Local refinable finitely generated shift-invariant spaces play a significant role in many areas of approximation theory and geometric design. In this paper we present a new approach to the construction of such spaces. We begin with a refinable function ψ : R → Rm which is supported on [0, 1]. We are interested in spaces generated by a function φ : R → Rn built from the shifts of ψ.

T total cost of moving goods by truck over a highway system involves two basic compon~nts: -the public costs associated with construction and maintenance of the road network, and the privately financed costs of acquiring, operating, and maintaining a fleet of trucks. These publicly and privately financed costs are directly linked in many ways. For instance, the more trucks there are, the more w...

Ruled surface design and its applications are widely used in CAGD(Computer Aid Geometric Design) and industrial areas. In this paper, the hyperbolic paraboloid is a particular ruled surface, which is drawn by using the dual De Casteljau algorithm [15]. The characteristics of the hyperbolic paraboloid are analysed in order to match the requirement of the dual De Casteljau algorithm. A new method...

This paper applies dimensional synthesis to explore the geometric design of dexterous three-fingered robotic hands for maximizing precision manipulation workspace, in which the hand stably moves an object with respect to the palm of the hand, with contacts only on the fingertips. We focus primarily on the tripod grasp, which is the most commonly used grasp for precision manipulation. We systema...

The synthesis theory for spatial linkage systems can be formulated in a way that is compatible with the geometric design of serial and parallel chain robotic systems. Mechanism design generally seeks exact solutions for a finite approximation to the trajectory of a moving frame. In contrast, robots must have a sixdegree-of-freedom workspace with specific characteristics such as shape and size. ...

The optimal design of risers for castings has been the subject of numerous investigations and this paper determines the optimal dimensions when Chvorinov’s rule for solidification is obeyed by both the riser and casting and solidification time is the only constraint involved .This problem can be formulated to minimize the riser volume subject to the constraint that the riser solidification time...

1 Currently with HKS 2 Corresponding author ([email protected]) ABSTRACT Feature technology has been evolving since the early 1980s, yet is still found in few commercial CAD systems. Traditional CAD systems provide support for geometric design and limited parametric design. Two basic approaches to feature modeling have been developed: design by features and feature recognition. Each of these me...

The developable surface is an important surface in computer aided design, geometric modeling and industrial manufactory. It is often given in the standard parametric form, but it can also be in the implicit form which is commonly used in algebraic geometry. Not all algebraic developable surfaces have rational parametrizations. In this paper, we focus on the rational developable surfaces. For a ...