Four-sided Patches Research Articles

Analytical Polarizable Continuum Model for Wavelets on NURBS Patches

This article concerns the application of wavelet techniques on molecular surfaces constituted of four-sided patches. The Polarizable Continuum Model, which is governed by the Poisson-Boltzmann equation, is treated by means of boundary integral equations. The media inside and outside the molecular surface consist respectively of the solute and the solvent. For a given electrically charged molecule, the principal unknown is the electrostatic solvation energy when the permittivity is specified. The wavelet basis functions are constructed on the unit square which are subsequently mapped onto the patches that are assumed to be isotropically shaped and to admit similar surface areas. The initial transmission problem is recast as an integral equation in term of both the single and the double layers. Domain decomposition preconditioner serves as acceleration of the linear solver of the single layer which is badly conditioned.

Generation of bi-monotone patches from quadrilateral mesh for reverse engineering

Thanks to recent improvements, computational methods can now be used to convert triangular meshes into quadrilateral meshes so that the quadrilateral elements capture well the principal curvature directional fields of surfaces and intrinsically have surface parametric values. In this study, a quadrilateral mesh generated using the mixed integer quadrangulation technique of Bommes et al. is used for input. We first segment a quadrilateral mesh into four-sided patches. The feature curves inside these patches are then detected and are constrained to act as the patch boundaries. Finally, the patch configuration is improved to generate large patches. The proposed method produces bi-monotone patches, which are appropriate for use in reverse engineering to capture the surface details of an object. A shape control parameter that can be adjusted by the user during the patch generation process is also provided to support the creation of patches with good bi-monotone shapes. This study mainly targets shape models of mechanical parts consisting of major smooth surfaces with feature curves between them.

Wavelet BEM on molecular surfaces: solvent excluded surfaces

The present paper is concerned with the rapid solution of a boundary integral equation for the apparent surface charge which arises from solvation continuum models. In order to apply the wavelet Galerkin scheme the molecular surface needs to be represented as a parametric surface consisting of smooth four-sided patches. We develop an algorithm which decomposes a solvent excluded surface into a set of globally continuous four-sided NURBS patches. Numerical experiments are carried out to demonstrate the feasibility and scope of the present approach.

From Computer Aided Design to wavelet BEM

This paper develops an interface between Computer Aided Design (CAD) and the wavelet Galerkin scheme for boundary integral equations. The key issue is an algorithm that decomposes a technical surface which was generated by CAD tools into a regular collection of parameterized four-sided patches. By a postprocessing step the global continuity of the parametrization is guaranteed. Numerical results are reported to illustrate the approach. In particular, the decomposition techniques are applied to real CAD data which come from IGES files.

Wavelet BEM on molecular surfaces: parametrization and implementation

The present paper is dedicated to the rapid solution of boundary integral equations arising from solvation continuum models. We apply a fully discrete wavelet Galerkin scheme for the computation of the apparent surface charge on van der Waals or solvent accessible surfaces. The molecular surface is described in parametric form as a set of four-sided spherical patches. Each patch is exactly represented as rational Bezier surface. Numerical results are reported to illustrate the approach.

On global continuity of Coons mappings in patching CAD surfaces

We tessellate a closed surface bounding a solid into four-sided patches P i . Each patch P i is the image of the unit square by γ i which is the composition of a 2D Coons mapping and a bivariate function coming from a trimmed surface. Here, we concentrate on the analysis of the global continuity of the mappings γ i over the whole surface. While using Coons functions to generate the mappings γ i , arc length parametrization ensures that the images of the functions γ i match pointwise at surface joints independently of the blending functions. We will describe a reparametrization technique based on cubic Bézier whose goal is to keep the shape of the initial curves while achieving arc length parametrization. The required accuracy of length computation is shown in L ∞ -norm in order not to deteriorate the accuracy of the cubic spline approximation. Practical results from simulated and real CAD data which come from IGES files are reported.

344 隣接パッチ間のG^1連続な接続について(次世代CAD/CAM/CAE/CG/CSCW/CAT/C-Control(1),OS22 次世代CAD/CAM/CAE/CG/CSCW/CAT/C-Control)

Reverse engineering is a process to convert real objects into digital data and has received a lot of attention recently. In reverse engineering, reconstructed models are represented by four-sided patches. Problem arises when an originally smooth part is expressed as an edge at the boundary between adjacent patches. This paper presents a method of modifying B-Spline/NURBS surfaces to meet G^1 continuity. The proposed method uses knot insertion to make breakpoints and enables calculation of the appropriate control points at those breakpoints. By using this method repeatedly, it is possible to join a boundary between adjacent patches with G^1 continuity.

HOW EFFECTIVE IS GF-120 FRUIT FLY BAIT SPRAY APPLIED TO BORDER AREA SORGHUM PLANTS FOR CONTROL OF MELON FLIES (DIPTERA: TEPHRITIDAE)?

Application of bait spray to non-host sorghum plants bordering host plants of melon flies, Bactrocera cucurbitae Coquillet, is a common practice for melon fly control in Hawaii. In a field study conducted in 2003 in Hawaii, we first asked whether GF-120 Fruit Fly bait spray applied to sorghum plants that bordered only two (opposite) sides of a patch of cucumbers was as effective in protecting cucumbers against melon flies as similar spray applied to sorghum plants that bordered all four sides of a cucumber patch. Second, we asked whether mature melon fly females carrying a high egg load but deprived of protein during the previous 24 h were more responsive to bait spray than mature females having continuous access to protein. Color-marked melon fly females were released outside of patches of sorghum-bordered cucumbers. We found no significant differences between two-sided and four-sided patches of sorghum or between protein-deprived (for 24 h) and protein-fed (continuously) mature females in percentages of released females that found cucumbers in bait-sprayed plots. Moreover, none of these percentages was significantly less than percentages of released females that found cucumbers in unsprayed plots, indicating an overall ineffectiveness of bait spray application. During the 24 h after alighting on cucumbers, released females that were captured alive on cucumbers and placed in cups with cucumbers laid on average almost as many eggs (insignificantly fewer) when taken from bait-sprayed plots as when taken from unsprayed plots. An overriding factor may have been the presence of just a narrow swath of sorghum (arising from a single row of plants), which may have permitted females easy access to cucumbers and masked potential differences among treatments. Bait spray applied to broader swaths of sorghum may be more effective.

Biquartic C1-surface splines over irregular meshes

C 1-surface splines define tangent continuous surfaces from control points in the manner of tensor-product (B-)splines, but allow a wider class of control meshes capable of outlining arbitrary free-form surfaces with or without boundary. In particular, irregular meshes with non-quadrilateral cells and more or fewer than four cells meeting at a point can be input and are treated in the same conceptual frame work as tensor-product B-splines; that is, the mesh points serve as control points of a smooth piecewise polynomial surface representation that is local and evaluates by averaging. Biquartic surface splines extend and complement the definition of C 1-surface splines in a previous paper (Peters, J SLAM J. Numer. Anal. Vol 32 No 2 (1993) 645–666) improving continuity and shape properties in the case where the user chooses to model entirely with four-sided patches. While tangent continuity is guaranteed, it is shown that no polynomial, symmetry-preserving construction with adjustable blends can guarantee its surfaces to lie in the local convex hull of the control mesh for very sharp blends where three patches join. Biquartic C 1-surface splines do as well as possible by guaranteeing the property whenever more than three patches join and whenever the blend exceeds a certain small threshold.

The Cut&Glue mesh generation algorithm

This paper describes a technique for generating quadrilateral finite element meshes on convex, four-sided patches, given an arbitrary number of elements along each side of the patch. The technique first generates a subdivision with the correct topological structure and smoothes the subdivision to obtain elements of acceptance shape for finite element analysis. The correct mesh topology is obtained from a regular subdivision by cutting rectangular corners of appropriate size and interconnecting the sides introduced by the cuts. The method can also be applied on three-dimensional patches producing meshes of brick elements with gradations in all directions.

Designing complex surfaces based on curve networks with irregular topology

The traditional way of designing the bounding surfaces of complex free-form objects is to define the characteristic curves and interpolate them by some mathematical technique. Most of the known methods—and all of the commercially available CAD/CAM systems—are based on a very inconvenient constraint, that is four-sided patches need to be arranged into a regular, rectangular topology. In practical design situations, however, the designer may wish to specify the characteristic lines of the surface without being restricted by the topology of the curve network. In this paper a new concept for designing smooth surfaces is outlined, which resolves topological restrictions. The method supports the use of N- sided surface patches which can be arranged into an irregular topological structure. Description of the FFS-GT surface modeller is also given together with examples of surfaces defining complex industrial objects.

三辺形パッチの接続とその応用

This paper presents a general method of free-form surface synthesis using only triangular patches with control points and also a method of embedding a triangular patch in a usual spline surface net. Degree of surface patches is two and their connection is in C1, though their degree may be higher. In the first part, a geometric condition for connection of triangular patches is established : control quadrilaterals which derived from the control points of the constituent patches are a basis for their C1 connection. Since they are tightly constrained to adjacent ones, local control of shapes are not so easy as spline nets of four-sided patches. To give more freedom in shape control in using triangular patches, an idea of corrective across-boundary tangent vector is introduced in the second part. For practical use and explanation of this method, smooth embedding a triangular patch in a usual spline net is treated. This is an important technique to produce special shapes which appear in rounding parts of vertices of box type shape. Uses of these two methods are shown by several application examples which are not produced from usual spline nets of surface. And also their evaluation of connection of quality is examined by contour line patterns.

Non-four-sided patch expressions with control points

This paper introduces new mathematical expressions which describe surface patches with three, five or six sides. Each side of a patch is given as a space curve expressed in Bézier type of second or third degree. Patch shape is modified predictably by moving its control points in the same way as with a four-sided patch. Distribution of cross tangent vectors along a patch boundary is also expressed in the same form with a few control vectors belonging to the boundary concerned. Therefore it can be connected with its surrounding four-sided patches smoothly. A general method of derivation of these equations is explained for further applications.

A construction for visual C1 continuity of polynomial surface patches

A geometric construction is described which ensures tangent plane (visual C 1) continuity between adjacent polynomial surface patches. The algorithm works for both three- and four-sided patches.