Localized Surface Interpolation Method for Irregular Meshes

Chiyokura, Hiroaki

doi:10.1007/978-4-431-68036-9_1

Cited by 23 publications

(16 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The formulas for this computation are given in Appendix B. For example, using the template concept with the degree of freedomx 18 Assuming the contact element in Figure 12 and using the input (87) in (B1) thereby produces contributions to the conjugate forces (r 1 ; r 2 ; r 3 ; r 4 ; r 7 ; r 8 ; r 9 ) which must be scattered appropriately.…”

Section: Interior Control Point Formulasmentioning

confidence: 99%

A 3D contact smoothing method using Gregory patches

Puso

Laursen

2002

Numerical Meth Engineering

114

View full text Add to dashboard Cite

In this work, a method is developed for smoothing three-dimensional contact surfaces. The method can be applied to both regular and irregular meshes. The algorithm employs Gregory patches to interpolate ÿnite element nodes and provide tangent plane continuity between adjacent patches. The resulting surface interpolation is used to calculate gaps and contact forces, in a variationally consistent way, such that contact forces due to normal and frictional contact vary smoothly as slave nodes transition from one patch to the next. This eliminates the 'chatter' which typically occurs in a standard contact algorithm when a slave node is situated near a master facet edge. The elimination of this chatter provides a signiÿcant improvement in convergence behaviour, which is illustrated by a number of numerical examples. Furthermore, smoothed surfaces also provide a more accurate representation of the actual surface, such that resulting stresses and forces can be more accurately computed with coarse meshes in many problems.

show abstract

Section: Interior Control Point Formulasmentioning

confidence: 99%

A 3D contact smoothing method using Gregory patches

Puso

Laursen

2002

Numerical Meth Engineering

114

View full text Add to dashboard Cite

show abstract

“…These two vectors may be chosen in any fashion that uses information available to both patches, where the construction from both sides gives the same vectors with opposite sign. For example, in a later paper [3], Chiyokura defines Co and C1 as _ vo -lo…”

Section: Tangent Plane Continuitymentioning

confidence: 98%

“…Note that we may use Nielson's proof above to show that F interpolates the tangent plane fields along all edges. 3 A third way to view Herron's scheme is as a "three point" triangular Gregory patch. By rewriting (8.9) in Bernstein form, it is easily seen that Herron's method constructs a quartic Bézier patch, where each internal control point is a blend of three of the internal control points of the Fis.…”

Section: Qa = Brbq + Bgbr + Brbpmentioning

confidence: 99%

8. A Survey of Parametric Scattered Data Fitting Using Triangular Interpolants

Mann¹,

Loop²,

Lounsbery³

et al. 1992

Curve and Surface Design

View full text Add to dashboard Cite

“…The tangent plane continuity between adjacent split patches across a network curve is enforced by the Chiyokura-Kimura constraints [1]. Farin's method [4] is used to ensure the smooth patch-patch joints in the interior of the 3 x 4-split-patch.…”

Section: Interpolatory Surface Fittingmentioning

confidence: 99%

Fair Surface Reconstruction Using Quadratic Functionals

Kolb¹,

Pottmann²,

Seidel³

1995

Computer Graphics Forum

View full text Add to dashboard Cite

An algorithm for surface reconstruction from a polyhedron with arbitrary topology consisting of triangular faces is presented. The first variant of the algorithm constructs a curve network consisting of cubic Bézier curves meeting with tangent plane continuity at the vertices. This curve network is extended to a smooth surface by replacing each of the networks facets with a split patch consisting of three triangular Bézier patches. The remaining degrees of freedom of the curve network and the split patches are determined by minimizing a quadratic functional. This optimization process works either for the curve network and the split patches separately or in one simultaneous step. The second variant of our algorithm is based on the construction of an optimized curve network with higher continuity. Examples demonstrate the quality of the different met hods.The constructed curve network is filled with triangular Bézier patches interpolating the curve network, such that neighboring patches meet smoothly. C-470A. Kolb et al. / Fair Surface Reconstruction using Quadratic Functions © Eurographics Association, 1995 Lounsbery et al [10], Mann [11] and Peters [15] give an overview on methods that are based on these construction steps. Basically, the existing methods can be divided into heuristic methods and optimizing methods.The main characteristic of the heuristic methods is that all free parameters of the curves and patches that are not determined by any of the constraints (interpolation conditions/smoothness conditions at vertices and along patch-boundaries) are set by heuristic rules. The resulting algorithms are, in general, very easy to implement. Furthermore they are relatively fast. The major drawback of the heuristic methods is that the resulting surfaces are often of very poor quality (see Mann [11]).On the other hand, optimizing methods try to overcome the shortcomings of the traditional heuristic methods utilizing the idea of variational design. Nielson [14] proposes a method applying the basic ideas of the minimum norm networks known from functional scattered data interpolation (see [13] and Section 2.2) to the general situation. Nielson uses a quadratic functional to optimize a curve network. This reduces the optimization process to solving a linear system (see Section 2.1). The curve network is filled with so-called transfinite interpolants, a very special class of rational surfaces not supported by any CAD system. The underlying representation of the curve network yields a relatively large number of unknowns for the optimization. Moreover, this representation can not be extended to curve networks with higher continuity. These seem to be the major disadvantages of this method.A . Kolb et al. /Fair Surface Reconstruction using Quadratic Functions © Eurographics Association, 1995 The representation of our curve network is based on the idea of a functional MNN (see Section 2.2). Due to the unrestricted topology of our polyhedron we can not, in general, parameterize our curve network globally. The intr...

show abstract

Localized Surface Interpolation Method for Irregular Meshes

Cited by 23 publications

References 7 publications

A 3D contact smoothing method using Gregory patches

A 3D contact smoothing method using Gregory patches

8. A Survey of Parametric Scattered Data Fitting Using Triangular Interpolants

Fair Surface Reconstruction Using Quadratic Functionals

Contact Info

Product

Resources

About