Delaunay triangulating the 2d polygon with holes

Question

I want to triangulate the complex (but not self-intersecting) polygon with holes, so that resulting triangles all lay inside the polygon, cover that polygon completely, and obey

Answer 1

It sounds like you want constrained Delaunay triangulation. The "holes" can be implemented by constraining input edges to remain unbroken in the triangulation.

See the Triangle and poly2tri projects for implementations.