Non-iterative stippling of greyscale three-dimensional polygon meshed models

Abstract

This study develops a three-dimensional (3D) stippling technique, which includes a 3D sampling phase followed by a 3D surface half-toning phase for greyscale 3D polygon-meshed models. With the proposed technique, a 3D model is represented in a list of uni-colour, fixed-size points, which can be used by laser crystal engravers to generate its appearance. In the 3D sampling phase, based on the strategy of marching-cube operation, the space containing the entire model is divided into many equal-sized sample cubes. For each valid sample cube, only one sample point is placed. The location of the sample point is determined by calculating the centroid of the greyscale-weighted surface segments contained in the cube. Then, the sample points are dithered in the 3D surface half-toning phase to generate the surface tone of the model. The proposed method provides a closed-form solution and gives satisfactory results without any need of iterative programming.