A combinatorial technique for generation of digital plane using GCD

A digital plane is a digitization of a Euclidean plane. A plane is specified by its normal, which is a 3D vector with integer coordinates, as considered in this case. It is established here that a 3D digital straight line segment, shifted by an integer amount, can produce the digitized plane. 3D plane’s normals are classified based on the Greatest Common Divisor (GCD) of its components, and the net code is calculated separately for each case. Experimental results are provided for several normals. Also, we show that the digital plane segment generated is a connected digital plane. The proposed method mainly involves integer arithmetic.