We present a method of speed adjustment as a means of controlling motion in of key-frame animation. This method is designed for key-point trajectories that are expressed as differentiable parametric curves. The animator is given a means of influencing the speed of a trajectory 's traversal by the direct manipulation of a speed-profile curve. Any adjustment of this curve is translated into an ad...

Recently the CP trajectory diagram was introduced to demonstrate the difference between the intrinsic CP violating effects to those induced by matter for neutrino oscillation. In this paper we introduce the T trajectory diagram. In these diagrams the probability for a given oscillation process is plotted versus the probability for the CPor the T-conjugate processes, which forms an ellipse as th...

Abstract: Let R be an open equivalence relation on a topological space E. We define on E a new equivalence relation ̃︀ R by x̃︀ Ry if the closure of the R-trajectory of x is equal to the closure of the R-trajectory of y. The quotient space E/̃︀ R is called the trajectory class space. In this paper, we show that the space E/̃︀ R is a simple model of the quotient space E/R. This model can provide a f...

We present a fast algorithm for solving the problem of the verification of a trajectory for a 6-DOF parallel manipulator with respect to its workspace: i.e., given two different postures for the end-effector, is the straight line joining these two postures in the parameters space fully inside the workspace ? This algorithm is based on the analysis of the algebraic inequalities describing the co...

Continuously moving objects are prevalent in many domains. Although there have been attempts to combine both spatial and temporal relationships from a reasoning, a database, as well as from a logical perspective, the question remains how to describe motion adequately within a qualitative calculus. In this paper, a Qualitative Trajectory Calculus (QTC) for representing and reasoning about moving...

in this paper, a robust tracking control method for automatic take-off and trajectory tracking of a quadrotor helicopter is presented. the designed controller includes two parts: a position controller and an attitude controller. the attitude controller is designed by using the sliding mode control (smc) method to track the desired pitch and roll angles, which are the output of position controll...

z y x − − = & ay x y + = & x b z ( − + = & (1) z c) Abstract – It is shown that symbolic sequence can be used to reconstruct a trajectory of a chaotic system with high precision. Examples of construction of symbolic sequence and trajectory reconstruction are given. A method that demonstrates exponential increase in precision with the length of processing is developed. Microtriode generator is d...

In this paper, we study the following version of the Travelling Salesperson Problem: Find the fastest closed trajectory for a controlled dynamic system such that its output visits all points in a given (finite) set. We present an algorithm that, if the n points are randomly sampled from a uniform distribution, produces an output trajectory the expected duration of which scales within a constant...

Introduction: We present a method to compute the fastest possible gradient waveforms for a given k-space trajectory. In our design, we exploit the fact that each gradient set has its own limitation. This is an extension of our previous method described in [1]. In that solution, the worst-case magnitude gradient and slew constraints were considered. This has the advantage of resulting in wavefor...