The behaviour of critical points of Gaussian scale-space images is mainly described by their creation and annihilation. In existing literature these events are determined in so-called canonical coordinates. A description in a user-defined Cartesian coordinate system is stated, as well as the results of a straightforward implementation. The location of a catastrophe can be predicted with subpixe...

The calculation of the uncertainty in an estimated rotation requires a parametrization of the rotation group; that is, a unique mapping of the rotation group to a point in 3-D Euclidean space, R3. Numerous parametrizations of a rotation exist, including: (1) the latitude and longitude of the axis of rotation and the angle of rotation; (2) a representation as a Cartesian vector with length equal...

The direct geodesic problem on an oblate spheroid is described as an initial value problem and is solved numerically in geodetic and Cartesian coordinates. The geodesic equations are formulated by means of the theory of differential geometry. The initial value problem under consideration is reduced to a system of first-order ordinary differential equations, which is solved using a numerical met...

To facilitate the use of group theory in the analysis of vibrational spectra, a set of Maple procedures is provided generating the normal coordinates and determining the spectral activities of polyatomic molecules. Our program, called BETHE, is based on the frequently applied point groups and provides an interactive access to the group data as needed in physical chemistry and elsewhere. Owing t...

Any quantization introduces errors. An important question is how to suppress their visual effect. In this paper we present a new quantization method for the geometry of 3D meshes, which enables aggressive quantization without significant loss of visual quality. Conventionally, quantization is applied directly to the 3-space coordinates. This form of quantization introduces high-frequency errors...

The level of detail of an image can be expressed in terms of its topology, i.e. the distribution of Morse critical points and their types, which in turn is governed by resolution. We study the behaviour of critical points as a function of resolution for Gaussian scale-space images using catastrophe theory. Unlike existing literature, in which one employs local, so-called canonical coordinates f...

In this paper the flow behaviour over a number of car bodies is studied. For this purpose the unsteady 2-D incompressible Navier-Stokes equations have been applied. After averaging and nondimensionalizing the equations, the system of equations has been transformed from the Cartesian (x-y) coordinates to a body fitted generalized (-) coordinate. As the flow is incompressible, the density in the ...

Implementations of the Bayes filtering for vision based aircraft tracking suffer fundamental difficulties in the Cartesian coordinate. This is because of the uncertainty of the noise model in the flight dynamic equation when the aircraft state is described in these coordinates. Recently, the Logarithmic Polar Coordinate (LPC) framework has been successfully applied in the bearings-only tracking...

Rotational and vibrational distributions for the exchange reaction H + H2->H2+ H are obtained numerically for reaction in a plane and compared with the vibrationally adiabatic solutions. Evidence is obtained regarding the two adiabatic solutions for the final rotational state predicted earlier and for. the disappearance of one of these at higher initial relative velocity. Good agreement between...

Llde, A., Trajectory generation from noisy positions of object features for teaching robot paths, Robotics and Autonomous Systems, 11 (1993) 113-127. In this paper we discuss a method for generating a trajectory describing robot path using a sequence of noisy positions of features belonging to a moving object obtained from a robot's sensor system. In order to accurately estimate this trajectory...