On global continuity of Coons mappings in patching CAD surfaces

We tessellate a closed surface bounding a solid into four-sided patches . Each patch is the image of the unit square by 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 over the whole surface. While using Coons functions to generate the mappings , arc length parametrization ensures that the images of the functions 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.     

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 Bézier surface. Numerical results are reported to illustrate the approach.     

On transfinite interpolations with respect to convex domains

We propose an approach for constructing a transfinite interpolation where the domain of definition is a convex polytope. For multifaceted domains which are not of tensor product type, it is difficult to directly generalize the usual approach of transfinite interpolation which blends opposite faces and which then substracts that by a mixed term. Therefore, we suggest a short formula which uses topologic entities of the convex domain. Our formula uses some projection operator onto the faces of the polytope. Both representations (V-setting and H-setting) of a polytope are used. We show also that the transfinite interpolation is stable under affine transformations. As a supplement to the theoretical demonstrations, we show some interesting practical illustrations.     

Experimental observations and computer simulations of spherical aluminum-alloy projectiles impacting plane limestone targets

The stress distribution within spherical aluminum-alloy (2024) projectiles impacting plane limestone (calcite) targets was observed by converting residual microhardness maps obtained for cross-sections of recovered projectiles impacting from 0.8 to 1.3 km/s. A maximum residual yield stress zone was observed to migrate toward the rear of the impacting projectiles with increasing impact velocity. The maximum occurred at a normalized depth z/a _m 0.5 (where a _m is the contact radius); consistent with the theoretical result for elastic impacts. Computer simulations showed good agreement with experiment, and demonstrated that elastic assumptions were valid well into the plastic deformation regime.     

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.