Unstructured grid generation is concerned with discretizing surfaces and volumes in 3D space by tiangles and tetrahedra. The tetrahedra discretize a volume in a surface's interior or surrounding a surface on its outside. This paper presents a new technique for unstructured grid generation based on intersecting lines with a given geometry and inserting grid points yielding an adapted grid whose point density decreases with increasing distance to the geometry. The technique is completely automatic.