory of Hermite-Birkhoff interpolation with radial basis functions, some generalized interpolants with different interpolation constraints are developed, including the anisotropic radial basis functions (ARBF) interpolant [14], the generalized radial basis functions (GRBF) interpolant [15] and the generalized Hermite radial basis functions (GHRBF) interpolant [16]. Gois et al [17] applied the GHRBF to reconstruct implicit surface from polygonal meshes. Liu et al [18] utilized the ARBF to interpolate images with local feature orientations (anisotropic intensities).…”

Section: A Related Workmentioning

confidence: 99%

Extended Hermite Radial Basis Functions for Sparse Contours Interpolation

Zhong

Wang

2020

IEEE Access

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In this paper, we present an extended Hermite radial basis functions interpolant for surface reconstruction of sparse contours that allows for shape control with interactive constraints. Similar to the differential operator, the difference operator is used to construct gradient constraint and tangent constraint. Based on the theory of Hermite-Birkhoff interpolation, to construct more flexible geometry constraints, we incorporate the differential operator and difference operator to construct interpolation conditions in the interpolant. We construct some constraint rules to control the local trend of shape interactively. It is useful when the method interpolates sparse data that satisfies all the constraints but exhibits an undesirable trend of shape. For example, the interactive constraints can be used to fix holes or intersections for geometrically valid meshes. Regarding the geometry domain as a signed distance field of implicit function, we implement a constraint-based approach to interpolate the contours using the interpolant. The improved method can flexibly handle both parallel and non-parallel sparse contours. The numerical results of real geological and medical data show the robustness and performance of the extended Hermite radial basis functions interpolant. INDEX TERMS Hermite radial basis functions, radial basis functions, contours interpolation, signed distance field, geometry constraints.

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“…Liu et al [13] proposed a closed-form HRBF implicits method to solve the problem of large-scale point cloud data reconstruction by quasi-interpolation. Recently, several generalized interpolants based on the theory of Hermite-Birkhoff interpolation with RBFs were developed, such as generalized RBF (GRBF) [14] and generalized HRBF (GHRBF) [15]. To handle problems with large numbers of constraint points, efficient methods such as FastRBF [16] and PetRBF [17] are developed based on the RBF method.…”

Section: Implicit Functionmentioning

confidence: 99%

Orebody Modeling from Non-Parallel Cross Sections with Geometry Constraints

et al. 2019

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In this paper, we present an improved approach to the surface reconstruction of orebody from sets of interpreted cross sections that allows for shape control with geometry constraints. The soft and hard constraint rules based on adaptive sampling are proposed. As only the internal and external position relations of sections are calculated, it is unnecessary to estimate the normal directions of sections. Our key contribution is proposing an iterative closest point correction algorithm. It can be used for iterative correction of the distance field based on the constraint rules and the internal and external position relations of the model. We develop a rich variety of geometry constraints to dynamically control the shape trend of orebody for structural geologists. As both of the processes of interpolation and iso-surface extraction are improved, the performance of this method is excellent. Combined with the interactive tools of constraint rules, our approach is shown to be effective on non-trivial sparse sections. We show the reconstruction results with real geological datasets and compare the method with the existing reconstruction methods.

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Generalized Hermitian Radial Basis Functions Implicits from polygonal mesh constraints

Cited by 12 publications

References 35 publications

Combination Constraints of Multiple Fields for Implicit Modeling of Ore Bodies

Combination Constraints of Multiple Fields for Implicit Modeling of Ore Bodies

Extended Hermite Radial Basis Functions for Sparse Contours Interpolation

Orebody Modeling from Non-Parallel Cross Sections with Geometry Constraints

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