There is a fair amount of software available which implements some of the basic
spatial data structures of computational geometry.
This page provides pointers to some resources.
CGAL is the major computational geometry library, developed by
a consortium in Europe and Israel. It includes not only the best freely
distributed Delaunay triangulation code, but also many other data structures,
and various geometric predicates which can be instantiated to use filtered
exact arithmetic, giving a good trade-off between robustness and efficiency.
Triangle is Jonathan Shewchuk's 2D quality mesh generation software.
If you want the 3D analog, at least for parts of it, you can discuss it with Jonathan.
ANN is a library for approximate nearest neighbor searching in arbitrary dimensions.