The Basic Theories of the 4×4 Determinant Method in Geometric Interference Problems

Abstract

Theories of the 4×4 determinant approach to interference problems are described, in detail, in succession to the former paper. First, various cases of the 4×4 determinant are discussed including the geometric implications. Secondly, normalization of the determinant is proposed. Lastly, an intersection formula in homogeneous coordinates is verified which makes it possible to do consistent homogeneous coordinate processing from the very beginning of geometric modeling to the very last of displaying objects. This article will provide theoretical foundations for the 4×4 determinant approach in computer graphics and geometric modeling.