Curve generation of implicit functions by incremental computers.

Department of Electronic Engineering, Yamagata University, Yonezawa, Japan
Computers & Graphics (Impact Factor: 1.03). 01/1983; 7(2):161-167. DOI: 10.1016/0097-8493(83)90007-9
Source: DBLP

ABSTRACT The conventional numerical solution of an implicit function f(x, y) = 0 is substantially complicated for calculating by any computer. We propose a new method representing the argument of the implicit function as a unary function of a parameter, t, if the continuous and unique solution of f(x, y) = 0 exists. The total differential constitutes simultaneous differential equations of which the solution about x and y is unique. The Newton-Raphson method must be used to calculate the values near singular points of an implicit function and then the sign of dt has to be decided according to four special cases. Incremental computers are suitable for curve generation of implicit functions by the new method, because the incremental computer can perform more complex algorithms than the analog computer and can calculate faster than the digital computer. This method is easily applicable to curve generation in three-dimensional space.

  • [Show abstract] [Hide abstract]
    ABSTRACT: The paper presents an algorithm for general 3D and 2D parametric curve interpolation. This is an incremental step algorithm, and it uses two simple principles; firstly, each selected step has to follow a given direction along the curve, and, secondly, each selected step has to be at the closest distance from the curve. The mathematical formulation of the algorithm permits the interpolation of any kind of parametric curve, which is an important aspect of modern cad/cam systems. Its software implementation on risc workstations and the in-house academic tests to date have shown promising results, and it is hoped that it can be applied in the next generation of computerized numerical control systems.
    Computer-Aided Design 11/1994; 26(11-26):850-856. DOI:10.1016/0010-4485(94)90100-7 · 1.52 Impact Factor
  • Journal of Manufacturing Science and Engineering 01/1997; 119. DOI:10.1115/1.2831191 · 0.78 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: This paper presents a CNC machine tool interpolator with a path compensation method for a repeated contour machining process. In addition to a conventional contour interpolation algorithm, the proposed interpolator also includes contour-error calculation, data extraction and contour-error interpolation algorithms so that the previous contour machining result can be introduced to improve the accuracy of the subsequent repeated machining. Mathematical analysis and experimental evaluation are presented in this paper.
    Computer-Aided Design 01/1998; 30(1-30):55-62. DOI:10.1016/S0010-4485(97)00053-5 · 1.52 Impact Factor