LOOK: A lazy object-oriented kernel design for geometric computation. We describe and discuss a new kernel design for geometric computation in the plane. It combines different kinds of floating-point filter techniques and a lazy evaluation scheme with the exact number types provided by LEDA allowing for efficient and exact computation with rational and algebraic geometric objects. It is the first kernel design which uses floating-point filter techniques on the level of geometric constructions. The experiments we present – partly using the CGAL framework – show a great improvement in speed and – maybe even more important for practical applications – memory consumption when dealing with more complex geometric computations.