A comparison between zero and first order approximation algorithms for layered manufacturing

Abstract

Current rapid prototyping processes are mainly based on layered manufacturing techniques using 2.5D slices. Defines manufacturing by means of 2.5D slices as a zero order approximation. A disadvantage of this approximation is the staircase effect, requiring thin layers to be used. If the outer surfaces of the slices can be inclined, speaks of a first order approximation. This approximation is achieved by linear interpolation between adjacent contours, resulting in ruled slices. Describes a method to approximate a given model geometry in a layered fashion not exceeding a user‐defined error δ using either a zero or a first order approximation and an adaptive layer thickness. Analyses the model geometry for curvature and inclination in order to determine the adaptive layer thickness. Provides a method for matching corresponding contours from adjacent slices. Several test objects have been processed using both zero and first order approximation. Shows that the first order approximation significantly reduces the number of required layers for a given δ when compared to the zero order approximation.