Showing papers on "Cartesian coordinate system published in 1995"

Transformation between Cartesian and pure spherical harmonic Gaussians

Abstract: Spherical Gaussians can be expressed as linear combinations of the appropriate Cartesian Gaussians. General expressions for the transformation coefficients are given. Values for the transformation coefficients are tabulated up to h-type functions. © 1995 John Wiley & Sons, Inc.

VARIANT: VARIational Anisotropic Nodal Transport for Multidimensional Cartesian and Hexagonal Geometry Calculation

Abstract: The theoretical basis, implementation information and numerical results are presented for VARIANT (VARIational Anisotropic Neutron Transport), a FORTRAN module of the DIF3D code system at Argonne National Laboratory. VARIANT employs the variational nodal method to solve multigroup steady-state neutron diffusion and transport problems. The variational nodal method is a hybrid finite element method that guarantees nodal balance and permits spatial refinement through the use of hierarchical complete polynomial trial functions. Angular variables are expanded with complete or simplified P₁, P₃ or P₅5 spherical harmonics approximations with full anisotropic scattering capability. Nodal response matrices are obtained, and the within-group equations are solved by red-black or four-color iteration, accelerated by a partitioned matrix algorithm. Fission source and upscatter iterations strategies follow those of DIF3D. Two- and three-dimensional Cartesian and hexagonal geometries are implemented. Forward and adjoint eigenvalue, fixed source, gamma heating, and criticality (concentration) search problems may be performed.

On generalized Kelvin solutions in a multilayered elastic medium

Abstract: This paper presents fundamental singular solutions for the generalized Kelvin problems of a multilayered elastic medium of infinite extent subjected to concentrated body force vectors. Classical integral transforms and a backward transfer matrix method are utilized in the analytical formulation of solutions in both Cartesian and cylindrical coordinates. The solution in the transform domain has no functions of exponential growth and is invariant with respect to the applied forces. The convergence of the solutions in the physical domain is rigorously and analytically verified. The solutions satisfy all required constraints including the basic equations and the interfacial conditions as well as the boundary conditions. In particular, singular terms of the generalized Kelvin solutions associated with the point and ring types of concentrated body force vectors are obtained in exact closed-forms via an asymptotic analysis. Numerical results presented in the paper illustrate that numerical evaluation of the solutions can be easily achieved with very high accuracy and efficiency and that the layering material inhomogeneity has a significant effect on the elastic field.

Function representation for sweeping by a moving solid

Abstract: This paper studies a function representation of point sets swept by moving solids. The original solid-generator is defined by an inequality f(x, y, z, t) 2 0 where x, y, zare Cartesian coordinates and tis treated as the time. This definition allows us to include solids which change their shapes in time. Constructive solids can be used as generators also when described by R-functions. The trajectory of the generator can be defined in parametric form as movement of its local coordinate system. In the paper, we did it with superposition of time-dependent affine transformations. To get the function representation F(x, y, z) 2 0 of the swept solid, we apply the concept of envelope used before basically for boundary represented objects. We have reduced the problem of swept solid description to global extremum search by t variable. The algorithm of procedural swept solid modeling is discussed. The benefit of our model is that it is applied not only for visualization but allows one to use the swept solid as an argument for other operations. For example, the swept solid can be intersected with other ones that are useful for the implementation of such operations as cutting and drilling. Ordinary texture mapping and hypertexturing can also be applied to it. The possibility of using a functionally defined generator with the variable shape allows us to achieve a complexity of the swept solids which was hardly possible before. Index Terms-Solid modeling, sweeping, implicit functions, R-functions, function representation.

On automating domain connectivity for overset grids

Abstract: An alternative method for domain connectivity among systems of overset grids is presented. Reference uniform Cartesian systems of points are used to achieve highly efficient domain connectivity, and form the basis for a future fully automated system. The Cartesian systems are used to approximate body surfaces and to map the computational space of component grids. By exploiting the characteristics of Cartesian systems, Chimera type hole-cutting and identification of donor elements for intergrid boundary points can be carried out very efficiently. The method is tested for a range of geometrically complex multiple-body overset grid systems. A dynamic hole expansion/contraction algorithm is also implemented to obtain optimum domain connectivity; however, it is tested only for geometry of generic shapes.

A normal form augmentation approach to adaptive control of space robot systems

Abstract: In this paper, we model a free-floating space robot system as anextended robot which is composed of a pseudo-arm representing the base motion resulting from six hyperthetic passive joints, and a real robot arm. The model allows us to categorize the space robot as an under-actuated system, and reveal fundamental properties of the system. Through input-output linearization of the model, we demonstrate a non-trivial internal dynamics, and propose an adaptive control scheme based on a normal form augmentation approach. This approach overcomes two fundamental difficulties in adaptive control design of space robot systems, i.e., nonlinear parameterization of the dynamic equation, and uncertainty of kinematic mapping from Cartesian space to joint space.

Three‐dimensional Cartesian finite element method for the time dependent Schrödinger equation of molecules in laser fields

Abstract: A finite element (FE) method in three‐dimensional Cartesian coordinates is described to solve the time dependent Schrodinger equation for H+2, H2, and H+3 in the presence of time dependent electromagnetic fields. The ionization rates and harmonic generation spectra have been calculated for these molecules for field directions parallel or perpendicular to the molecular axis. Nonlinear optical susceptibilities of H+2 have been also obtained for different laser field directions. The time dependent Hartree–Fock results are compared to frozen core calculations for H2. Comparisons of present FE numerical results with previously published calculations show the FE method reproduces perturbative results and can also treat nonperturbatively the effect of intense short laser pulses as the method includes both bound and continuum electronic states.

Analysis of kinematic invariances of multijoint reaching movement

Abstract: There is a no unique relationship between the trajectory of the hand, represented in cartesian or extrinsic space, and its trajectory in joint angle or intrinsic space in the general condition of joint redundancy. The goal of this work is to analyze the relation between planning the trajectory of a multijoint movement in these two coordinate systems. We show that the cartesian trajectory can be planned based on the task parameters (target coordinates, etc.) prior to and independently of angular trajectories. Angular time profiles are calculated from the cartesian trajectory to serve as a basis for muscle control commands. A unified differential equation that allows planning trajectories in cartesian and angular spaces simultaneously is proposed. Due to joint redundancy, each cartesian trajectory corresponds to a family of angular trajectories which can account for the substantial variability of the latter. A set of strategies for multijoint motor control following from this model is considered; one of them coincides with the frog wiping reflex model and resolves the kinematic inverse problem without inversion. The model trajectories exhibit certain properties observed in human multijoint reaching movements such as movement equifinality, straight end-point paths, bell-shaped tangential velocity profiles, speed-sensitive and speed-insensitive movement strategies, peculiarities of the response to double-step targets, and variations of angular trajectory without variations of the limb end-point trajectory in cartesian space. In humans, those properties are almost independent of limb configuration, target location, movement duration, and load. In the model, these properties are invariant to an affine transform of cartesian space. This implies that these properties are not a special goal of the motor control system but emerge from movement kinematics that reflect limb geometry, dynamics, and elementary principles of motor control used in planning. All the results are given analytically and, in order to compare the model with experimental results, by computer simulations.

Close conjunction detection on parallel computer

Abstract: The text should mention that the algorithm described as applied to a single Cartesian coordinate is then successively applied to the other coordinates in the obvious way to select satellites that are within a specified distance of one another.

Use of Corner Point Geometry in Reservoir Simulation

Abstract: At the present time, field-scale reservoir simulations are usually carried out with Cartesian grids. However, the use of these grids does not permit a good representation of reservoir geological features and reservoir description. Different approaches have been investigated to overcome the disadvantages of Cartesian grids. The corner point geometry (distorted grids) is often used as an alternative for complex full-field studies. This approach can better adapt the grid to reservoir boundaries, faults, horizontal wells and flow patterns and is easily used in standard finite difference reservoir simulators. The key problems for this technique are the preservation of the accuracy of fluid flow modelling and well treatment. In this paper, we will present a technique well suited to the corner point geometry and discuss its application range. Results are presented for test cases, comparing different control-volume type approximations.

Real‐ time geometric modeling using models in an actuator space and cartesian space

Abstract: In this article, three models in two different spaces are compared for use with an image processing system working in real time. A static geometric model of a robot work-cell is held in computer memory as several solid polyhedra. This model is updated as new objects enter or leave the workplace. Similar 2-D slices in joint space, spheres, and simple polyhedra are used to model these objects. The three models are compared for their ability to be updated with new information and for the efficiency of the whole system in accessing data concerning new objects. The system supplies data to a “Path Planner.” The path planner contains a geometric model of the static environment and a robot. The robot machinery structure is modeled as connected cylinders and spheres and the range of motion is quantized. © 1995 John Wiley & Sons, Inc.

The Cartesian composition of fuzzy finite state machines

Abstract: Studies the concept of the Cartesian composition of fuzzy finite state machines. Shows that fuzzy finite state machines and their Cartesian composition share many structural properties. Some of these properties are singly generated; retrievability, connectedness, strong connectedness, commutativity, perfection and state independence. Thus a fuzzy finite state machine which is a Cartesian composition of submachines can be studied in terms of smaller machines.

Bias compensation for improved recursive bearings-only target state estimation

Abstract: In recursive bearings-only tracking the Cartesian coordinate EKF provides poor convergence and erratic behavior due to the lack of observability of the target range. The EKF formulated in modified polar (MP) coordinates, which decouples the observable and unobservable components of the target state, has been shown to provide improvements in estimation convergence over the Cartesian EKF. A new Cartesian coordinate method is developed which estimates the range bias to compensate the position estimates of the filter. The resulting filter, called the bias compensated Cartesian filter(BCCF) is shown to provide improved velocity estimation and comparable position estimation with the MP method.

Fourier descriptors for computer graphics

Abstract: The two dimensional coding of contours by Fourier descriptors which have been used extensively in shape discrimination and pattern recognition in the past is extended into three dimensions so as to enhance the ability to geometrically transform surfaces in Euclidean space. A set of Fourier descriptors are used as a specific example of a linear transform for arbitrary closed shape contours in three dimensional Cartesian space which enhance data compression compared to computer graphics storage algorithms utilizing raw data. The Fourier descriptors can also be used for three dimensional graphical reconstruction of objects represented by data sets depicting consecutive contours or collections of quadrilaterals in space. These descriptors maintain linearity, thus they can be utilized for geometric transformations of these data sets, which may not be possible with non-linear data compression such as Huffman coding. Thus geometric transformations, such as those utilized in computer aided design (CAD) systems, of such contour data sets can be performed with less computation and storage requirements in the linear transform space than current techniques that transform data in the data space. >

Visual servoing in the task-function framework: A contour following task

Abstract: We describe an approach to contour following unknown objects using a handeye robotic system. Relevant and sufficient feature points providing optical flow data are extracted from the edges of the target object. The desired motion of the end-effector is computed with the objective of keeping the visual features always at the same target location in the image plane. A cartesian PD controller is used to perform the desired motion by the robot's end-effector. To address thecontrol issues, we take advantage of the unifying robot control theory stated in the literature as thetask-function approach [21]. To validate our approach, we restricted our experiments to motionless objects positioned in a plane parallel to the image plane: three degrees of freedom (two of translation, one of rotation) are thus controlled.

A new Fourier method for fan beam reconstruction

Abstract: For parallel beam geometry the Fourier reconstruction works via the central slice theorem. For fan beam geometry the central slice theorem in its simple form does not exist. This paper introduces a generalized central slice theorem for fan beam geometry. Using this method the frequency plane is filled by adding up the contributions from all projections individually. Thereby the values in the Fourier plane are directly calculated for Cartesian coordinates such avoiding the interpolation from polar to Cartesian coordinates in the frequency domain. The new approach has been implemented and tested. This method is appropriate for the short scan case where the scanning covers less than 360/spl deg/. It works for arbitrary ray-sampling schemes including equally spaced collinear detectors, equiangular rays and circle cameras as used for PET and SPECT systems.

Extending the Point Distribution Model Using Polar Coordinates

Abstract: The Point Distribution Model (PDM) has already proved useful for many tasks involving the location or tracking of deformable objects. A principal limitation lies in the fact that non-linear variation must be approximated by a combination of linear variations, resulting in a non-optimal model which can produce implausible object shapes. The Polynomial Regression PDM improves on the PDM by allowing polynomial deformation. However, computational complexity is greatly increased, and the model still fails for objects in which bending or pivoting occurs. We propose an extension to the PDM which selectively uses polar coordinates at little computational cost, and give examples to show that models produced are both more compact and less likely to generate implausible shapes than either of the above methods. We also give an algorithm which automatically classifies model landmark points into the Cartesian or polar domain, based on training set analysis.

Calibrating device for three-axis accelerometer

Abstract: PURPOSE: To make it possible to perform calibration simply in a short time by setting X and Y axes at the specified slant angles with respect to a horizontal plane under the state, wherein the Z axis of a three-axial accelerometer becomes parallel with the horizontal plane, and providing a calibrating plane, which supports a supporting body under this state. CONSTITUTION: A case body 1 comprises seven planes, and accelerometers 2, 3 and 4 for detecting the acceleration in the directions of X, Y and Z axes are fixed to a bottom plane 1a. A calibrating plane 1b is orthogonal to the bottom plane 1a and has the angle of 45 degrees in both directions of X and Y axes. At first, the bottom plane 1a is set on the horizontal plane. The X and Y axes are made parallel with the horizontal plane, and the Z axis is made orthogonal with the horizontal plane. The accelerometers 2 and 3 are set at an output 0, and the output of the accelerometer 4 is calibrated to gravity 1G. Then, the calibrating plane 1b is set on the horizontal plane, the X and Y axes are set at 45 degrees with the horizontal plane and the Z axis is set in parallel with the horizontal plane. The accelerometers 2 and 3 are calibrated to the output 0 and 707G, and the accelerometer 4 is calibrated to the output 0. In this way, the calibration can be quickly performed without removing the accelerometers 2, 3 and 4. COPYRIGHT: (C)1996,JPO

Three-dimensional solid arranging/editing method in a computer graphic system and system

Abstract: A solid graphic arranging/editing method enables a user to enter or edit a solid graphic viewed on a display According to the method, three points of a rectangular parallelepiped are specified, and the solid is arranged to be inscribed within the parallelepiped A reference plane is then defined and a first point on the reference plane is specified A local coordinate plane is also defined and a second point is specified on the local coordinate plane A rectangle lying in the local coordinate plane and having the first and second points as diagonal vertices is then displayed Auxiliary lines perpendicular to the local coordinate plane and passing the second point are also displayed and a third point on a selected auxiliary line is displayed A rectangular parallelepiped is then displayed having the rectangle as one surface and the third point as a vertex The position of the solid and the scales are then adjusted such that the solid is inscribed in the rectangular parellelepiped

Automated pivot location for the Cartesian-Polar hybrid point distribution model

Abstract: The Point Distribution Model (PDM) has already proved useful for many tasks involving the location or tracking of deformable objects. A principal limitation is that non-linear variations must be approximated by combining linear variations, which sometimes results in a non-optimal model producing implausible object shapes. The Cartesian-Polar Hybrid PDM helps to overcome this limitation; selective use of polar geometry allows bending or pivotal deformation to be modelled more accurately; model components which exhibit no such trend remain in the Cartesian domain. Use of the Hybrid PDM currently requires the identification of pivot points by hand. In this paper we present a method for automatically identifying rigid model parts and pivot points from the training data. Experimental results are given for real data from human hands and for synthetic data from a simple jointed object.

Unstructured Cartesian/prismatic grid generation for complex geometries

Abstract: The generation of a hybrid grid system for discretizing complex three dimensional (3D) geometries is described. The primary grid system is an unstructured Cartesian grid automatically generated using recursive cell subdivision. This grid system is sufficient for computing Euler solutions about extremely complex 3D geometries. A secondary grid system, using triangular-prismatic elements, may be added for resolving the boundary layer region of viscous flows near surfaces of solid bodies. This paper describes the grid generation processes used to generate each grid type. Several example grids are shown, demonstrating the ability of the method to discretize complex geometries, with very little pre-processing required by the user.

A spherical basis function neural network for pole-zero modeling of head-related transfer functions

Abstract: This paper describes a neural network for approximating the parameters of a pole-zero model of the head-related transfer function (HRTF). The von Mises basis function (VMBF) is described whose response depends on spherical rather than Cartesian input coordinates. The VMBF neural network is ideally suited to the problem of learning a continuous mapping from spherical coordinates to acoustic parameters that specify sound source direction. A method for computing the common poles of a set of HRTFs is also discussed.

Small‐amplitude protein conformational dynamics: Second‐order analytic relation between cartesian coordinates and dihedral angles

Abstract: An analytic expression for protein atomic displacements in Cartesian coordinate space (CCS) against small changes in dihedral angles is derived. To study time-dependent dynamics of a native protein molecule in CCS from dynamics in the internal coordinate space (ICS), it is necessary to convert small changes of internal coordinate variables to Cartesian coordinate variables. When we are interested in molecular motion, six degrees of freedom for translational and rotational motion of the molecule must be eliminated in this conversion, and this conversion is achieved by requiring the Eckart condition to hold. In this article, only dihedral angles are treated as independent internal variables (i.e., bond angles and bond lengths are fixed), and Cartesian coordinates of atoms are given analytically by a second-order Taylor expansion in terms of small deviations of variable dihedral angles. Coefficients of the first-order terms are collected in the K matrix obtained previously by Noguti and Go (1983) (see ref. 2). Coefficients of the second-order terms, which are for the first time derived here, are associated with the (newly termed) L matrix. The effect of including the resulting quadratic terms is compared against the precise numerical treatment using the Eckart condition. A normal mode analysis (NMA) in the dihedral angle space (DAS) of the protein bovine pancreatic trypsin inhibitor (BPTI) has been performed to calculate shift of mean atomic positions and mean square fluctuations around the mean positions. The analysis shows that the second-order terms involving the L matrix have significant contributions to atomic fluctuations at room temperature. This indicates that NMA in CCS involves significant errors when applied for such large molecules as proteins. These errors can be avoided by carrying out NMA in DAS and by considering terms up to second order in the conversion of atomic motion from DAS to CCS. © 1995 by John Wiley & Sons, Inc.

Change of variables for fully numerical electronic-structure calculations that concentrates the grid points in the atomic-core regions and is adequate for fast Fourier transforms

Abstract: A change of variables is proposed with the following property: given a {ital preselected} {ital density}, when a {ital uniform} grid in the new coordinates is mapped into Cartesian coordinates, the resulting grid points are distributed according to the preselected density. The preselected density is chosen so that the grid points are concentrated in the atomic-core regions. The grids generated in this way are useful for fully numerical or basis-set-free electronic-structure calculations, in particular those using plane-wave expansions: they give a good treatment of the nuclear cusps (because of the high density of grid points in the core regions) {ital and} the fast Fourier transform can be used for numerical interpolation (because the grids are uniform in the new coordinates). When compared with uniform or flat grids in Cartesian coordinates, the present scheme is clearly superior: it gives numerical integration errors that are typically two orders of magnitude smaller, and it very accurately interpolates atomic and molecular densities, even for atoms like uranium, which have a very high core density.

On young's modulus for anisotropic media

Abstract: If a piece of homogeneous anisotropic elastic material is subject to simple tension along a direction n for which Young’s modulus E(n ) is an extremum, then the corresponding strain field is coaxial with the simple tension stress field. An appropriate set of rectangular cartesian coordinate axes may be introduced such that three of the elastic compliances are zero. In this coordinate system the displacement field may be written explicitly and corresponds to a pure homogeneous deformation.

On reference trajectory modification approach for Cartesian space neural network control of robot manipulators

Abstract: It is well known that computed torque robot control is subjected to performance degradation due to uncertainties in robot model, and application of neural network (NN) compensation techniques are promising. In this paper we examine the effectiveness of NN as a compensator for the complex problem of Cartesian space control. In particular we examine the differences in system performance when the same NN compensator is applied at different locations in the controller. It is found that using NN to modify the reference trajectory to compensate for model uncertainties is much more effective than the traditional approach of modifying joint torque/force. To facilitate the analysis, a new NN training signal is introduced. The study is extended to non-model based Cartesian control problem. Simulation results are also presented.