The fundamental goal of this paper aims to bridge the large gap between the shape versatility of arbitrary topology and the geometric modeling limitation of conventional tensor-product splines for solid representations. Its contribution lies at a novel shape modeling methodology based on tensorproduct trivariate splines for solids with arbitrary topology. Our framework advocates a divide-andcon...

We present a method for calculating the envelope of the swept surface of a solid along a path in three-dimensional space. The generator of the swept surface is a trivariate tensorproduct Bèzier solid and the path is a non-uniform rational B-spline curve. The boundary surface of the solid is the combination of parametric surfaces and an implicit surface where the determinant of the Jacobian of t...

In this paper we present an electric field volume integral equation approach to simulate surface plasmon propagation along metal/dielectric interfaces. Metallic objects embedded in homogeneous dielectric media are considered. Starting point is a so-called weak-form of the electric field integral equation. This form is discretized on a uniform tensorproduct grid resulting in a system matrix whos...

Analysis-suitable T -splines (AS T -splines) are a mildly topological restricted subset of T -splines which are linear independent regardless of knot values [1–3]. The present paper provides some more iso-geometric analysis (IGA) oriented properties for AS T splines and generalizes them to arbitrary topology AS T -splines. First, we prove that the blending functions for analysis-suitable T -spl...

Multiresolution triangulation meshes are widely used in computer graphics for 3-d modeling of shapes. We propose an image representation and processing framework using a multiscale triangulation of the grayscale function. Triangles have the potential of approximating edges better than the blocky structures of tensorproduct wavelets. Among the many possible triangulation schemes, normal meshes a...

Engineers encounter the problem of friction in any mechanical system. Friction force is strongly nonlinear and varies considerably while the system is working. In the case of high-precision applications friction makes the situation even more complex, as the stick-slip effect occurs near the target position. This paper introduces a pneumatic servo-system for investigation of the behavior of fric...

We describe a physically based framework for real-time modeling and interactive cutting of 3-dimensional soft tissue that can be used for surgery simulation. Unlike existing approaches which are mostly designed for tensorproduct grids our methods operate on tetrahedral decompositions giving more topological and geometric flexibility for the efficient modeling of complex anatomical structures. W...

We describe a physically based framework for real-time modeling and interactive cutting of 3-dimensional soft tissue that can be used for surgery simulation. Unlike existing approaches which are mostly designed for tensorproduct grids our methods operate on tetrahedral decompositions giving more topological and geometric flexibility for the efficient modeling of complex anatomical structures. W...

The Body Centered Cubic (BCe) and Face Centered Cubic (FCC) lattices along with a set of box splines for sampling and reconstruction of trivariate functions are proposed. The BCC lattice is demonstrated to be the optimal choice of a pattern for generic sampling purposes. While the FCC lattice is the second best choice for this purpose, both FCC and BCC lattices significantly outperform the accu...