A totally four-dimensional approach computer-aided geometric design

This thesis consist of three sections. After giving some short explanations about the subjectin the first section, complexity of perfect geometric tests in the Euclidean space and geometric figures after perspective transformations are introduced in the second section. In the last section, Plücker coordinates and Plücker coefficients simplices depending on them are given. Furthermore, coincidence, coplanarity, concurrency and collinearity conditions depending on Plücker coordinates and Plücker coefficients and also interference conditions between homogenous simplices and dual homogenous simplices in both projective space and two-sided space are given.