Movimientos simétrico lineales esféricos segmentados para interpolación de orientaciones en planificación de trayectorias de herramienta en CNC de 5 Ejes

RESUMEN: Este artículo emplea biarcos cuaterniónicos para interpolar un conjunto de orientaciones con restricciones de velocidad angular. La curva cuaterniónica resultante representa un movimiento simétrico lineal esférico segmentado con continuidad C1 . El propósito de este esfuerzo es poner en uso los movimientos simétrico lineales desde el punto de vista de aproximación e interpolación de movimiento y presentar su potencial aplicación en la simulación de mecanizado por Control Numérico Computarizado (CNC) y planeación de trayectorias de herramienta. Los biarcos cuaterniónicos pueden ser usados para aproximar curvas B-spline cuaterniónicas que representan movimientos esféricos racionales, los cuales tienen aplicaciones en planeación de trayectorias de robots, en CAD/CAM y en gráficas por computador.ABSTRACT: This paper employs quaternion biarcs to interpolate a set of orientations with angular velocity constraints. The resulting quaternion curve represents a piecewise line-symmetric spherical motion with C1 continuity. The purpose of this effort is to put line-symmetric motions into use from the viewpoint of motion approximation and interpolation, and to present their potential applications in Computerized Numerical Control (CNC) machining simulation and tool path planning. Quaternion biarcs may be used to approximate B-spline quaternion curves that represent rational spherical motions that have applications in robot path planning, CAD/CAM and computer graphics

AUTOMATIC FAIRING OF TWO-PARAMETER RATIONAL B-SPLINE MOTION

This paper deals with the problem of automatic fairing of two-parameter B

DETC2008-50105 DRAFT: A SUBDIVISION SCHEME FOR DISCRETE MOTION GENERATION AND SWEPT VOLUME ANALYSIS

ABSTRACT I

AUTOMATIC FAIRING OF TWO-PARAMETER RATIONAL B-SPLINE MOTION

This paper deals with the problem of automatic fairing of two-parameter B-Spline spherical and spatial motions. The concept of two-parameter freeform motions brings together the notion of the analytically determined two-parameter motions in Theoretical Kinematics and the concept of freeform surfaces in the field of Computer Aided Geometric Design (CAGD). A dual quaternion representation of spatial displacements is used and the problem of fairing two-parameter motions is studied as a surface fairing problem in the space of dual quaternions. By combining the latest results in surface fairing from the field of CAGD and computer aided synthesis of freeform rational motions, smoother (C 3 continuous) two-parameter rational B-Spline motions are generated. The results presented in this paper are extensions of previous results on fine-tuning of oneparameter B-spline motions. The problem of motion smoothing has important applications in the Cartesian motion planning, camera motion synthesis, spatial navigation in visualization, and virtual reality systems. Several examples are presented to illustrate the effectiveness of the proposed method.

Hierarchical Image-based and Polygon-based Rendering for Large-Scale Visualizations

this paper we study the relative advantages and disadvantages of these approaches to learn how best to combine these competing techniques towards a hierarchical, robust, and hybrid rendering system for large data visualizatio