Associate Professor of Mathematics
Rose-Hulman Institute of Technology

MA 423 Topics in Geometry
Applied Projective Geometry
"All geometry is projective geometry", Arthur Cayley


Projective geometry is the geometry of straight lines. It may be defined either axiomatically in the manner of Euclidean geometry or by building upon linear algebra. Axiomatically, projective geometry pertains to the geometric constructions that can be accomplished with a straight-edge alone (no measurement is possible). This is entirely different than the standard Euclidean geometry, you are familiar with, and at first glance it may seem that this is too restrictive to generate any structure of interest. However, there is a great deal of structure. It is just different. In fact, projective geometry is the correct geometry to study and apply to optical systems, computer vision, and computer graphics.

In this course, we will examine the axiomatic approach but focus on building the structure of projective geometry from linear algebra. We will focus our attention on the use of projective geometry to transfer 3D objects to 2D images, and the use of projective geometry as a tool for describing a 3D object as a 2D image. The ultimate goal in this second objective is to use projectuve geometry as a tool in CAGD (computer aided geometric design) to develop the language to describe NURBS (non-uniform rational B-splines).