Optimize Geometry Division to Construct Clustered Dot Dithering Matrix

The indirect approach to construct clustered dot dithering matrix has 3 steps: 1. having clustered dot center; 2. calculate the geometry division of the halftone plane by taking the centers as point set; 3. make dithering matrix. According to the existing related research work, it usually makes the center of each face of the division as the centre of clustered dot for shadow. The vertex of the division will be the center of clustered dot for highlight. In the dithering matrix produced with above method, the clustered dot density for shadow and highlight may have big difference. To make clustered dot density for shadow and highlight balanced, an optimize algorithm based on two theorems deducted from Euler theorem is proposed. In the experiment with the algorithm, ratio between the clustered dot density for shadow and highlight are improved to 0.90392 from original 0.50220.