For the immediate future, however, we envisage a research impulse towards algorithmic algebraic geometry turning the fascinating insights of inconstructive algebraic geometry into algorithmic methods for geometric reasoning. The three techniques covered in this survey evolved in the past two decades. They solve problems of increasing generality and scope of applicability. The solvability of these problems has immediate applications for important geometric engineering problems as, for example, robot collision detection, robot path finding, inverse kinematics for dynamic systems, consistency analysis in computer-aided design, curve tracing, construction of blending surfaces and others. The practical applicability of these algebraic methods is limited by their intrinsic complexity.
Much research is conducted aiming at improvements of the methods for special classes of input.
Also, these methods should be seen in a preprocessing context. The Digital Library is published by the Association for Computing Machinery.