International Journal of Computer Graphics Vol. 3, No. 1, May, 2012 17 A Mid -point Ellipse Drawing Algorithm on a Hexagonal Grid M. Prabukumar and Bimal Kumar Ray School of Information Technology & Engineering, VIT University Vellore – 632 014 India mprabukumar@vit.ac.in, bimalkumarray@vit.ac.in Abstract In this paper, the idea of Mid-point ellipse drawing algorithm on a hexagonal grid is proposed. The performance of the proposed algorithm is compared to that of the conventional ellipse drawing algorithm on a square grid. The qualitative and execution time analysis proves that the proposed algorithm performs better than the conventional ellipse drawing algorithm on a square grid. Keywords: Hexagonal grids, rasterization, scan conversion, aliasing, computer graphics, frame buffer 1. Introduction In addition to lines and circles another useful curve in graphics applications is the ellipse. A significant body of work in curve drawing algorithms on a square grid for raster display devices has already been published [1-11]. In this paper the mid-point approach for scan converting a non parametric equation of an ellipse into scan conversion algorithm on a hexagonal grid, that draws the ellipse into a bit-mapped frame buffer and that drives a raster display, is proposed. The proposed approach produces algorithms that are computationally efficient by means of reducing the number of multiplication operations required and also reduces the scan conversion error. We summarize the related work to our proposed research as follows. Wuthrich and Stucki [12] provided a systematic proof for the similarity in the characteristics of digitized curves on square and hexagonal grids. Efficient hexagonal grid implementation of the algorithm was pointed out to give high stand for the possibility to build graphics devices on hexagonal grids. Liu Yong-Kui [13] used only integer arithmetic and developed an algorithm for the generation of straight line on hexagonal grid. Liu Yong-Kui [14] found the closest integer coordinates to the actual circular arc by using only integer arithmetic and designed two algorithms that can generate circular arc on hexagonal grids. Krzysztof T. Tytkowski [15] having discussed some advantages of hexagonal lattice over the conventional one and proposed the construction of hexagonal mesh hardware for a graphics display unit. He also presented a new approach for the representation of a pixel in raster graphics. The properties and advantages of grids based on rhombic truncated octahedral tilings were given in a study by Miller [16]. Using local counting algorithms, better perimeter estimates can be obtained using hexagonal or triangular grids. A method to trace lines in non-orthogonal grids in any dimension using only additions during the line tracing process was proposed by Luis Ibáñez et. al. [17] and achieved good performance. L. V. Pittway [18] presented an algorithm that could outline ellipses, circles, or any of the other conic sections on a hexagonal lattice. The basic algorithm requires just one test, three addition operations in the inner loop and an additional test to detect a change in the