René Descartes (1596-1650) introduced systems of coordinates based on orthogonal (right angle) coordinates. These two and three-dimensional systems used in analytic geometry are often referred to as Cartesian systems. Similar systems based on angles from baselines are often referred to as polar systems. Plane Coordinate Systems. There are many basic coordinate systems familiar to students of geometry and trigonometry. These systems can represent points in two-dimensional or three-dimensional space.