Analytic projective geometry for computer graphics

Abstract

The motivation of this paper was the development of computer geometry course for students of mathematical specialties. The term “computer geometry” hereafter refers to the mathematical foundations of machine graphics. It is important to emphasize separately that this course should be designed for second-year students and, therefore, they can only be required to have prior knowledge of a standard course in algebra and mathematical analysis. This imposes certain restrictions on the material presented. When studying the thematic literature, it was found out that the de facto standard in modern computer graphics is the use of projective space and homogeneous coordinates. However, the authors faced a methodological problem-the almost complete lack of suitable educational literature in both Russian and English. This paper was written to present the information collected by the authors on this issue.

Keywords

• projective geometry
• asymptote system
• plücker coordinates
• proper and improper points
• lines and planes