In this work, we present a simple framework to synthesize human motion. Our main goal is propose methodology tailored for inexperienced users initiate their research in motion simulation and trajectory optimization. The novelties of the work include following. First, trigonometric splines are used instead traditional B-splines discretize generalized coordinates velocities. Second, useful identi...

A new class of spline curves in polar coordinates has been presented in 12] and independently considered in 3]. These are rational trigonometric curves in Cartesian coordinates and can be represented as NURBS. From the relationship existing with the correspondent curves in Cartesian coordinates an alternative way to derive some useful tools for modelling splines in polar coordinates has been pr...

Abstract In this paper, the numerical solution of a mixed derivative type Hunter–Saxton equation is addressed. A given discretized transforming it into system ODEs with use cubic trigonometric B-splines based differential quadrature method. The further solved using fifth-order optimized one-step hybrid block Three illustrations validate efficiency proposed scheme and show its better performance...

In this work, the relationship between splines and the linear control theory has been analyzed. We show that spline functions can be constructed naturally from the control theory. By establishing a framework based on control theory, we provide a simple and systematic way to construct splines. We have constructed the traditional spline functions including the polynomial splines and the classical...

This article presents a generalized B-spline surface subdivision scheme of arbitrary order with a tension parameter.We first propose a tensor-product subdivision scheme that produces ku×kv order generalized B-spline limit surfaces. Generalized B-spline surface is the unified and extended form of B-splines, trigonometric B-splines and hyperbolic B-splines (Fang et al. 2010). The tensor product s...

This paper proposes a fast method for the calculation of exponential B-splines sampled at regular intervals. This algorithm is based on a combination of FIR and IIR filters which enables a fast decomposition and reconstruction of a signal. When complex values are selected for the parameters of the exponentials, complex trigonometric functions are obtained. Only the real part of these functions ...