We introduce curvature continuous regular free-form surfaces with triangular control nets. These surfaces are composed of quartic box spline surfaces and are piecewise polynomial multisided patches of total degree 8 which minimize some energy integral. The B ezier nets can be computed eeciently form the spline control net by some xed masks, i.e. matrix multiplications. k-free-form surfaces need...

Deformable surfaces have many applications in surface reconstruction, tracking and segmentation of range or volumetric data. Many existing deformable surfaces connect control points in a predefined and inflexible way. This means that the surface topology is fixed in advance, and also imposes severe limitations on how a surface can be described. For example a rectangular grid of control points c...

This paper presents a generalization of Catmull-Clark-variant Doo-Sabin surfaces and non-uniform biquadratic B-spline surfaces called NURDSes (Non-Uniform Recursive Doo-Sabin Surfaces). One step of NURDS refinement can be factored into one non-uniform linear subdivision step plus one dual step. Compared to the prior non-uniform Doo-Sabin surfaces (i.e., quadratic NURSSes), NURDSes are convergen...

This paper is concerned with a study of some new formulations of smoothness conditions and conformality conditions for multivariate splines in terms of B-net representation. In the bivariate setting, a group of new parameters of bivariate quartic and quintic polynomials over a planar simplex is introduced, new formulations of smoothness conditions of bivariate quartic C1 splines and quintic C2 ...

In this paper an efficient numerical scheme to approximate the solutions of fifth-order boundary value problems in a finite domain with two different types of boundary conditions has been prsented, by taking basis functions with quartic Bsplines and weight functions with quintic B-splines in PetrovGalerkin method. In this method, the quartic B-splines and quintic B-splines are redefined into ne...

This paper proposes explicit formulae for the addition step and doubling step in Miller’s algorithm to compute Tate pairing on Jacobi quartic curves. We present a geometric interpretation of the group law on Jacobi quartic curves, which leads to formulae for Miller’s algorithm. The doubling step formula is competitive with that for Weierstrass curves and Edwards curves. Moreover, by carefully c...

Interpolation by rational spline motions is an important issue in robotics and related fields. In this paper a new approach to rational spline motion design is described by using techniques of geometric interpolation. This enables us to reduce the discrepancy in the number of degrees of freedom of the trajectory of the origin and of the rotational part of the motion. A general approach to geome...

In parametric excitation walking, up-and-down motion of the center of mass restores mechanical energy and sustainable gait is generated. Not only walking performance but also walking ability strongly depends on the reference trajectory of the center of mass. In this paper, we propose an optimization method for the reference trajectory, in which the reference trajectory is confined to the quarti...

The basic idea of the Meir/Sharma/Hall/Meyer error analysis for cubic spline interpolation (see [SM66], [H68], [HM76]) has been extended to cover also certain deficient quartic and quintic spline interpolation schemes, the latter already by them, the former by Howell/Varma [HV89] and, perhaps, others. It is the purpose of this note to describe the most general situation to which this idea appli...