A semi‐analytic approach for direct slicing of free form surfaces for layered manufacturing

Abstract

PurposeThis paper aims to develop an efficient surface‐plane intersection (SPI) algorithm for direct slicing of free‐form surfaces to be produced by layered manufacturing.Design/methodology/approachA semi‐analytical method for direct slicing has been formulated and tested on Bezier and B‐spline surfaces commonly used in CAD modeling. This method solves for the intersection points by a “root” finding procedure and establishes their connectivity, unlike the conventional “marching” procedures.FindingsThe proposed algorithm solves intersection contours between free form surfaces and planes. The solution procedure is efficient with respect to computational time and accuracy (feature detection) over some of the conventional SPI strategies. The method involves a global solution procedure in contention with the traditional methodologies which are generally spatially distinctive in approach.Research limitations/implicationsUse of higher order terms in the representation of parametric surfaces makes the algorithm computationally intensive and time‐expensive.Practical implicationsThis algorithm would be of practical use in the direct slicing of free form surfaces used in CAD modeling. Direct slicing methods solve for the actual intersection of surface and plane without resorting to “tessellation.” Reducing the computation time and detection of features within a given resolution is of primary importance for developing commercial rapid prototyping software, which is achieved in the present paper.Originality/valueA novel method has been developed for SPI for use in direct slicing of CAD models. While a major proportion of the direct slicing strategies employ the “marching” procedure involving determination of “critical points,” the proposed method utilizes the evaluation of “roots” of a surface in a global manner to determine the intersection points with proper connectivity. Hence, it is effective in reducing the computation time and is simple but generic in approach. Although Bezier and B‐spline surfaces are used as the representative cases, the algorithm can be extended for any parametric surface for direct slicing.