Third Dimensional Computations Using Non Linear Projection Methods in Spherical Projection Plane

Abstract

Literature review revealed that attempts were made to apply non-linear projection methods such as perspective projection methods, for computing Z field (Z) or depth field in a given 3D Environment (3DE). Literature also revealed that the study was confined to using Flat Picture Planes (FPP) and Cylindrical Picture Planes (CPP). A high degree of non-linearity was reported between the depth as seen on Flat Picture Planes (FPP) or Cylindrical Picture Planes (CPP) and the actual depth (Z). This non-linearity was reported to be higher for depth (Z) values nearer to and far away from Flat Picture Planes (FPP) or Cylindrical Picture Planes (CPP). This non-linear behavior is mainly due to the Flat and Cylindrical nature of the projection planes. A slight decrease in non-linearity was reported while using CPP. An attempt is made is this paper to use Picture Planes having spherical geometry and to investigate whether the non-linearity further decreases and if so, to quantity the decrease. A set of known Z values are considered and the computer generated graphical model of the Z – field is obtained using FPP & SPP. The depth values as seen on the FPP & SPP namely df & ds are computed. Using numerical methods, nth order equations are proposed between computed depth Zf and df for FPP and Zs and ds for SPP, where Zf and Zs are the computed depths under FPP & SPP methods. The percent variations (pf or ps) of Zf with Z and Zs with Z during the entire region of Z are computed. It has been concluded that SPP method offered the least percent variation and lies with in +5%. Hence with in an accuracy of + 5% of actual depth (Z) the computed depth Zs can be used for depth computations. This model can be suitably interfaced with the kinematic design of Robots, in order that the Robot can generate its own commands for fixing the coordinates of the negotiating objects, with in an accuracy of + 5%.